From 91b3422f04e0a2ff8ac5369d3de6cea103242b78 Mon Sep 17 00:00:00 2001 From: fischerl Date: Tue, 31 Jan 2012 16:55:37 -0500 Subject: [PATCH 1/4] more subs --- subs/3NIegrCmA5k.srt.sjson | 5 + subs/EG-fRTJln_E.srt.sjson | 5 + subs/G_2F9wivspM.srt.sjson | 191 ++++++++++++++++++++++ subs/SMVp8kv_rlg.srt.sjson | 152 +++++++++++++++++ subs/bmys8aKCjCo.srt.sjson | 113 +++++++++++++ subs/eLAyO33baQ8.srt.sjson | 326 +++++++++++++++++++++++++++++++++++++ subs/pnHDLuxmXHo.srt.sjson | 251 ++++++++++++++++++++++++++++ subs/rysqcHqcuBw.srt.sjson | 266 ++++++++++++++++++++++++++++++ subs/wO-WqB_k9QQ.srt.sjson | 272 +++++++++++++++++++++++++++++++ 9 files changed, 1581 insertions(+) create mode 100644 subs/3NIegrCmA5k.srt.sjson create mode 100644 subs/EG-fRTJln_E.srt.sjson create mode 100644 subs/G_2F9wivspM.srt.sjson create mode 100644 subs/SMVp8kv_rlg.srt.sjson create mode 100644 subs/bmys8aKCjCo.srt.sjson create mode 100644 subs/eLAyO33baQ8.srt.sjson create mode 100644 subs/pnHDLuxmXHo.srt.sjson create mode 100644 subs/rysqcHqcuBw.srt.sjson create mode 100644 subs/wO-WqB_k9QQ.srt.sjson diff --git a/subs/3NIegrCmA5k.srt.sjson b/subs/3NIegrCmA5k.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/3NIegrCmA5k.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/EG-fRTJln_E.srt.sjson b/subs/EG-fRTJln_E.srt.sjson new file mode 100644 index 0000000000..bc505bb0d1 --- /dev/null +++ b/subs/EG-fRTJln_E.srt.sjson @@ -0,0 +1,5 @@ +{ + "start": [], + "end": [], + "text": [] +} \ No newline at end of file diff --git a/subs/G_2F9wivspM.srt.sjson b/subs/G_2F9wivspM.srt.sjson new file mode 100644 index 0000000000..34fc42d535 --- /dev/null +++ b/subs/G_2F9wivspM.srt.sjson @@ -0,0 +1,191 @@ +{ + "start": [ + 0, + 1800, + 2440, + 7270, + 11690, + 13030, + 17060, + 21240, + 24980, + 29930, + 33740, + 37930, + 40340, + 46830, + 50200, + 52890, + 59450, + 60430, + 66640, + 69640, + 72148, + 77730, + 83080, + 99630, + 110800, + 118220, + 121940, + 131580, + 134300, + 137730, + 140540, + 143860, + 146050, + 149850, + 157140, + 161820, + 164460, + 165600, + 169520, + 174040, + 176290, + 178310, + 181070, + 182920, + 184160, + 189960, + 192630, + 193480, + 199020, + 201540, + 204520, + 208180, + 211470, + 217120, + 220790, + 224490, + 227200, + 229150, + 232940, + 236320, + 239070 + ], + "end": [ + 1800, + 2440, + 7270, + 11690, + 13030, + 17060, + 21240, + 24980, + 29930, + 33740, + 37930, + 40340, + 46830, + 50200, + 52890, + 56355, + 60430, + 66640, + 69640, + 72148, + 73398, + 83080, + 84330, + 103660, + 114250, + 121940, + 131580, + 134300, + 137730, + 140540, + 143860, + 146050, + 147300, + 157140, + 161820, + 164460, + 165600, + 169520, + 174040, + 176290, + 178310, + 181070, + 182920, + 184160, + 189960, + 192630, + 193480, + 199020, + 201540, + 204520, + 208180, + 211470, + 217120, + 220790, + 224490, + 227200, + 229150, + 232940, + 236320, + 239070, + 242480 + ], + "text": [ + "SPEAKER 1: So I want to show you a simple circuit that", + "looks like this.", + "And let's go ahead and measure some voltages and currents.", + "In terms of terminology, remember", + "this is called a loop.", + "So if I start from the point C, and I travel through the", + "voltage source, come to the node A, down through R1 and", + "all the way down through R2 back to C, that's a loop.", + "Similarly, this point A is a node where the register R1,", + "the voltage source V0 and R4 are connected.", + "Just make sure your terminology is correct.", + "So what I'll do is let me make some quick measurements for", + "you, and show you that these KVL and KCL are indeed true.", + "So the circuit's up there.", + "So let me take some measurements.", + "And why don't you write down what I measure on the board.", + "Let me borrow another piece of chalk here.", + "What I'll do is focus on this loop here and focus on this", + "node and make some measurements.", + "So you see the circuit up there.", + "[INAUDIBLE]", + "So I get three volts for the voltage from C to A. So why", + "don't you write down three volts.", + "OK, so the next one is minus 1.6.", + "And so that will be I'm doing AB, VAB.", + "And then let me do the last one.", + "And it is minus 1.37.", + "Within the bonds of experimental error, notice", + "that if I add up these three voltages, they", + "nicely sum up to zero.", + "OK, next let me focus on this node here.", + "And at this node, let me go ahead and", + "measure some currents.", + "What I'll do now is change to an AC voltage so that I can go", + "ahead and measure the current without breaking my circuit.", + "This time around, you'll get to see the measurements that", + "I'm taking as well.", + "What I have here is three wires that I have pulled out", + "from D. And this is the node D. So three wires coming into", + "the node D just to make it a little bit easier for me to", + "measure stuff.", + "So everybody keep your fingers crossed so I don't", + "look like a fool here.", + "Hope this works out.", + "So it's about 10 millivolts peak to peak out there.", + "Let's say that if the wave form rises on the left hand", + "side, it's positive.", + "So it's positive 10 millivolts.", + "And another positive 10 millivolts.", + "So that's 20 millivolts.", + "And this time it's a negative, roughly 20, I", + "guess, negative 20.", + "So I'm getting, in terms of currents, I have a positive", + "10, a positive 10 and a negative 20 that adds up to 0.", + "But more interestingly, I can show you the same thing by", + "holding this current measuring probe", + "directly across that node.", + "And notice that the net current that is entering into", + "this node here is zero.", + "So that should just show you that KCL does indeed hold in", + "practice, and it is not just a figment of our imaginations." + ] +} \ No newline at end of file diff --git a/subs/SMVp8kv_rlg.srt.sjson b/subs/SMVp8kv_rlg.srt.sjson new file mode 100644 index 0000000000..b0d89f501d --- /dev/null +++ b/subs/SMVp8kv_rlg.srt.sjson @@ -0,0 +1,152 @@ +{ + "start": [ + 180, + 2190, + 6270, + 6900, + 10280, + 13270, + 14500, + 17120, + 21170, + 26140, + 29450, + 33330, + 36300, + 39110, + 40960, + 45450, + 47030, + 50360, + 52660, + 56320, + 57970, + 59910, + 63260, + 63900, + 67040, + 70980, + 75460, + 80410, + 81910, + 86060, + 88590, + 92730, + 95200, + 97660, + 99650, + 100850, + 102080, + 105240, + 109550, + 111640, + 115310, + 116480, + 119270, + 120560, + 122710, + 125160, + 126070, + 128780 + ], + "end": [ + 2190, + 6270, + 6900, + 10280, + 13270, + 14500, + 17120, + 21170, + 26140, + 29450, + 33330, + 36300, + 39110, + 40960, + 45450, + 47030, + 50360, + 52660, + 56320, + 57970, + 59910, + 63260, + 63900, + 67040, + 70980, + 75460, + 80410, + 81910, + 86060, + 88590, + 92730, + 95200, + 97660, + 99650, + 100850, + 102080, + 105240, + 109550, + 111640, + 115310, + 116480, + 119270, + 120560, + 122710, + 125160, + 126070, + 128780, + 132100 + ], + "text": [ + "All right, this is the sub circuit.", + "And what I've done here is I've have to turn the current", + "source off.", + "So notice that out here, I create an open circuit.", + "And that is the result of my current source", + "being turned off.", + "And this is my usual ground note.", + "And let me call this node voltage, with the voltage", + "source acting alone, as ev. So ev is the partial response of", + "the circuit to the voltage source acting alone.", + "Now how do we go about solving for ev?", + "Notice that we have a known pattern here.", + "We have a voltage source connected to a pair of", + "registers, R1 and R2.", + "And ev is simply the voltage across R2.", + "Now, this is a known pattern.", + "So one thing you should keep in mind is that in circuits,", + "and electronics, we use patterns a lot.", + "Whenever we see a pattern, we can directly go and write down", + "what the output response is going to look like.", + "What I'm going to do is throughout this course, as we", + "see more and more patterns, I'm going to alert you to", + "these patterns.", + "So right here is a voltage divider pattern.", + "So for the voltage divider pattern, I can write down ev.", + "I can write down ev as being some fraction of the source", + "voltage v. And by the divider action, we simply R2 divide by", + "R1 plus R2.", + "So it is simply the voltage across R2, and that is given", + "by R2 divided by R1 plus R2.", + "And this is a known pattern that you'll find very helpful", + "as you analyze circuits very quickly.", + "Next, let's look at I acting alone.", + "Before we do that, what do we have so far?", + "Again, recall, this is the circuit", + "we're trying to analyze.", + "We are trying to get the voltage e.", + "And so far, we have computed the partial voltage ev, due to", + "the voltage source acting alone.", + "As a next step-- again, this is still step one of the", + "superposition method--", + "let's look at the partial response of the circuit due to", + "the current acting alone.", + "To get the response for the current acting alone, I need", + "to build a circuit in which the voltage", + "source is turned off.", + "I'll let you think for a couple of seconds as to what", + "the circuit will look like before I draw it out for you." + ] +} \ No newline at end of file diff --git a/subs/bmys8aKCjCo.srt.sjson b/subs/bmys8aKCjCo.srt.sjson new file mode 100644 index 0000000000..af25915a53 --- /dev/null +++ b/subs/bmys8aKCjCo.srt.sjson @@ -0,0 +1,113 @@ +{ + "start": [ + 530, + 1580, + 4780, + 6870, + 9220, + 12320, + 13820, + 19230, + 22940, + 26010, + 30210, + 32480, + 34580, + 36875, + 39590, + 41220, + 45150, + 46710, + 50570, + 53550, + 59710, + 64280, + 67170, + 69750, + 70590, + 73250, + 77710, + 81300, + 84390, + 92215, + 93420, + 100620, + 101650, + 104740, + 107970 + ], + "end": [ + 1580, + 4780, + 6870, + 9220, + 12320, + 13820, + 19230, + 22940, + 26010, + 30210, + 32480, + 34580, + 36875, + 39590, + 41220, + 45150, + 46710, + 50570, + 53550, + 59710, + 64280, + 67170, + 69750, + 70590, + 73250, + 77710, + 81300, + 84390, + 92215, + 93420, + 100620, + 101650, + 104740, + 107970, + 470140 + ], + "text": [ + "OK, let's go ahead.", + "So to turn off this voltage source, all I have to do is", + "replace it with a short circuit like so.", + "So notice that I have replaced the voltage source with a", + "short circuit, and I've left the current source in place.", + "I have my ground node here.", + "And notice that my goal is to find the partial voltage eI", + "that is a result of the current source acting alone.", + "So notice that I have a second pattern here.", + "And in this case, this is a current divider pattern.", + "Actually, this is a even simpler pattern.", + "I simply have a current that is flowing", + "into a pair of resistors.", + "OK, so I have a current, I, that is flowing into a pair of", + "resistors, R1 and R2.", + "And so I can compute the voltage across the pair of", + "resistors very straightforwardly.", + "So eI is simply the resistance times the current.", + "And the resistance of a paralel pair of resistors is", + "simply R1 R2 divide by R1 plus R2 times the current I.", + "OK, so now I have computed both ev and eI, the two", + "partial voltages with each of the voltages acting alone.", + "And now I am ready for step two of the", + "superposition method.", + "And the step two of the superposition method simply", + "says that you sum the two partial voltages, ev and eI.", + "So my resulting voltage e is simply the sum of the two", + "partial voltages ev and eI.", + "And I have those as R2 divide by R1 plus R2 times v. And I", + "sum that to eI.", + "And eI is R1 R2 divide by R1 plus R2 times I. And", + "there you have it.", + "Not surprisingly, this expression here is identical", + "to the expression that you obtained by using the node", + "method in the previous lecture." + ] +} \ No newline at end of file diff --git a/subs/eLAyO33baQ8.srt.sjson b/subs/eLAyO33baQ8.srt.sjson new file mode 100644 index 0000000000..4d2f5069ab --- /dev/null +++ b/subs/eLAyO33baQ8.srt.sjson @@ -0,0 +1,326 @@ +{ + "start": [ + 430, + 3070, + 5680, + 9120, + 12590, + 13280, + 17280, + 20200, + 23630, + 26720, + 29450, + 32700, + 35920, + 39280, + 43310, + 44850, + 46400, + 48270, + 52110, + 54140, + 57570, + 61600, + 63040, + 64410, + 66980, + 69920, + 72490, + 75110, + 77540, + 80680, + 84430, + 87190, + 91790, + 94420, + 97830, + 101030, + 104180, + 106960, + 108320, + 110885, + 113180, + 115630, + 119930, + 122740, + 129590, + 131000, + 134200, + 138470, + 142200, + 145410, + 150500, + 153590, + 158000, + 160290, + 164600, + 167370, + 169272, + 173420, + 176650, + 180460, + 183390, + 185200, + 188940, + 190750, + 194040, + 196510, + 198060, + 202670, + 206860, + 209980, + 213620, + 219130, + 221760, + 222700, + 227050, + 230340, + 234810, + 236930, + 239030, + 241390, + 246630, + 248200, + 252220, + 255370, + 257160, + 258709, + 263370, + 264280, + 266840, + 270190, + 275640, + 277790, + 280880, + 282680, + 285990, + 287870, + 290740, + 294140, + 299760, + 305270, + 308230, + 310160, + 311540, + 314150, + 316160, + 316440 + ], + "end": [ + 3070, + 5680, + 9120, + 12590, + 13280, + 17280, + 20200, + 23630, + 26720, + 29450, + 32700, + 35920, + 39280, + 43310, + 44850, + 46400, + 48270, + 52110, + 54140, + 57570, + 61600, + 63040, + 64410, + 66980, + 69920, + 72490, + 75110, + 77540, + 80680, + 84430, + 87190, + 91790, + 94420, + 97830, + 101030, + 104180, + 106960, + 108320, + 110885, + 113180, + 115630, + 119930, + 122740, + 129590, + 131000, + 134200, + 138470, + 142200, + 145410, + 150500, + 153590, + 158000, + 160290, + 164600, + 167370, + 169272, + 173420, + 176650, + 180460, + 183390, + 185200, + 188940, + 190750, + 194040, + 196510, + 198060, + 202670, + 206860, + 209980, + 213620, + 219130, + 221760, + 222700, + 227050, + 230340, + 234810, + 236930, + 239030, + 241390, + 246630, + 248200, + 252220, + 255370, + 257160, + 258709, + 263370, + 264280, + 266840, + 270190, + 275640, + 277790, + 280880, + 282680, + 283930, + 287870, + 290740, + 294140, + 299760, + 305270, + 308230, + 310160, + 311540, + 314150, + 316160, + 316440, + 318500 + ], + "text": [ + "SPEAKER 1: In this sequence, are going to look at a whole", + "bunch of techniques for analyzing circuits.", + "Think of these as your tool chest. So you are embarking on", + "6.002 and going on to build lots of useful electronic", + "systems.", + "But before we go and build these systems, much like a", + "carpenter who needs to go build a house, much like a", + "carpenter has to go and buy a set of tools from the local", + "store, we need to go and make sure that you have the tools", + "in your tool chest to analyze these circuits.", + "This tool chest will include things like the KVL KCL", + "method, the Node method and so on.", + "But before I begin talking about these techniques for", + "your tool chest, I'd like to do a extremely quick review--", + "as is my usual practice--", + "of what you've covered so far.", + "So remember our EECS playground.", + "We've gotten into this place by promising that we are going", + "to observe the lumped matter discipline.", + "By observing the discipline recall that the complexities", + "of Maxwell's equations and the differential equations that", + "you have to solve-- the partial differential", + "equations-- goes away.", + "And you're left with very simple linear equations.", + "And you will see a lot of that today.", + "As you make the lumped matter discipline, you end up with", + "these lumped elements, like resistors and voltage", + "sources and so on.", + "And what you do with these lumped elements is we can", + "label what are called the branch variables or the", + "terminal variables for these lumped elements, OK?", + "So for example, v is the voltage across the element.", + "And i is the current through the element.", + "The power consumed by the element is given by vi.", + "Continuing with our review, the lumped matter discipline", + "enables us to create the lumped circuit abstraction.", + "So you take these lumped elements and you connect them", + "with ideal wires.", + "So in this case, I have a resistor which is a lumped", + "element, a voltage source.", + "And I connect them with these ideal wires.", + "And what you end up with is called a lumped circuit.", + "But this is your lumped circuit abstraction.", + "Well as we made the transition from physics to EECS by", + "adhering to the lumped matter discipline.", + "I had discussed in the last sequence that Maxwell's", + "equations turn into very simple algebraic equations.", + "And these are captured by Kirchoff's voltage and current", + "laws, called KVL and KCL.", + "So KVL says that for all loops in your circuit, the sum of", + "the voltages around the loops add up to zero.", + "Similarly for all the nodes in the circuit, the currents that", + "enter into a node add up to zero.", + "And in the same matter, if I just summed the currents", + "leaving a node, they also add up to zero.", + "So whether you sum the currents entering the node or", + "currents leaving a node, they would add up to zero by KCL.", + "And the beauty of this was by adhering to lump matter", + "discipline, recall the complexities Maxwell's", + "equations whether an integral form or", + "differential form went away.", + "And we were now left with extremely simple algebraic", + "expressions of the sort.", + "And you will see shortly that you will end up solving", + "extremely simple linear equations", + "as we analyze circuits.", + "So as one example here is a linear circuit.", + "It has one, two, three, four, five, six elements.", + "It's got a voltage source of a voltage v zero.", + "It's got a resistor, r one and so on and so forth.", + "So for this circuit according to our abstraction and the", + "laws of KVL and KCL, the following", + "are going to be true.", + "So for instance if I look at node a, then according to KCL,", + "the currents entering the node must be zero.", + "So in other words, the current here is ica.", + "And I can sum to that the current", + "entering from the d direction.", + "So that would be plus ida.", + "And then there is a current from the ba direction and iba.", + "Those are going to sum to zero.", + "Now I can multiply the whole thing by minus 1.", + "And that would give me the sum of the currents leaving the", + "node are also going to be zero.", + "So that is KCL.", + "Now I can also write KVL in this case for this loop, for", + "instance, here.", + "For this loop I can add up the voltages around the loop.", + "And by KVL they must add up to zero.", + "So for example if I look at the voltage vca, I can add", + "that to the next voltage here.", + "That is to vab and then add that to the", + "final voltage, vbc.", + "And by KCL--", + "so all of those must add up to be zero.", + "Now if you go back to our circuit here that you see on", + "the left hand side, I am going to show you a little demo that", + "will look at these currents, ica, ida, and iba, and also", + "look at the voltages, vcabab and bbc and actually go and", + "look at the circuit, make the measurements, and show that", + "they indeed sum up to zero.", + "Not surprising.", + "KVL and KCL really work.", + "And so the demo should also work.", + "OK.", + "So let's go and do our demo." + ] +} \ No newline at end of file diff --git a/subs/pnHDLuxmXHo.srt.sjson b/subs/pnHDLuxmXHo.srt.sjson new file mode 100644 index 0000000000..6a6f2be8d6 --- /dev/null +++ b/subs/pnHDLuxmXHo.srt.sjson @@ -0,0 +1,251 @@ +{ + "start": [ + 200, + 960, + 4620, + 8960, + 11150, + 12420, + 15490, + 16430, + 21270, + 23350, + 26680, + 27640, + 30660, + 33870, + 35400, + 38440, + 42690, + 45660, + 48420, + 52700, + 54000, + 56210, + 58070, + 60140, + 63270, + 65420, + 67780, + 69250, + 72920, + 78070, + 80770, + 82250, + 82640, + 84470, + 88630, + 92050, + 95180, + 97790, + 101090, + 103030, + 106090, + 107230, + 109350, + 111210, + 112595, + 116310, + 118410, + 121680, + 124690, + 129570, + 132520, + 137390, + 140520, + 142440, + 144980, + 146010, + 147590, + 152290, + 155730, + 160665, + 161620, + 163020, + 166860, + 168950, + 175060, + 176090, + 179260, + 182890, + 184530, + 186900, + 187490, + 190670, + 192890, + 200310, + 200870, + 201680, + 203260, + 206280, + 210140, + 216000, + 217640 + ], + "end": [ + 960, + 4620, + 8960, + 11150, + 12420, + 15490, + 16430, + 21270, + 23350, + 26680, + 27640, + 30660, + 33870, + 35400, + 38440, + 42690, + 45660, + 48420, + 52700, + 54000, + 56210, + 58070, + 60140, + 63270, + 65420, + 67780, + 69250, + 72920, + 78070, + 80770, + 82250, + 82640, + 84470, + 88630, + 92050, + 95180, + 97790, + 101090, + 103030, + 106090, + 107230, + 109350, + 111210, + 112595, + 116310, + 118410, + 121680, + 124690, + 129570, + 132520, + 137390, + 140520, + 142440, + 144980, + 146010, + 147590, + 152290, + 155730, + 160665, + 161620, + 163020, + 166860, + 168950, + 175060, + 176090, + 177340, + 182890, + 184530, + 186900, + 187490, + 190670, + 192890, + 194140, + 200870, + 201680, + 203260, + 206280, + 210140, + 216000, + 217640, + 220450 + ], + "text": [ + "SPEAKER 1: OK.", + "I'm now going to show you a demo of superposition in", + "action with something you see every day in real life.", + "So in this demo, I am going to have an empty", + "vat to begin with.", + "And then what I'm going to do is I'm going to pour some salt", + "water into it.", + "OK, some salt water poured into it will behave like a", + "distributed resistance.", + "And so each small volume of water can be modeled as a", + "lumped resistor.", + "And so you end up with this three-dimensional connected", + "network of resistors.", + "Now, this is a linear circuit.", + "And we will see superposition in action with this circuit.", + "So what do is I'll connect one input to it, which will be a", + "high-frequency triangular wave, like so.", + "OK, that'll be input at one part of the water.", + "And then I will input a low-frequency sinusoid at a", + "different location.", + "So those are my two inputs.", + "And as we've seen before, you can think of", + "these as V1 and V2.", + "And what I'm going to do is I'm going to observe the", + "output at a third port.", + "And my goal will be to take a look at what", + "this input looks like.", + "If superposition truly holds true, then this output should", + "really show both a component that relates to V1 and another", + "component that clearly relates to V2, if", + "superposition really worked.", + "OK?", + "So let's go on to the demo.", + "And as I said before, in the demo, you will see a vat, an", + "empty vat to begin with, into which I will add salt water.", + "And then we will take a look at what happens at the output", + "as I apply two input voltages to it.", + "This is a vat of nothing, right, and it's all empty.", + "So this is a screen of the oscilloscope now.", + "So notice that I have a sinusoid, and I have a", + "triangular wave.", + "And the output is zero.", + "And the reason is there's nothing in this vat.", + "It's empty.", + "Previously when I taught this course, I would get salt water", + "and pour salt water.", + "Then we discovered a much better source of water that", + "conducted electricity, like one real mean", + "fluid, Cambridge water.", + "It just works very pleasantly.", + "It just conducts electricity like nothing at all.", + "And I've been thinking of using Charles River water next", + "time and see what happens.", + "Although there, we'd probably get some biological organisms", + "doing strange things at you.", + "But go ahead.", + "OK, so our friendly demonstration expert, Lorenzo,", + "will pour some water into the vat.", + "And you should begin seeing the output begin superposition", + "now of the two.", + "You see that?", + "So you do see the sinusoidal articulation", + "and the jagged waveform.", + "And just to have some more fun, what I can do is increase", + "one of the voltages.", + "And you'll see.", + "[LAUGHTER]", + "SPEAKER 1: Now you know what would have happened if I'd", + "used Charles River water.", + "OK.", + "So my output keeps increasing as I increase the", + "corresponding waveform.", + "OK?", + "I could do this.", + "This is fun.", + "OK.", + "So let me pause there and go on to the next topic.", + "So that little demonstration showed you that even something", + "as simple as this physical entity, a vat of water,", + "behaves like a linear system.", + "And we can model that linear system as a set of resistors." + ] +} \ No newline at end of file diff --git a/subs/rysqcHqcuBw.srt.sjson b/subs/rysqcHqcuBw.srt.sjson new file mode 100644 index 0000000000..92b5ee3afb --- /dev/null +++ b/subs/rysqcHqcuBw.srt.sjson @@ -0,0 +1,266 @@ +{ + "start": [ + 430, + 2360, + 5150, + 7530, + 8800, + 10650, + 12550, + 15580, + 20230, + 21470, + 24710, + 28570, + 33080, + 36910, + 37760, + 41340, + 43580, + 46300, + 49210, + 50790, + 54340, + 55560, + 58730, + 61340, + 63680, + 66160, + 67470, + 71970, + 75080, + 76780, + 80630, + 82170, + 84340, + 87600, + 89220, + 92530, + 93690, + 97000, + 99880, + 103900, + 105270, + 107520, + 111150, + 113850, + 117880, + 120410, + 124200, + 126160, + 131250, + 134610, + 135730, + 139440, + 143280, + 146180, + 149720, + 153030, + 156110, + 159210, + 161260, + 162656, + 167810, + 169130, + 171970, + 172770, + 175480, + 177160, + 180260, + 183360, + 186880, + 187670, + 191830, + 193640, + 196620, + 198110, + 201380, + 204390, + 205390, + 208400, + 212220, + 213750, + 217710, + 221690, + 225630, + 227170, + 229870, + 232430 + ], + "end": [ + 2360, + 5150, + 7530, + 8800, + 10650, + 12550, + 15580, + 20230, + 21470, + 24710, + 28570, + 33080, + 36910, + 37760, + 41340, + 43580, + 46300, + 49210, + 50790, + 54340, + 55560, + 58730, + 61340, + 63680, + 66160, + 67470, + 71970, + 75080, + 76780, + 80630, + 82170, + 84340, + 87600, + 89220, + 92530, + 93690, + 97000, + 99880, + 103900, + 105270, + 107520, + 111150, + 113850, + 117880, + 120410, + 124200, + 126160, + 131250, + 134610, + 135730, + 139440, + 143280, + 146180, + 149720, + 153030, + 156110, + 159210, + 161260, + 162656, + 167810, + 169130, + 171970, + 172770, + 175480, + 177160, + 180260, + 183360, + 186880, + 187670, + 191830, + 193640, + 196620, + 198110, + 201380, + 204390, + 205390, + 208400, + 212220, + 213750, + 217710, + 221690, + 225630, + 227170, + 229870, + 232430, + 235170 + ], + "text": [ + "INSTRUCTOR: Based on the previous method or the", + "previous property that you saw for linear circuits, we are", + "now ready to define the superposition method for", + "circuit analysis.", + "Note that the superposition method", + "applies to linear circuits.", + "And again, to refresh your memory, remember, we are in", + "the EECS playground that we got into by adhering to the", + "lumped matter discipline.", + "And within that, we looked at the node method and the KVL", + "KCL method that applies all over the EECS playground.", + "And then what we'll now do is look at some methods that will", + "apply to only a region of this playground where linear", + "circuits reside.", + "So the first of these methods is the superposition method.", + "And again, it applies to linear circuits.", + "So the method is very simple and inspired by the", + "superposition property that we studied for linear circuits.", + "So the method simply says this.", + "You first find the responses of the circuit to each source", + "acting alone.", + "Think of this as a divide and conquer method where you take", + "your entire circuit, and you find the responses of the", + "circuit to each source acting alone.", + "You turn off all the sources, and you find the response to", + "each source acting alone.", + "Then what you do is simply sum those individual responses.", + "Note that this technique applies to", + "independent sources only.", + "So if I have a linear circuit, then this technique applies to", + "independent sources only.", + "Now we will look at what happens when you have", + "dependent sources and so on in later lectures.", + "OK, let's move ahead.", + "The first step was find the response of the circuit to", + "each source acting alone.", + "But what does it mean for each source to act alone?", + "What it means is that you turn off all the other sources.", + "So for example, suppose we are focused on a", + "voltage source here.", + "What does it mean to turn off this voltage source?", + "In other words, if I want to set this voltage to 0, what", + "does it mean in terms of my circuit?", + "So in terms of my circuit, what this means is that I am", + "going to short the source.", + "So what you do is you short the source, and you end up", + "with a short circuit here.", + "And that is my voltage source having been set to 0.", + "And so I take all my voltage sources in the circuit and", + "simply short them out.", + "And this would be making each of the sources to act alone.", + "OK, next let's look at a current source and see what it", + "means to set a current source to 0.", + "So in this case, what you do is much as you set a voltage", + "source to 0 by shorting it out, you set the current", + "source to 0 by open-circuiting it like so.", + "So you create an open circuit in place of the current", + "source, and that's what it means to set a", + "current source to zero.", + "OK, so now we are ready to go try out an example using the", + "method of superposition.", + "And again, remember the method of superposition has", + "two parts to it.", + "In the first part, you find the responses of the circuit", + "to each source acting alone.", + "And then second, you sum up the partial responses.", + "So let's go back to our old faithful example.", + "In this example, we have two sources, a voltage source and", + "a current source.", + "And let's say our goal is to find the node voltage e taken", + "with respect to this ground.", + "And we are going to use the superposition", + "method to do the circuit.", + "So I showed the circuit on the right-hand corner here.", + "And notice that e is the node voltage that I", + "need to figure out.", + "So by the superposition method, I have two steps.", + "My first step is find the responses of the circuit to", + "each source acting alone.", + "So what I'm going to do is let me start with finding the", + "response of the circuit to the voltage source acting alone.", + "So what do I do to get a subcircuit in which the", + "voltage source is acting alone?", + "So I want you to think about this and try to figure out", + "what the resulting subcircuit is going to look like.", + "I'll give you a few seconds to do that before I do it myself." + ] +} \ No newline at end of file diff --git a/subs/wO-WqB_k9QQ.srt.sjson b/subs/wO-WqB_k9QQ.srt.sjson new file mode 100644 index 0000000000..4061525c2e --- /dev/null +++ b/subs/wO-WqB_k9QQ.srt.sjson @@ -0,0 +1,272 @@ +{ + "start": [ + 410, + 3130, + 7160, + 9660, + 12020, + 15930, + 19810, + 23480, + 26240, + 28450, + 33260, + 36660, + 40420, + 41770, + 44840, + 47260, + 51110, + 54160, + 56780, + 59990, + 64470, + 67762, + 68900, + 72300, + 73340, + 75660, + 78530, + 81620, + 84910, + 86050, + 91100, + 94680, + 96400, + 99420, + 100900, + 103800, + 107460, + 114830, + 118120, + 119350, + 123220, + 124600, + 126980, + 130310, + 132020, + 135180, + 136990, + 138860, + 144970, + 146860, + 149330, + 153420, + 157580, + 161500, + 164040, + 165950, + 167635, + 169320, + 170550, + 172780, + 177670, + 179560, + 182670, + 184370, + 185610, + 187270, + 189890, + 191325, + 195050, + 200140, + 204810, + 209390, + 213530, + 215270, + 219950, + 223760, + 224360, + 225620, + 228980, + 231670, + 235915, + 240830, + 244580, + 247860, + 248640, + 251430, + 254530, + 256560 + ], + "end": [ + 3130, + 7160, + 9660, + 12020, + 15930, + 19810, + 23480, + 26240, + 28450, + 33260, + 36660, + 40420, + 41770, + 44840, + 47260, + 51110, + 54160, + 56780, + 59990, + 64470, + 67762, + 68900, + 72300, + 73340, + 75660, + 78530, + 81620, + 84910, + 86050, + 91100, + 94680, + 96400, + 99420, + 100900, + 103800, + 107460, + 114830, + 118120, + 119350, + 123220, + 124600, + 126980, + 130310, + 132020, + 135180, + 136990, + 138860, + 144970, + 146860, + 149330, + 153420, + 157580, + 161500, + 164040, + 165950, + 167635, + 169320, + 170550, + 172780, + 177670, + 179560, + 182670, + 184370, + 185610, + 187270, + 189890, + 191325, + 195050, + 200140, + 204810, + 209390, + 213530, + 215270, + 219950, + 223760, + 224360, + 225620, + 228980, + 231670, + 235915, + 240830, + 244580, + 247860, + 248640, + 251430, + 254530, + 256560, + 258410 + ], + "text": [ + "SPEAKER 1: So before I wrap up the node method, I wanted to", + "take some time and show you something interesting, largely", + "for your cultural interest. This is not required for the", + "course, and so this is optional.", + "I want to show you how these equations are really solved in", + "real life and how computers can be used to do this for us.", + "So if you go back to step four of the node method, you recall", + "we had these two equations and two unknowns, where the", + "unknowns were e1 and e2.", + "I can turn these into matrix form, like so, where I have", + "matrix times a column vector equals another column vector,", + "and where I get a two-by-two matrix called the", + "conductivity matrix.", + "I get a column vector of the unknown node voltages.", + "And I get a column vector of the source voltages.", + "So I've taken my system of equations and converted them", + "into the matrix notation, like so.", + "And the way this works is each of these equations can be", + "obtained by doing a row column multiply.", + "So if I multiply the first row with this column here, I take", + "e1, multiply that by G1 plus G2 plus G3, I get", + "the first term here.", + "I take e2, multiply that by minus G3, I", + "get the second term.", + "And I equate that to G1V0.", + "Similarly, to get the second equation, I would take the", + "second row and multiply that by the same column vector.", + "Now, let's take a look at how things like", + "this might be solved.", + "So here is my matrix equation again, with a two-by-two", + "matrix multiplying a column vector equal", + "another column vector.", + "So we can use many sophisticated techniques to", + "analyze systems like this.", + "And if you've done courses in linear algebra, you would've", + "noticed that linear algebra spends a lot of time trying to", + "analyze systems of this sort, where A is some matrix, x is a", + "column vector of unknowns, and b is a", + "column vector of knowns.", + "And so you often have to go and solve for the column", + "vector of unknowns.", + "Now, with circuit analysis, if I have a circuit containing", + "millions of elements, I would have a column vector here,", + "which had a million elements.", + "And so clearly we would love to use computers to do that.", + "And not surprisingly, that is what to", + "do in circuit analysis.", + "In fact, the lab that you work on in 6002-X has the schematic", + "capture system where you can build circuits.", + "But for the analysis, the computer programs that are", + "used to analyze the voltages and so on, and show them to", + "you, use methods very similar to this, where you use these", + "sophisticated linear algebraic solvers that solve systems of", + "equations of the form Ax equals b.", + "So back to our system.", + "I can go ahead and solve the system.", + "I won't bore you with the details of", + "the agony of algebra.", + "I've gone ahead and solved these equations for you.", + "And so I get e1 and e2 are expressed as fairly big", + "equations of the sort.", + "So one interesting fact that I mentioned to you was you end", + "up with systems of equations that you", + "can solve with computer.", + "There's one other interesting fact.", + "Notice that the circuit that we used, our demo", + "circuit, was linear.", + "It was composed of linear elements and so on.", + "And so notice here that e1 is also related to a set of", + "linear terms. So notice that this equation here is linear", + "in V0, i1, V0, and so on.", + "And it is all in linear terms. Also note that there are no", + "negatives in the denominator.", + "So the fact that this is linear in the constant sources", + "will be used in a later sequence that we will cover in", + "a few days.", + "So watch out for that.", + "So just to wrap up and just go through the motions here, let", + "me just go ahead and solve for e2 just for kicks.", + "And I'll do it for values G1, G5, and then so on and so", + "forth, given here, and for i1 chosen to be 0, just for fun.", + "And so if I plug these numbers into the equation for e2 that", + "I just showed you, I'm going to get e2 as a function of V0,", + "as follows.", + "Then e2 is going to be 0.6 times V0.", + "And so if I pick V0 to be three volts, then e2 is going", + "to be 1.8 volts.", + "So there you have it." + ] +} \ No newline at end of file From d0d858c967b26f049c6458b30057519adaef091a Mon Sep 17 00:00:00 2001 From: Piotr Mitros Date: Tue, 31 Jan 2012 18:22:20 -0500 Subject: [PATCH 2/4] Subs moved to data --- subs | 1 + 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360510, - 361800, - 363950, - 366400, - 367510, - 370020, - 372210, - 378580, - 381780, - 383870, - 386220, - 389320, - 390820, - 396230, - 399940, - 403010, - 407210, - 409480, - 411580, - 413875, - 416590, - 418220, - 422150, - 423710, - 427570, - 430550, - 436710, - 441280, - 444170, - 446750, - 447590, - 450250, - 454710, - 458300, - 461390, - 469215, - 470420, - 477620, - 478650, - 481740, - 484970, - 487140 - ], - "text": [ - "INSTRUCTOR: Based on the previous method or the", - "previous property that you saw for linear circuits, we are", - "now ready to define the superposition method for", - "circuit analysis.", - "Note that the superposition method", - "applies to linear circuits.", - "And again, to refresh your memory, remember, we are in", - "the EECS playground that we got into by adhering to the", - "lumped matter discipline.", - "And within that, we looked at the node method and the KVL", - "KCL method that applies all over the EECS playground.", - "And then what we'll now do is look at some methods that will", - "apply to only a region of this playground where linear", - "circuits reside.", - "So the first of these methods is the superposition method.", - "And again, it applies to linear circuits.", - "So the method is very simple and inspired by the", - "superposition property that we studied for linear circuits.", - "So the method simply says this.", - "You first find the responses of the circuit to each source", - "acting alone.", - "Think of this as a divide and conquer method where you take", - "your entire circuit, and you find the responses of the", - "circuit to each source acting alone.", - "You turn off all the sources, and you find the response to", - "each source acting alone.", - "Then what you do is simply sum those individual responses.", - "Note that this technique applies to", - "independent sources only.", - "So if I have a linear circuit, then this technique applies to", - "independent sources only.", - "Now we will look at what happens when you have", - "dependent sources and so on in later lectures.", - "OK, let's move ahead.", - "The first step was find the response of the circuit to", - "each source acting alone.", - "But what does it mean for each source to act alone?", - "What it means is that you turn off all the other sources.", - "So for example, suppose we are focused on a", - "voltage source here.", - "What does it mean to turn off this voltage source?", - "In other words, if I want to set this voltage to 0, what", - "does it mean in terms of my circuit?", - "So in terms of my circuit, what this means is that I am", - "going to short the source.", - "So what you do is you short the source, and you end up", - "with a short circuit here.", - "And that is my voltage source having been set to 0.", - "And so I take all my voltage sources in the circuit and", - "simply short them out.", - "And this would be making each of the sources to act alone.", - "OK, next let's look at a current source and see what it", - "means to set a current source to 0.", - "So in this case, what you do is much as you set a voltage", - "source to 0 by shorting it out, you set the current", - "source to 0 by open-circuiting it like so.", - "So you create an open circuit in place of the current", - "source, and that's what it means to set a", - "current source to zero.", - "OK, so now we are ready to go try out an example using the", - "method of superposition.", - "And again, remember the method of superposition has", - "two parts to it.", - "In the first part, you find the responses of the circuit", - "to each source acting alone.", - "And then second, you sum up the partial responses.", - "So let's go back to our old faithful example.", - "In this example, we have two sources, a voltage source and", - "a current source.", - "And let's say our goal is to find the node voltage e taken", - "with respect to this ground.", - "And we are going to use the superposition", - "method to do the circuit.", - "So I showed the circuit on the right-hand corner here.", - "And notice that e is the node voltage that I", - "need to figure out.", - "So by the superposition method, I have two steps.", - "My first step is find the responses of the circuit to", - "each source acting alone.", - "So what I'm going to do is let me start with finding the", - "response of the circuit to the voltage source acting alone.", - "So what do I do to get a subcircuit in which the", - "voltage source is acting alone?", - "So I want you to think about this and try to figure out", - "what the resulting subcircuit is going to look like.", - "I'll give you a few seconds to do that before I do it myself.", - "All right.", - "This is the subcircuit.", - "And what I've done here is I've had to turn the current", - "source off.", - "So notice that out here I create an open circuit, and", - "that is the result of my current source", - "being turned off.", - "And this is my usual ground node.", - "And let me call this node voltage with the voltage", - "source acting alone as ev. So ev is the partial response of", - "the circuit to the voltage source acting alone.", - "Now how do we go about solving for ev?", - "Notice that we have a known pattern here.", - "We have a voltage source connected to a pair of", - "resistors, R1 and R2.", - "And ev is simply the voltage across R2.", - "Now this is a known pattern.", - "So one thing you should keep in mind is that in circuits", - "and electronics, we use patterns a lot.", - "Whenever we see a pattern, we can directly go and write down", - "the what the outward response is going to look like.", - "What I'm going to do is throughout this course, as you", - "we more and more patterns, I am going to alert", - "you to these patterns.", - "So right here is a voltage divider pattern.", - "So for the voltage divider pattern, I can write down ev", - "as being some fraction of the source voltage v. But the", - "divider action is simply R2 divide by R2 plus R2.", - "So it is simply the voltage across R2, and that is given", - "by R2 divide by R1 plus R2.", - "And this is a known pattern that you will find very", - "helpful as you analyze circuits very quickly.", - "Next let's look at I acting alone.", - "Before we do that, what do we have so far?", - "Again, recall, this is the circuit we", - "are trying to analyze.", - "We are trying to get the node voltage e.", - "And so far we have computed the partial voltage ev due to", - "the voltage source acting alone.", - "As the next step-- again, this is still step one of the", - "superposition method--", - "let's look at the partial response of the circuit due to", - "the current acting alone.", - "To get the response for the current acting alone, I need", - "to build a circuit in which the voltage", - "source is turned off.", - "I'll let you think for a couple of seconds as to what", - "the circuit will look like before I draw it out for you.", - "OK, let's go ahead.", - "So to turn off this voltage source, all I have to do is", - "replace it with a short circuit like so.", - "So notice that I have replaced the voltage source with a", - "short circuit, and I've left the current source in place.", - "I have my ground node here.", - "And notice that my goal is to find the partial voltage eI", - "that is a result of the current source acting alone.", - "So notice that I have a second pattern here.", - "And in this case, this is a current divider pattern.", - "Actually, this is a even simpler pattern.", - "I simply have a current that is flowing", - "into a pair of resistors.", - "OK, so I have a current, I, that is flowing into a pair of", - "resistors, R1 and R2.", - "And so I can compute the voltage across the pair of", - "resistors very straightforwardly.", - "So eI is simply the resistance times the current.", - "And the resistance of a paralel pair of resistors is", - "simply R1 R2 divide by R1 plus R2 times the current I.", - "OK, so now I have computed both ev and eI, the two", - "partial voltages with each of the voltages acting alone.", - "And now I am ready for step two of the", - "superposition method.", - "And the step two of the superposition method simply", - "says that you sum the two partial voltages, ev and eI.", - "So my resulting voltage e is simply the sum of the two", - "partial voltages ev and eI.", - "And I have those as R2 divide by R1 plus R2 times v. And I", - "sum that to eI.", - "And eI is R1 R2 divide by R1 plus R2 times I. And", - "there you have it.", - "Not surprisingly, this expression here is identical", - "to the expression that you obtained by using the node", - "method in the previous lecture." - ] -} \ No newline at end of file diff --git a/subs/227NDapJIz0.srt.sjson b/subs/227NDapJIz0.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/227NDapJIz0.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/27GsG_REo_w.srt.sjson b/subs/27GsG_REo_w.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/27GsG_REo_w.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/2SwT6JnfCq8.srt.sjson b/subs/2SwT6JnfCq8.srt.sjson deleted file mode 100644 index 35339bbfe0..0000000000 --- a/subs/2SwT6JnfCq8.srt.sjson +++ /dev/null @@ -1,1907 +0,0 @@ -{ - "start": [ - 17000, - 20153, - 26459, - 34000, - 40105, - 43473, - 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Good morning.", - "Let's get going. In today's lecture we continue", - "with the operational amplifier, \"op amp\" for short.", - "And what we are going to do is just build up a bunch of fun", - "building blocks using the op amp.", - "As a quick review --", - "To quickly review what we've seen about the op amp --", - "We represented the op amp as a device that looked like this", - "where the amplifier had an incredibly high gain.", - "So, if I had a small voltage difference here --", - "I call this v plus and this v minus with respect to ground.", - "And if I had a small voltage difference then this gain here", - "would multiply the difference by a large number and thereby", - "giving me an output that was on the order of a million times", - "greater than this difference. And because of that when I use", - "the op amp in a mode like this without any negative feedback", - "the output would usually crank up to the positive rail or the", - "negative rail. We also saw that it had", - "infinite input resistance so that the current flowing in here", - "or here was zero and also had zero output resistance.", - "This is my ideal op amp where irrespective of what load I", - "connect here the op amp would supply pretty much any current.", - "Now, in practical op amps that's not the case.", - "But suffice it to say that when used as an ideal op amp the", - "output impedance, the output resistance is going", - "to be zero. The op amp is a huge workhorse", - "of the analog industry. You will see based both on what", - "you've done on Tuesday and Wednesday but also today that", - "it's very, very simple to build circuits using the op amp.", - "When you use the amplifier, you don't have to worry about", - "things like nonlinear analysis. You don't have to worry about", - "am I really meeting the criteria for saturation limits and so on?", - "To some extent you have to think about that with the op", - "amp, too, because if the output hits the positive rail or", - "negative rail it isn't going to behave like you expect it to.", - "But fundamentally with this primitive model,", - "this idea model it becomes really simple to build circuits", - "with the op amp. Therefore it has become a key", - "building block for circuits. When circuit designers build", - "analog circuits very often their primitive building blocks are", - "really an amplifier of this sort, an op amp,", - "resistors, capacitors and some of our other primitive building", - "elements. If you look at the course notes", - "the readings are -- There are a bunch of examples", - "solved in Chapter 16. And you will see that using the", - "op amp it is indeed possible to build current sources that look", - "like more or less ideal current sources.", - "It is also possible to build voltage sources and so on.", - "It is an incredibly neat building block using which you", - "can do all kinds of cool stuff.", - "In this course you will see a whole bunch of example circuits", - "using the op amp. In today's lecture you will see", - "things like a subtractor. You will also see integrators", - "and a differentiator. And then in your lab,", - "lab four, you will build a really fun mixed signal circuit", - "involving both digital and analog components.", - "And you will build what is called a digital to an analog", - "converter using the op amp. And of course I can build all", - "our good-old amplifiers and circuits of that sort.", - "In a later lecture you will also see how we can build", - "filters using an op amp. This is going to be using the", - "knowledge you learn in terms of connecting resistors,", - "capacitors and inductors together and doing a frequency", - "domain analysis, well we can throw the op amp in", - "there and build filters, too.", - "This is just to give you a preview of upcoming attractions.", - "For today I am going to focus on these circuits.", - "I won't be covering any new theory or any new set of", - "foundations but pretty much take the simple properties that I", - "have explained to you about the op amp.", - "And using those simple properties very quickly build up", - "a bunch of circuits that you can use to analyze signals in a", - "variety of ways. Let's start with the following", - "circuit. With op amps I start with this", - "little guy. And what I am going to do is", - "use two voltage sources, v1, and this is a resistor,", - "not an inductor. And value R1,", - "value R2. So, I have a voltage connected", - "by a divider, voltage divider to the plus", - "input. And I am going to provide some", - "negative feedback in the following way.", - "This is going to be R2, the same as this one here,", - "a resistor R1. And then a voltage source v2", - "that I connect out here. So notice that- Oh,", - "and I take the output vOUT out here.", - "And that vOUT of course is with respect to ground,", - "and R2, v1 and v2 are also connected to ground.", - "What I am going to do is analyze the circuit it two", - "different ways, and as I analyze it describe", - "some other interesting properties to you.", - "In the last lecture the technique I used to analyze op", - "amps was one in which I replaced the op amp with its ideal model", - "involving a dependent source and so on with a large gain A and", - "showed that. I wrote the expression and then", - "I let A increase to infinity to the limits and got an expression", - "that was independent of A. And then in recitation", - "yesterday you would have covered another technique which makes it", - "much simpler to analyze op amps. Let me very quickly review that", - "method. We fondly call that technique,", - "there is no formal name for it, but we fondly call that v plus", - "more or less equal to v minus method.", - "This is also variously called the virtual ground method and so", - "on, but we shall call it the v plus more or less equal to v", - "minus method. The insight here is that", - "whenever I use the op amp in a way in which I am giving it", - "negative feedback, so I am feeding some portion of", - "the output to its negative input.", - "I am giving it negative feedback.", - "That's one property. Second property is that my", - "inputs, v1 and v2, and my resistance values are", - "chosen such that the output is not in saturation.", - "So, the op amp is not at the plus VS rail or minus VS rail.", - "Rather it's somewhere in the middle in its active region.", - "When that happens we claim that the v minus and v plus for the", - "op amp are more or less equal. And to give you some intuition", - "as to why that is so, let's say the output is 6 volts", - "and my supply is plus/minus 12. This is 6 volts and the", - "amplifier is a gain of a million, ten to the six.", - "To sustain 6 volts at the output all I need is a", - "difference of 6 microvolts here. Six divided by ten to the six", - "is the difference between v plus and v minus.", - "It's very, very, very small.", - "It's so small as to make v plus more or less equal to v minus.", - "All it takes is a very small differential voltage here to", - "give you 6 volts at the output. The key thing to observe is", - "under negative feedback, when the op amp is not in", - "saturation the property that v plus equals v minus holds.", - "And the way it works is that it's not that it's a magical", - "property. It is simply that when I apply", - "negative feedback the negative feedback is such that it will", - "force this v minus node here to be at more or less the same", - "voltage as v plus. Remember the when in doubt", - "simply go back and think about the anti lock brakes example we", - "did last time. For example if v plus increases", - "the output will increase and so will the voltage here and tend", - "to make these two equal. What we can do,", - "being rather tricky here, what we'll do is say look,", - "if we know for a fact that under negative feedback the op", - "amp is going to engineer these two node voltages to be more or", - "less equal then why don't I just use that fact to begin with and", - "analyze my circuit assuming that it's true.", - "This is just a bit of inverted logic here that says look,", - "the circuit is going to make that happen.", - "If the circuit is going to make that happen to analyze the", - "circuit in its steady state, why don't I just go ahead and", - "assume that to begin with? This again goes back to us", - "wanting to be engineers here and do whatever is simply and find", - "the simplest possible way of getting some place.", - "I want to use that method, the v plus equals v minus", - "method. Let me just first write down", - "some values that I know about. I know that v plus is simply a", - "voltage divider relation here. That's v1 times R2 divided by", - "R1 plus R2. And by the v plus equals v", - "minus method I know that this is going to be equal to v minus.", - "And this is going to be true because I am giving you negative", - "feedback here. And we are going to engineer", - "the values of R1, R2, v1 and v2 such that the op", - "amp is not in saturation. So, we know that.", - "The next thing that we know, let's say this is a current i.", - "This current i flows here. Know that there is no current", - "going in here. Op amp has an infinite input", - "resistance so there is nothing going in there.", - "There is no current going in there.", - "If there is no current going in here, what must happen to i?", - "Remember, from the foundations of the universe Maxwell's", - "equations and therefore KVL and KCL hold.", - "KVL and KCL simply come straight from nature.", - "You and I cannot mess with that.", - "Bad things happen to you if you do.", - "So, nature, Maxwell's equations, KVL,", - "KCL. It's simply nature.", - "So, KCL applies here. Current comes in here.", - "Nothing goes there. Don't argue.", - "The current has to go here, period.", - "No if, ands or buts. There is i coming in here,", - "nothing goes there, so that current must flow here.", - "It has no choice. It's from basic nature.", - "I can write down what my current i is going to look like.", - "What is i going to look like? Well, I know v2,", - "I know v minus. v minus is the same as v plus.", - "And v plus is the i expression given here.", - "So, I can write i as v2 minus v minus divided by R1.", - "Let me keep track of those two and then go ahead and compute", - "vOUT. So, my goal in life is compute", - "vOUT as a function of the two input voltages v1 and v2.", - "And just for kicks I have gone ahead and computed some of the", - "intermediate node voltages and currents.", - "How do I write vOUT? What is vOUT?", - "vOUT is simply v minus from KVL.", - "vOUT is simply v minus minus the drop across this resistor.", - "So, the drop across that resistor is simply iR2.", - "From good-old KVL from the first lecture,", - "a voltage minus the drop across the resistor is equal to vOUT.", - "Therefore it's simply v minus minus iR2.", - "One thing to be very cautious about, I will tell you right", - "now, is that the output here relates to the inversion of the", - "voltage across this resistor R2. Be very, very careful in that", - "if I have a voltage across this resistor here that impacts vOUT", - "with a minus sign attached to it.", - "Notice that iR2 is the voltage across R2 and vOUT relates to", - "the negative of that. Be very cautious.", - "That's one of the commonest silly mistakes I have seen", - "people make in solving problems like this.", - "Let's go ahead. I know v minus and I don't know", - "i. Let me substitute for i for", - "now, and that is v2 minus v minus divided by R1 times R2.", - "Let me go ahead and collect all the v minuses.", - "v minus, I get a one here, minus minus becomes a plus,", - "and so I get R2 divided by R1 out there.", - "And then I minus v2 R2 divided by R1.", - "That is vOUT. Now let me go ahead and", - "substitute for v minus. And that is simply v1 R2", - "divided by R1 plus R2. That is v minus.", - "And this character here is simplified to be R1,", - "R1 plus R2 minus v2 R2 divided by R1.", - "What do we get? I cancel these two suckers out", - "and what I end up with is v1 R2 divided by R1 minus v2 R2", - "divided by R1, which is simply R2/R1(v1-v2).", - "What is interesting here is that what I have ended up", - "building is a very primitive subtractor.", - "So, my output relates to v1 minus v2 multiplied by the", - "constant factor given by R2 divided by R1.", - "Again, as I pointed out to you at the beginning of this", - "lecture, no knew foundations today, no new theories,", - "no new disciplines, no new laws.", - "We are just going to take what you have learned --", - "Three simple things, infinite gain,", - "infinite input resistance, zero output resistance,", - "plus this new thing v plus equals v minus.", - "And just being armed with those four principles we are just", - "going to charge ahead and analyze a bunch of circuits.", - "It is purely intellectual and pure applications today.", - "This is one way of doing it. There is another way of solving", - "it. We can solve the circuit.", - "Remember, whenever you see a linear circuit and you see two", - "sources or three sources, just think superposition,", - "right? You see a linear circuit and", - "two or three sources, think superposition.", - "We should be able to apply superposition to this.", - "The op amp is simply another building block.", - "It's a linear circuit. So, let's see if we get the", - "same answer. Let's try to solve the circuit", - "using superposition and see if we get the same answer.", - "To do superposition what I am going to do is build two", - "subcircuits. One subcircuit in which v1 is", - "zero, and that subcircuit looks like this.", - "If I set v1 to be zero then I get R1 parallel R2 going to", - "ground. So, if v1 is set to zero then", - "R1 goes to ground. And I get R1 parallel R2 here.", - "And of course I have v2 as before.", - "And this was R1, this was R2,", - "and let me call that vOUT1. Oh, I'm sorry.", - "Let me call it vOUT2 corresponding to that component", - "of the output that relates to v2 acting alone.", - "Remember superposition? Build two subcircuits,", - "one that depends on v2 and another one that depends on v1.", - "Let's do the second one, too.", - "Second one is v2 going to zero. Here is my little op amp.", - "And what I will do is simply flip the op amp just to see if", - "you can identify some interesting patterns.", - "Just flip the op amp around. And this is v1 as before.", - "And recall that v1 was going to the plus node through a resistor", - "R1. And then I had a R2 to ground.", - "And then let me short v2 to ground.", - "And when I short v2 to ground what happens?", - "When I short v2 to ground what happens is that the tail of R1", - "here goes to ground. And so it is as if the output", - "is connected to the node v minus through a resistor,", - "so it as if the output v R2 is connected to the minus input", - "through a resistor. We will draw it like this.", - "And the minus input goes through a resistor R1,", - "to ground. If you thought that patterns", - "were important in the earlier part of the course doing voltage", - "divider patterns and current divider patterns and amplifier", - "pattern, the source follower pattern, op amps is all about", - "patterns. You should remember two or", - "three simple patterns and be able to write down the", - "expression for those just by observation.", - "So, this is one common pattern that you have seen before in the", - "very first lecture. And I just wrote it down in", - "that manner. Let me go ahead and solve this", - "circuit. It turns out that this is also", - "a pattern. I will analyze it today but in", - "the future v2 going to this node through R1 and then R2 to the", - "output. You have probably also seen", - "this in your recitation. This one is called an inverting", - "connection and this one here is called a non-inverting", - "connection. Let's go ahead and do vOUT2.", - "vOUT2 is simply given by, notice that since this is", - "ground, no current flowing here, this voltage is zero.", - "If this voltage is zero, this voltage is zero by the v", - "plus equals v minus method. If this is zero,", - "the current that goes through here is v2 divided by R1.", - "And that same current must flow through the resistance R2 as", - "well. If the current v2 divided by R1", - "flows through this resistor, the drop across this resistor", - "is simply given by, let me hide this for a second,", - "is simply given by v2. So, v2 divided by R1 is the", - "current here. This is zero.", - "So, the drop across this resistor is v2 R1 multiplied by", - "R2. That's a drop across this", - "resistor. This voltage is simply zero", - "minus a drop across the resistor.", - "So, it's zero minus the drop across the resistor and that", - "gives me v2. Again, remember this minus sign", - "comes in when I want to convert this to get the output voltage", - "from that. This is a very common pattern.", - "It's called an inverting connection where the output is", - "some factor of the input voltage and the factor is given by R2", - "divided by R1. Let's go ahead and analyze this", - "guy now. What is vOUT1 equal to?", - "I should have called this vOUT1 because it relates to v1.", - "vOUT1. There is a v plus here.", - "From our first lecture I know that vOUT1 relates to v plus in", - "the following way. I know that it is v plus times", - "the sum of the resistances divided by R1.", - "Based on the first lecture this is true.", - "vOUT1 is simply an amplified version of v plus where the", - "amplification factor is given by R1 plus R2 divided by R1.", - "And I know v plus is simply a voltage divider action here.", - "And I can take a simple voltage divider action here because the", - "current going in is zero. Looking in here this is as if", - "it's an infinite resistance, so it is as if the element", - "simply does not exist. The voltage here is simply v1", - "divided by R1 plus R2 multiplied by R2, our voltage divider", - "pattern. So, I get v1 times R2 divided", - "by R1 plus R2 times R1 plus R2 divided by R1.", - "These two cancel out which gives me vOUT1 is simply v1 R2", - "divided by R1. To get vOUT I add up the two.", - "vOUT is vOUT1 plus vOUT2, which is my goal.", - "And that is simply v1 R2 by R1 minus v2 R2 by R1.", - "Thankfully what we have here is the same as here.", - "Again, there is really nothing new that I am going to cover", - "today. Simply apply,", - "apply, apply, four simple principles.", - "Here I have used superposition and I am showing you a circuit.", - "So, it turns out with op amps you should really remember that", - "pattern. You will see it again and again", - "and again. And each time you see it,", - "it will save you six minutes of having to solve the circuit", - "without knowing the pattern. So, remember this pattern.", - "You can pick up another three or four minutes by remembering", - "this pattern here. This pattern is simply v2 R2", - "divided by R1. Imprint those two patterns into", - "your brains. OK, so those are a couple of", - "simple circuits using the op amp.", - "We built a subtractor. The next step,", - "let's go ahead and try to build an integrator.", - "Using this little building block we can go ahead and try to", - "build a bunch of circuits. We can build filters,", - "A to D converters and so on. Let's build an integrator.", - "Abstractly I need to build this box.", - "Which when fed a vI, I want that box to integrate", - "and give me a vO which is vI integrated over time.", - "That is what I want to build. How do I go about building it?", - "What I would like to do next is give you some flavor for design.", - "How do you go about designing things with an op amp?", - "Knowing that you do not know the pattern for this yet,", - "how do you go about designing things?", - "Well, let's start with the following intuition.", - "The intuition that I begin with is that if I have a current i,", - "and remember that capacitors and inductors related to,", - "you saw differentiation and integration happening when we", - "dealt with capacitors and inductors.", - "So, I think we have to invoke a capacitor here or an inductor.", - "In this example I invoke a capacitor.", - "Notice that if I stick a capacitor in here this current", - "is i, capacitance C, then my voltage vO is given by", - "what? Voltage is simply the integral", - "of the current flowing through it or vice versa i is C dv/dt.", - "If i is C dv/dt then v is simply one by C integral.", - "If I can pass the current through a capacitor then the", - "voltage across the capacitor must be a current.", - "Notice then that vO is related to i dt.", - "I have some multiplying constants and so on,", - "but fundamentally what I have found is if I can stick a", - "current through a capacitor then the voltage across the capacitor", - "relates to the integral of the current.", - "OK, that's interesting. So, I have an integral in", - "there. But I have a current.", - "Notice my goal was to integrate a voltage.", - "What I figured out how to do was if I can turn that voltage", - "into a current -- If I can turn that voltage into", - "a proportional current and then pump that current through a", - "capacitor I will get the integration that I want.", - "How do I convert my vI to i? How do I do that?", - "Well, let's take a stab at it. Here is my vI.", - "Let's take the resistor R. And remember I need to stick", - "the capacitor here. I have some current I here.", - "I don't know what the current is yet.", - "And I stick a voltage here. And what I am trying to do is", - "trying to see if I stick a voltage and a resistance in", - "series then there is some relationship between the current", - "and this voltage. Recall that I am trying to make", - "this current be directly proportional to the voltage vI.", - "But it turns out that i here is not equal to vI divided by R.", - "If i was vI divided by R somehow, I am done.", - "If i was vI divided by R, by some magic,", - "then I have converted my voltage to a current,", - "I feed that current through my capacitor and vO is my integral", - "that I am looking for. But unfortunately i is not", - "equal to vI divided by R. You know that.", - "i relates to vI minus the capacitor voltage divided by R.", - "So, i is not simply vI divided by R for all time but i is", - "really vI minus the capacitor voltage divided by R.", - "And, in fact, when we did RC circuits you", - "wrote this equation to represent the dynamics of the circuit,", - "RC dvO by dt plus vO equals vI. We wrote down this circuit for", - "a first order RC, wrote this equation for a first", - "order RC circuit. Now, it does turn out,", - "to wrap up on this wild goose chase that we went on,", - "it does turn out that if this term here is much bigger than", - "that term. If this term is much bigger", - "than that term then I can ignore that term and write down RC dvO", - "by dt more or less equal to vI. If that were true,", - "this would be true, and then vO would be more or", - "less equal to one by RC integral of vI dt.", - "Again, if this were true. If this were true for all time", - "then vO would be integral of vI dt.", - "Again, remember this is all a wild goose chase.", - "Just write down WGC there just so you don't get confused.", - "I am on this wild goose hunt here trying to find a way to get", - "a current from a voltage which I can then feed into a capacitor.", - "This was one thing I knew, but this was not what I want.", - "But it does turn out to be what I want when vO is very,", - "very small. So, I see some glimmer of hope", - "but not quite. It turns that in R and C,", - "if I make R and C very, very big, if I have a huge time", - "constant, with a huge time constant the voltage vO looks", - "like an integral of vI, but only when I have a very", - "huge time constant. So, I give up on that track.", - "Instead I try something else.", - "Another try. I would like you to notice if", - "you take your op amp, here is your op amp,", - "if you take this op amp and you stick the positive terminal to", - "ground, under reasonable feedback, under reasonable", - "negative feedback what do you notice about the current?", - "If I had a current i flowing here what did you notice?", - "Look at this picture. I had a current i flowing in", - "here, v2 divided by R1. And because this resistance was", - "infinite all the current went through the upper terminal.", - "So, this is zero volts. And by the v plus equals v", - "minus method this is also more or less equal to zero.", - "And I have a current i flowing in here, nothing goes here,", - "so then the i must flow up there.", - "So, all I am doing here is causing a reflection of the", - "current from this grounded node. My current is being reflected", - "into, or deflected if you feel like it, the upper edge here", - "after coming in through this edge.", - "That is interesting. We are just one step away from", - "the key insight.", - "I have an i coming in here, an i going out there.", - "Notice that, as I said before,", - "this is zero volts. How do I get my voltage vI to", - "look like a current, to become proportional to a", - "current? It is simple now.", - "All I do is put a voltage vI and put a resistor R out there.", - "If I do that, and since this is zero,", - "the current i is given by vI divided by R.", - "I have gotten to where I want to be.", - "So, by using an op amp and using the fact that the minus", - "node here, v minus is at the same potential as v plus when", - "there is negative feedback then I can stick a resistor here.", - "And because this is zero the current here is simply vI", - "divided by R. I have gotten to the first", - "place. Now all I need to do is simply", - "pump this current through a capacitor and I get the integral", - "of the, the voltage becomes an integral of the current.", - "That is easy. I stick my capacitor here and I", - "get my answer out there as vO. Notice that when I do this,", - "let's say this is plus/minus VC.", - "This is zero. So, vO is minus VC.", - "Again, I will keep emphasizing it maybe 17 times throughout", - "this course that if this is zero then the output here is related", - "to the negative of this voltage, common, common,", - "common mistake. I will be very upset after", - "doing all this if I see this mistake happen in any of the", - "future homeworks or finals or whatever.", - "This should not happen. So, vO is a minus sign here VC.", - "And I know that if I have a current i through a capacitor", - "what is VC? If I have current i through a", - "capacitor than this is simply t i dt.", - "And i by design is -- So, I have my integrator.", - "It is a two-step process. I stuck a resistor here,", - "so the current became equal to vI divided by R.", - "Then I took that current and pumped it through a capacitor", - "through this terminal here, and the voltage across the", - "capacitor for a current i is given by this expression.", - "This is Capacitors 101. OK Capacitors 101 says that the", - "voltage across the capacitor is simply one by C integral i dt.", - "Another way of looking at it is the voltage across the capacitor", - "is C, I'm sorry, the current through a capacitor", - "is C dv/dt. This is simply the integral", - "form of that equation. And I am done with my", - "integrator. So, this is another very common", - "building block. Remember this.", - "Most of the circuits we will be seeing with op amps simply", - "involve something here and some there.", - "And the output in this inverting connection is the", - "output times, if it is a resistance it is", - "simply R2 divided by R1, if it's a capacitor I get the", - "integral form looking like this. Yes.", - "Can someone tell me where the negative sign went?", - "The blackboard ate it up. Good catch.", - "After all that lecture about watching the negative sign.", - "After this little bit of faux pas here, now I will be doubly", - "mad if you guys make that mistake.", - "All right. Now that we have built the", - "integrator, I could give this out as a homework problem.", - "And you should be able to design a differentiator based on", - "what you've learned here. You now have the tools to go", - "and do some design like this, but we don't have any more", - "homeworks left so I guess I will go ahead and solve this for you", - "right here and do the design for you.", - "The building block that we need looks like this,", - "d/dt here. Let me take a vI and stick a vI", - "in there. That's what I want to build.", - "And what I built here is that different integrator box.", - "And what I would like to do now is build a differentiator box.", - "How do I go about doing it? I will go really slow here so", - "you will have some time to think about it for yourselves and see", - "if you folks are crack op amp circuit designers already,", - "if you have the right instincts here.", - "Again, when you see differentiation integration", - "think capacitors or inductors, it doesn't matter.", - "In fact, as a homework exercise, you may want to go", - "back and see how you can get a similar effect using inductors.", - "Can you play with inductors and get a similar effect?", - "So, inductors are devices that are a dual of the capacitor.", - "Whatever we will do with capacitors, there must be a", - "corresponding way with inductors.", - "You can try it out in your spare time.", - "Let's go back to this one here. I will stick with the capacitor", - "way of looking at things. I need a differentiation now.", - "Remember this. If I have a vI and I stick this", - "across a capacitor, I have a current C and some", - "voltage vc across the capacitor, what does i relate to?", - "i is simply C dv/dt and vc in this case is simply C dvI/dt.", - "If I can stick a voltage across a capacitor, if my input voltage", - "is stuck across a capacitor then the resulting current relates to", - "dvI/dt. Here we have the opposite", - "problem. By doing this simple trick,", - "I can obtain a current that has the right form.", - "Now what I need to do is somehow convert that current", - "into a voltage because the abstraction that I need is a", - "voltage to voltage. The next step,", - "what I need to do is somehow convert a current to a voltage.", - "How do I go about doing that? Again, remember for the op amp,", - "if I have a current i flowing here then by the reflection", - "property i gets pushed up into this edge, provided that the", - "whole circuit is working with descent negative feedback.", - "Given this trick what I can do is say look, suppose I did this.", - "Remember, my goal here is how do I convert a current to a", - "voltage? I have a current i coming in", - "here, and I can turn that into a voltage because I know the", - "current must come out here, I know this current must come", - "out there. All I have to do is stick a", - "resistor in there. If I stick a resistor in there", - "what is vO equal to? vO is simply iR,", - "right? That's right.", - "vO, I get i here, so i pumps through here.", - "Remember, what comes in here must get reflected up because", - "the current going in here is zero.", - "All the i must come out here. So, that i must pump through", - "this resistor. The drop across this resistor", - "is iR. That's the voltage drop across", - "that resistor. And since this at a virtual", - "ground the output here is simply zero minus this drop which is", - "minus iR. So, I have gotten to where I", - "want to be. I have my current i being", - "converted to a voltage. I have taken my current,", - "and I have been able to convert that into a voltage by sticking", - "a resistor in here. As a final step,", - "I simply need to produce the current.", - "And that is pretty easy to do. Abstractly what I need to do,", - "again, this is design here so we will talk about abstract", - "stuff. If I had a voltage vI,", - "I need to produce a current which relates to C dvI/dt.", - "And I know I can do that by simply doing this.", - "By doing this I know my i is C dvI, correct?", - "If I can get this effect, I put this in quotes because", - "that's my pattern. I am looking for a pattern,", - "where a voltage vI is directly applied across a capacitor.", - "And when that happens the current relates to C dv/dt.", - "Let's go back to our op amp pattern here,", - "op amp circuit. So far I have achieved --", - "I just repeated this out there. And so somehow I need to take", - "this pattern here and learn from that pattern and apply the", - "pattern here. So, what I can do is,", - "this is a ground node, correct?", - "Now, the poor little capacitor, what does it care,", - "whether it's a ground node or a virtual ground node?", - "As long as it's a zero volt node down here what does it", - "care? What I am going to do is stick", - "this point, not here but into a virtual ground node.", - "I am going to grab that point, take it here and stick it here.", - "The poor little capacitor doesn't know the difference.", - "I have really suckered the little beast.", - "This is vI. Remember this.", - "My i through the capacitor is proportional to C dv/dt.", - "Instead what I have done is taken this guy and stuck it here", - "to get something like this. Just remember these four or", - "five little tricks. And you apply them in op amp", - "circuits again and again and again and again.", - "So, this is vI, this is my virtual ground.", - "As far as this poor little capacitor is concerned,", - "it is chugging along merrily thinking that it is connected to", - "ground. Little does it know it is only", - "a virtual ground, all right?", - "But the current i here is simply C dvI/dt.", - "And that current, the C dvI/dt,", - "that current flows through here and gives me vO as iR.", - "So, vO is simply minus R. Let me substitute for i there,", - "C dvI/dt. OK, so notice then that my vO", - "is now proportional to dvI/dt. So, vO is some RC time constant", - "times dvI/dt. Therefore, I have my", - "differentiator circuit. Remember this as a closing", - "thought. Remember this v plus more or", - "less equal to v minus trick. And to the extent possible", - "simply use that trick to analyze op amp circuits under feedback", - "and not in saturation. Just remember these two.", - "Very quickly for the demo, I have a square wave input here", - "to the op amp, that's my vI to the integrator.", - "And this is the output vO. The integral of a square wave", - "is a triangular wave, as you can see.", - "And we will do the same thing for a differentiator.", - "And for the differentiator, I input the square wave to this", - "differentiator circuit. And I get this,", - "wherever there is a sharp rise, I get this huge negative spike", - "and a positive spike because of the minus sign.", - "So, this is the differentiator circuit.", - "Then I feed this into the op amp.", - "OK. Thank you." - ] -} \ No newline at end of file diff --git a/subs/2deIoNhqDsg.srt.sjson b/subs/2deIoNhqDsg.srt.sjson deleted file mode 100644 index a613902b95..0000000000 --- a/subs/2deIoNhqDsg.srt.sjson +++ /dev/null @@ -1,194 +0,0 @@ -{ - "start": [ - 510, - 2820, - 5140, - 8310, - 12040, - 14870, - 16200, - 20400, - 22600, - 25050, - 27070, - 30540, - 31230, - 33960, - 36425, - 39860, - 43890, - 47040, - 50100, - 54110, - 57780, - 60780, - 63620, - 64700, - 66480, - 67670, - 71430, - 72830, - 76530, - 78930, - 81580, - 84660, - 85950, - 91560, - 96200, - 99880, - 100690, - 103220, - 106170, - 108900, - 111490, - 115520, - 116600, - 119100, - 120880, - 123800, - 126160, - 127890, - 130780, - 134840, - 137350, - 140760, - 143706, - 147270, - 150600, - 153660, - 156500, - 157680, - 161090, - 164640, - 167410, - 169500 - ], - "end": [ - 2820, - 5140, - 8310, - 12040, - 14870, - 16200, - 20400, - 22600, - 25050, - 27070, - 30540, - 31230, - 33960, - 36425, - 39860, - 43890, - 47040, - 50100, - 54110, - 57780, - 60780, - 63620, - 64700, - 66480, - 67670, - 71430, - 72830, - 76530, - 78930, - 81580, - 84660, - 85950, - 91560, - 96200, - 99880, - 100690, - 103220, - 106170, - 108900, - 111490, - 115520, - 116600, - 119100, - 120880, - 123800, - 126160, - 127890, - 130780, - 134840, - 137350, - 140760, - 143706, - 147270, - 150600, - 153660, - 156500, - 157680, - 161090, - 164640, - 167410, - 169500, - 170750 - ], - "text": [ - "SPEAKER 1: Before we begin the course, I wanted to cover a", - "few administrative details.", - "First of all, this course does have prerequisites.", - "To do well in the course, you must have a advanced placement", - "or AP-level understanding of electricity and", - "magnetism in physics.", - "And these are at the level of MIT 8.02 course, which you", - "might check out on MIT OpenCourseWare.", - "It's also useful for you to have a basic knowledge of", - "solving simple differential equations.", - "Now, they will cover how to solve some simple equations in", - "this course.", - "But if you come in with a knowledge of solving simple", - "differential equations, that will be extremely helpful.", - "There is a textbook for this course, it is \"Foundations of", - "Analog and Digital Electronic Circuits\" by Agarwal and Lang.", - "You can obtain a copy from Amazon if you like.", - "The book is not required, but certainly useful.", - "We will make available parts of the textbook in an", - "electronic form on our course site as well.", - "I want to draw special attention to some of the", - "underlined readings from this book in your course at a", - "glance handout.", - "This handout tells you what is going to happen", - "weekly in this course.", - "It also tells you week by week what are the readings that we", - "recommend that you do.", - "We really recommend that you at least skim through the", - "material that is assigned as reading.", - "Now, the underlying readings are particularly important, as", - "they stress intuition in how you solve circuits and", - "electronics problems.", - "Now in addition to the various forms of 6.002x material that", - "we will share with you, such as video lectures, interactive", - "exercises, and so on, that we will have several forms of", - "assessment.", - "We will give you weekly homeworks and laboratories.", - "These homeworks and laboratories must be completed", - "by the deadline indicated on the assignment, and we will", - "assign both homeworks and labs each week.", - "Now the video lectures and the exercises and so on are for", - "you to learn the material.", - "Your performance in the course will be assessed", - "using several methods.", - "One is, you will be assessed on homeworks, and those will", - "count for 15% of your grade.", - "And we will have about 10 homeworks.", - "There will be laboratories, again around 10 laboratories,", - "and they also count for 15% of your grade.", - "There will be a mid-term, which will count for 30%, and", - "a final, which will count for 40%.", - "Now, we will give you instructions on how to do the", - "midterm and the final in the course bulletin board that you", - "should be watching constantly.", - "We urge you to collaborate, if you have other friends taking", - "the course, on your lecture videos and on the", - "exercises and so on.", - "And you are also free to, and encouraged to, collaborate in", - "discussing high-level concepts and materials in this course.", - "However, the assessed materials, such as homeworks,", - "labs, midterms and final exams, must be", - "done on your own." - ] -} \ No newline at end of file diff --git a/subs/2vHGYdepKLw.srt.sjson b/subs/2vHGYdepKLw.srt.sjson deleted file mode 100644 index d33230ea47..0000000000 --- a/subs/2vHGYdepKLw.srt.sjson +++ /dev/null @@ -1,1928 +0,0 @@ -{ - "start": [ - 0, - 1541, - 5779, - 10691, - 14832, - 19263, - 22827, - 28317, - 34000, - 41131, - 44971, - 52651, - 58000, - 63348, - 67867, - 73400, - 75982, - 80317, - 85204, - 90000, - 95740, - 102946, - 110641, - 117603, - 123801, - 127128, - 131079, - 135237, - 138564, - 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2812018, - 2816703, - 2820000, - 2823194, - 2827013, - 2829444, - 2831736, - 2835416, - 2838263, - 2841250, - 2845000, - 2850000, - 2854607, - 2857785, - 2862313, - 2867000, - 2889440, - 2892064, - 2895738, - 2897779, - 2900520, - 2903086, - 2906410, - 2908859, - 2913000, - 2916186, - 2919720, - 2923255, - 2926615, - 2929917, - 2934000 - ], - "text": [ - "Good morning, OK.", - "Let's get started. We have one handout today.", - "That's your lecture notes. There's some copies still", - "outside for those who haven't picked one up.", - "In general, what I do is, in the lecture notes,", - "I leave out large amounts of material.", - "So, this will enable you to keep your hands busy while I'm", - "lecturing and take down some notes and so on.", - "So, don't assume that everything that I talk about is", - "on here. Please follow along.", - "OK, so as is my usual practice, let me start with a quick", - "review of what we covered so far.", - "So what we did primarily was looked at this discipline that", - "we call the lump matter discipline, which was very", - "similar, very reminiscent of the point mass simplification in", - "physics. And this discipline,", - "this set of constraints we imposed on ourselves,", - "allowed us to move from Maxwell's equations to a very,", - "very simple form of algebraic equations.", - "And specifically, the discipline took two forms.", - "One is, we said that we will deal with elements for whom the", - "rate of change of magnetic flux is zero outside of the elements,", - "and for whom the rate of change of charge I want to charge", - "inside the element was zero. So, if I took any element,", - "any element that I called a lump circuit element,", - "like a resistor or a voltage source, and I put a black box", - "around it, then what I'm saying is that the net charge inside", - "that is going to be zero. And this is not true in", - "general. We will see examples where,", - "if you choose some piece of an element for example,", - "there might be charge buildup, but net inside the,", - "if I put a box around the entire element,", - "I am going to assume that the rate of change of charge is", - "going to be zero. So, what this did was it", - "enabled us to create the lump circuit abstraction,", - "where I could take elements, some element of the sort,", - "this could be a resistor, a voltage source,", - "or whatever, and I could now ascribe a", - "voltage, some voltage across an element, and also some current,", - "\"i,\" that was going into the element.", - "And as I go forward, when I label the voltages and", - "currents across and through elements, I'm going to be", - "following a convention. OK, the convention is that I'm", - "going to label, if I label V in the following", - "manner, then I'm going to label \"i\" for that element as a", - "current flowing into the positive terminal.", - "It's just a convention. By doing this,", - "it turns out that the power consumed by the element is \"vi\"", - "is positive. OK, so by choosing I going in", - "this way into the positive terminal, the power consumed by", - "the element is going to be positive.", - "OK, so in general of even simply following this", - "convention, when I label voltages and currents,", - "I'll be labeling the current into an element entering in", - "through the plus terminal. Remember, of course,", - "if the current is going this way, let's have one amp of", - "current flowing this way, then when I compute the", - "current, \"i\" will come out to be negative.", - "OK, so by making these assumptions, the assumptions of", - "the lumped matter discipline, I said I was able to simplify", - "my life tremendously. And, in particular what it did", - "was it allowed me to take Maxwell's equations,", - "OK, and simplify them into a very simple algebraic form,", - "which has both a voltage law and a current law that I call", - "Kirchhoff's voltage law, and Kirchhoff's current law.", - "KVL simply states that if I have some circuit,", - "and if I measured the voltages in any loop in the circuit,", - "so if I look at the voltages in any loop, then the voltages in", - "the loop would sum to zero. OK, so I measure voltages in", - "the loop, and they will sum to zero.", - "Similarly, for the current, if I take a node of a circuit,", - "if I build the circuit, a node is a point in the", - "circuit where multiple edges connect.", - "If I take a node, then the current coming into", - "that node, the net current coming into a node is going to", - "be zero. OK, so if I take any node of", - "the circuit and sum up all the currents going into that node,", - "they will all net sum to zero. So, notice what I've done is by", - "this discipline, by this constraint I imposed on", - "myself, I was able to make this incredible leap from Maxwell's", - "equations to these really, really simple algebraic", - "equations, KVL and KCL. And I promise you,", - "going forward to the rest of 6.002, if this is all you know,", - "you can pretty much solve any circuit using these two very", - "simple relations. It's actually really,", - "really simple. It's all very simple algebra,", - "OK? So, just to show you an", - "example, let me do a little demonstration.", - "Let me build let me build a small circuit and measure some", - "voltages for you, and show you that the voltages,", - "indeed, add up to zero. So, here's my little circuit.", - "So, I'm going to show you a simple circuit that looks like", - "this, and let's go ahead and measure some voltages and", - "currents. In terms of terminology to", - "remember, this is called a loop. So if I start from the point C", - "and I travel through the voltage source, come to the node A down", - "through R1 and all the way down through R2 back to C,", - "that's a loop. Similarly, this point A is a", - "node where resistor R1 the voltage source V0,", - "and R4 are connected. OK, just make sure your", - "terminology is correct. So, what I'll do is I'll make", - "some quick measurements for you, and show you that these KVL and", - "KCL are indeed true. So, the circuits up there,", - "could I have a volunteer? Any volunteer?", - "All you have to do is write things on the board.", - "Come on over. OK, so let me take some", - "measurements, and why don't you write down", - "what I measure on the board? What I'll do is,", - "let me borrow another piece of chalk here.", - "What I'll do is focus on this loop here, and focus on this", - "node and make some measurements.", - "All right, so you see the circuit up there.", - "OK, so I get 3 volts for the voltage from C to A.", - "so why don't you write down 3 volts?", - "OK, so the next one is -1.6. And so that will be,", - "I'm doing AB, V_AB.", - "OK, and then let me do the last one.", - "It is -1.37. The measurements,", - "I guess, have been this way. So, what's written is V_AC.", - "But it's OK for now. Don't worry about it.", - "So, well, thank you. I appreciate your help here.", - "OK, so within the bonds of experimental error,", - "noticed that if I add up these three voltages,", - "they nicely sum up to zero. OK, next let me focus on this", - "node here. And at this node,", - "let me go ahead and measure some currents.", - "What I'll do now is change to an AC voltage so that I can go", - "ahead and measure the current without breaking my circuit.", - "OK, this time around, you'll get to see the", - "measurements that I'm taking as well.", - "So, what I have here, I guess you can see it this", - "way. What I have here is three wires", - "that I have pulled out from D. And this is the node D,", - "OK? So, I have three wires coming", - "into the node D just to make it a little bit easier for me to", - "measure stuff. OK, so everybody keep your", - "fingers crossed so I don't look like a fool here.", - "I hope this works out. So, you roughly get,", - "what's that, 10 mV.", - "OK, so it's about 10 mV peak to peak out there,", - "and let's say that if the waveform raises on the left-hand", - "side, it's positive. So, it's positive 10 mV.", - "And another positive 10 mV, so that's 20 mV.", - "And this time, it's a negative,", - "roughly 20, I guess, -20.", - "So, I'm getting, in terms of currents,", - "I have a -10, -10, I'm sorry,", - "positive 10, positive 10,", - "and a -20 that adds up to zero. But more interestingly,", - "I can show you the same thing by holding this current", - "measuring probe directly across the node.", - "And, notice that the net current that is entering into", - "this node here is zero. OK, so that should just show", - "you that KCL does indeed hold in practice, and it is not just a", - "figment of our imaginations. So, before I go on,", - "I wanted to point one other thing out.", - "Notice that I've written down two assumptions of the lumped", - "matter discipline, OK?", - "There is a total assumption of the lump matter discipline,", - "and that assumption is, in spirit, at least,", - "shared by the point mass simplification in physics as", - "well. Can someone tell me what that", - "assumption is? A total assumption,", - "which I did not mention, which you can read in your", - "notes in section 8.2 in the appendix, what's a total", - "assumption that is shared in spirit with the point mass", - "simplification? Anybody?", - "A total assumption to be made here is that in all the signals", - "that we will study in this course, we've made the", - "assumption that the signal speeds of interest,", - "transition speeds, and so on, are much slower than", - "the speed of light. OK, that my signal transition", - "speeds of interest are much slower than the speed of light.", - "Remember, the laws of motion, the discrete laws of motion", - "break down if your objects begin moving at the speed of light.", - "OK, the same token here, our lump circuit abstraction", - "breaks down if we approach the speed of light.", - "And there are follow on courses that talk about waveguides and", - "other distributed analysis techniques that deal with", - "signals that travel close to speeds of light.", - "OK, so with that, let me go on to talking about", - "method one of circuit analysis. This is called the basic KVL", - "KCL method. So just based on those two", - "simple algebraic relations, I can analyze very interesting", - "and complicated circuits. The method goes as follows.", - "So, let's say our goal is, given a circuit like this,", - "our goal is to solve it. OK, in this course,", - "we will do two kinds of things: analysis and synthesis.", - "Analysis says, given a circuit,", - "OK, what can you tell me about the circuit?", - "OK, so we'll solve existing circuits for all the voltages", - "and currents, voltages across elements,", - "and currents through those elements.", - "Synthesis says, given a function,", - "I may ask you to go and build circuits.", - "OK, so for analysis here, we can apply this method that I", - "want to show you. And the idea here is that,", - "given a circuit like this, let us figure out all the", - "voltages and currents that are a function of the way these", - "elements are connected. So, the basic KVL and KCL", - "method has the following steps. The first step is to write down", - "the element VI relationships. OK, right down the element VI", - "relationships for all the elements.", - "The second step is write KCL for all the nodes,", - "and the third step is to write KVL for all the loops in the", - "circuit. That's it.", - "Just go ahead and write down element rules,", - "KVL, and KCL, and then go ahead and solve the", - "circuit. So, what we'll do,", - "we'll do an example, of course.", - "But, just as a refresher, we've looked at a bunch of", - "elements so far, and for the resistor,", - "the element relation says that V is pi R, where R is the", - "resistance of the element here. For a voltage source,", - "V is equal to V nought. That's the element", - "relationship. And for a current source,", - "the element is the relation is, \"i\" is simply the current", - "flowing through the element. OK, so these are some of the", - "simple element rules for the devices that the current source,", - "voltage source, and the resistor.", - "So let's go ahead and solve this simple circuit.", - "And what I'll do is go ahead and solve the circuit for you.", - "OK, if you turn to page five of your notes, I'm going to go", - "ahead and edit the circuit here. You can scribble the values on", - "your notes on page five. OK, so as a first step of my", - "KVL KCL method, I need to write down all my", - "element VI relationships. So, before I do that,", - "let me go ahead and label all the voltages and currents that", - "are unknowns in the circuit. So, let me label the voltages", - "and currents associated with the voltage source as here.", - "Notice, I continue to follow this convention where whenever I", - "label voltages and currents for an element, I will show the", - "current going into the positive terminal of the element", - "variable, OK, after element variable voltage.", - "So here, I have V nought and I nought.", - "Let me pause here for five seconds and show you a point of", - "confusion that happens sometimes.", - "Often times, people confuse between what is", - "called the variable that is associated with the element", - "versus the element value. OK, notice that here,", - "capital V nought is the voltage that this voltage source", - "provides, while this name here, v nought, is simply a variable", - "that we've used to label the voltage across that element.", - "So, similarly, I can label v1 as the voltage", - "across the resistor, and i1 is the current flowing", - "through the resistor. So this method of labeling,", - "where I follow the convention, that the current flows into the", - "positive terminal is called the associated variables discipline.", - "I was trying to use the word discipline in situations where", - "you have a choice, OK, and of a variety of", - "possible choices, you pick one as the convention.", - "OK, so here, as a convention,", - "we use the associated variables discipline, and use that method", - "to consistently label the unknown voltages and currents in", - "our circuits. OK, so let me continue the", - "labeling here, v4, i4, i3, v3 here,", - "and v2 and i2, v5, and i5.", - "I think that's it. So, I've gone ahead and labeled", - "all my unknowns. So each of these voltages and", - "currents are the voltages and currents associated with each of", - "the elements. And my goal is to solve for", - "these. OK, so in terms of our solution", - "here, let's follow the method that I outlined for you.", - "So, as the first step I am simply going to go ahead and", - "write down all the element VI relationships.", - "OK, so as a first step, I'm going to go ahead and write", - "down all the VI relationships. So, can someone yell out for me", - "the VI relationship for the voltage source?", - "OK, good. So, v0 is capital V nought,", - "that is that the variable V nought is simply equal to the", - "voltage, v0. Similarly, I can write the", - "others. v1 is i1, R1.", - "v2 is i2, R2, and so on.", - "OK, and I have one, two, three, four,", - "five, six elements. So, I will get six such", - "equations. Step two, I'm going to go ahead", - "and write KCL for the nodes in my system.", - "So, let me start with node A. So, for node A,", - "let me take as positive the currents going out of the node.", - "So, I get i nought flowing out, plus i1 flowing out,", - "plus i4 flowing out, and they must sum to zero for", - "node A. Then, I can go ahead and do the", - "other nodes, let's say, for example,", - "I do node B. For node B, I have i2 going", - "out. That's positive,", - "i3, and i1 is coming in, so I get -i1 equals zero.", - "OK, so I have one, two, three, four,", - "I have four nodes. OK, so I would get four", - "equations. It turns out that the fourth", - "equation is not independent. You can derive it from the", - "others. So, I get three independent", - "equations out of this. I can then write KVL.", - "And for KVL, I just go down my loops here.", - "And let me go through this first loop here in this manner.", - "OK, and a simple trick that I use, you have to be incredibly", - "careful when you go through this in keeping your minuses and", - "pluses correct. Otherwise you can get", - "hopelessly muddled. Once you label it,", - "you need to be sure that you get all your minuses and pluses", - "correct. So, for KVL,", - "what I'd like to do is, let's say I start at C,", - "and from C I'm going to go to A.", - "For A I go to B, and from B I'm going to come", - "back to C. OK, that's how I traverse my", - "loop. And, the trick that I'm going", - "to follow is, as my finger walks through that", - "loop, I'm going to label the voltage as the first sign that I", - "see for that voltage. OK, so I'm going to start with", - "C, and I go up. I start by punching into the", - "voltage source element, and then punch into it,", - "I hit the minus sign for the V nought.", - "OK, so I'm just going to write down minus V nought,", - "plus then I go through and as I come up to A and go down to B,", - "I punch to the plus sign of the V1.", - "So, that's plus V1. And then I punch into the plus", - "sign of the V2, and so I get plus V2,", - "and that is zero. OK, good.", - "So, that matches what you have in your notes as well.", - "So, this is the first equation. Similarly, I can go through my", - "other loops and write down equations for each of the loops.", - "OK, and the convention that I like to follow is as I go", - "through the loop, I write down as a sign for the", - "voltage the first sign that I counter for that element.", - "OK, you can do the exact opposite, if you want,", - "just to be different. But, as long as you stay", - "consistent, you'll be OK. All right, so in the same", - "manner here, there are four loops that I can have,", - "so four equations. Again, one of them turns out to", - "be dependent on the others. So I end up getting three", - "independent equations. So, I get a total of 12", - "equations. I get 12 equations.", - "There are six elements, OK, voltage source,", - "and five resistors. So, there are six unknown", - "voltages, and six unknown currents.", - "So, I have 12 equations, and 12 unknowns.", - "OK, I can take all of the equations and put them through a", - "big crank, and sit there and grind.", - "And if I was really cruel, I'd give this as a homework", - "problem, and have you grind, and grind, and grind until you", - "get your six voltages and six currents.", - "OK, it works. OK, so you get 12 equations,", - "and this method just works. However, notice that this is", - "quite a grubby method. It's quite grungy.", - "I get 12 equations, and it's quite a pain even for", - "a simple circuit like this. However, suffice it to say that", - "this fundamental method is one step away from Maxwell's", - "equations, simply works. OK?", - "So what you'll do is the rest of this lecture,", - "I'll introduce you to a couple more methods.", - "One is an intuitive method, and another one called the node", - "method is a little bit more formal, but is much more,", - "I guess, terse Than the KVL KCL method.", - "Method 2. So the relevant section to read", - "in the course notes is section 2.4.", - "One of the things that I will be stressing this semester is", - "intuition. What you'll find is that as you", - "become EECS majors, and so on, and go on,", - "or if you talk to your TAs or your professors and so on,", - "you will find that very rarely do they actually go ahead and", - "apply the formal methods of analysis.", - "OK, by and large, engineers are able to look at a", - "circuit and simply by observation write down an", - "answer. And usually in the past,", - "what we have tried to do is kind of ignore that process and", - "told our students, look, we teach you all the", - "formal methods, and you will develop your own", - "intuition and be able to do it. What we'll try to do this term", - "is try to stress the intuitive methods, and try to show you how", - "the intuitive process goes, so you can very quickly solve", - "many of these circuits simply by inspection.", - "OK, so this method that I'm going to show you here is one", - "such an intuitive method. And I'll call it element", - "combination tools. OK, for many simple circuits,", - "you can solve them very quickly by applying this method.", - "The components of this method are these.", - "I learned about how to compose a bunch of elements.", - "So, let's say, for example,", - "I have a set of resistors, R1 through RN,", - "in series. OK, you can use KVL and KCL to", - "show that this is equivalent to a single resistor whose value is", - "given by the sum of the resistances.", - "OK, so if I have resistors in series, then effectively it's", - "the same as if there was a single resistor whose value is", - "the sum of all the resistances. OK, you can look at the course", - "notes for a proof for derivation of this fact.", - "Similarly, if I have resistances in parallel,", - "so let me call them conductances.", - "A conductance is the reciprocal of a resistance.", - "If resistance is measured in ohms, conductance is measured in", - "mhos, M-H-O-S. OK, so that's the conductance", - "is G1, G2, and G3. And effectively,", - "this is the same as having a single conductance whose", - "effective value is given by the sum of the conductances.", - "OK, the conductances in parallel add,", - "and resistances in series add. Similarly, for voltage sources,", - "if I have voltage sources in series, then they are tantamount", - "to the sum of the voltages. And similarly,", - "for currents, if I have currents in parallel,", - "then they can be viewed as a single current source,", - "whose currents are the sum of the individual parallel", - "currents. So, let's do a quick example.", - "So let's do this example. So, let's say I have a circuit", - "that looks like this, and three resistances.", - "And let's say all I care about is the current,", - "I, that flows through this wire.", - "All I care about is that current.", - "Of course, you can go ahead and write KVL and KCL.", - "You will get four equations, and there are four unknowns.", - "And you can solve it. But, I can apply my element", - "combination rules, and very quickly figure out", - "what the current I is, using the following technique.", - "So, what I can do is, I can, first of all,", - "take this circuit. And, I can compose these two", - "resistances and show that the circuit is equivalent as far as", - "this current, I, is concerned to the", - "following circuit, R1.", - "And I take the sum of the two conductances,", - "OK, and that comes out to be R1, R2, R3, R2 plus R3.", - "And then, I can further simplify it, and I get a single", - "resistance, whose value is given by R1 plus R2,", - "R3, R3. OK, I'm just simplifying the", - "circuit. Now, from this circuit,", - "I can get the answer that I need.", - "I is simply the voltage, V, divided by R1 plus.", - "OK, so in situations like this where I'm looking for a single", - "current, I can very quickly get to the answer by applying some", - "of these element combination rules.", - "And, I can get rid of having to go through formal steps.", - "So, in general, whenever you encounter a", - "circuit, by and large attempt to use intuitive methods to solve", - "it. And go to a formal method only", - "if some intuitive method fails. Even in your homework,", - "by and large, the homeworks are not meant to", - "be grungy. OK, if you find a lot of grunge", - "in your homework, just remember you're probably", - "not using some intuitive method. OK, so just be cautious.", - "All right, so let me go on to the third method of circuit", - "analysis, and the third method is called the node method.", - "So, the node method is simply a specific application of the KVL", - "KCL method and results in a much, much more compact form of", - "the final equations. If there's one method that you", - "have to remember for life, then I would say just remember", - "this method. OK, the node method is a", - "workhorse of the easiest industry.", - "OK, if there's one method that you want to consistently apply,", - "then this is the one to remember.", - "So, let me quickly outline for you to method,", - "and then work out an example for you.", - "The first step of the node method will be to select a", - "reference or a ground node. This is the symbol for a ground", - "node. The ground node simply says", - "that I'm going to denote voltages at that point to be", - "zero, and measure all my other voltages with reference to that", - "point. So, I'm going to select a", - "ground node in my circuit. Second, I want to label the", - "remaining voltages with respect to the ground node.", - "So, label voltages for all the other nodes with respect to the", - "ground node. Next, write KCL for each of the", - "nodes write KCL. OK, but don't write KCL for the", - "ground node. Remember, if you have N nodes,", - "the node equations will give you N-1 independent equations.", - "So, write KCL for the nodes, but don't do so for the ground", - "node. Then, solve for the node", - "voltages. So, let's say when we label", - "voltages. I want to be labeling them as E", - "something or the other. So, solve for the unknown node", - "voltages. And then, once I know all the", - "voltages associated with the nodes, I can then back solve for", - "all the branch voltages and currents.", - "OK, once I know all the node voltages, I can then go ahead", - "and figure out all the branch voltages and the branch", - "currents. So, let's go ahead and apply", - "this method, and work out an example.", - "Again, remember, if there's one method that you", - "should remember, it's the node method.", - "OK, and when in doubt, consistently apply the node", - "method and it will work whether your circuit is linear or", - "nonlinear, if the resistors are built in the US or the USSR it", - "doesn't matter. OK, the node method will simply", - "work, linear or nonlinear, OK?", - "So, what I'm going to do is I'm going to build a circuit that's", - "my old faithful. It's our old faithful,", - "plus I'll make it a little bit more complicated by adding in", - "the current source. So, let's go have some fun.", - "Let's do this. So here's my voltage source,", - "as before. OK, what I'll do is for fun,", - "add a current source out there. And, you can convince", - "yourselves that if you go ahead and apply the KVL KCL method,", - "it'll really be a mess of equations.", - "OK, so R1, R3, R4, R2, R5.", - "OK, so let's follow our method and just plug and chug here.", - "So let's apply the first step. I select a ground node.", - "It's a reference node from which I'll measure all my other", - "voltages. OK, now without knowing", - "anything about the node method, try to use intuition as to", - "which node you should choose as a ground node.", - "Remember, you want to label the ground node with the voltage", - "zero, and measure all the other voltages with respect to that", - "node. OK, a usual trick is to pick a", - "node which has the largest number of elements connected to", - "it as the ground node. OK, and in particular,", - "you will find out later it's useful to pick a node in which", - "all your voltage sources, the maximum number of your", - "voltage sources are also connected.", - "OK, so in this instance, I'm going to choose this as my", - "ground node. OK, that's my first step.", - "I chose that as my ground node. And I'm going to label that as", - "having a voltage zero. Second step,", - "I'll label voltages of the other branches with respect to", - "the ground node. OK, so what I'll do is add this", - "node here. So I'm going to label that", - "voltage E1. These are my unknowns.", - "Remember, node method, because my node voltages are my", - "unknowns. So, I label this as E1.", - "I label this one as my unknown voltage, E2.", - "What about this one here? Is that voltage unknown?", - "No. I know what the voltage is", - "because I know that this node is at a voltage,", - "V0, higher than the ground node.", - "OK, notice that to go from here to here, I directly go through a", - "voltage source. And so, this node has voltage", - "V0. And I'll simply write down V0.", - "OK, try to simplify the number of steps that you have to go", - "through, so directly go ahead and write down the voltage,", - "V0, for that node. What I will also do,", - "is for convenience, I'm going to write down,", - "I'm going to use conductances. So I'm going to use GI in the", - "place of one by RI, and write down a bunch of node", - "equations. OK, so step one,", - "I've chosen my ground node. Step two, I've labeled my node", - "voltages, E, OK? I've done that with two of my", - "steps. Now, let me go ahead and --", - "OK, so let me go ahead and apply step three.", - "And, step three says go ahead and apply KCL for each of the", - "nodes at which you have an unknown node voltage.", - "And then that will give you your equations.", - "So let me start by applying KCL at E1.", - "So, let me write KCL at E1. I do one more thing.", - "Notice, I don't have any currents there.", - "OK, so how do I write KCL? KCL simply says the sum of", - "currents into a node is zero again, remember,", - "by the lump matter discipline. So, if I don't have currents in", - "there, so the trick that I adopt is that to write KCL,", - "I use the node voltages, and implicitly substitute for", - "the node voltages, divide by the elemental the", - "resistance, for instance, so I take the node voltages,", - "and divide by the resistance, get the current.", - "OK, so I implicitly apply element relationships to get the", - "node currents. So, the example that make it", - "clear, so I take node E1 and, again, for currents going out", - "I'm going to assume to have, to be positive.", - "So, the current going up is E1 minus V nought,", - "divide by R1, so I multiplied by the G1.", - "That's the current going up. Plus, the current going down is", - "E1 minus zero where the ground node potential is zero,", - "G2, OK, plus the current that is going to resistor R3,", - "which is simply E1 minus E2, divide by R3.", - "So, E1 minus E2, divide by R3,", - "or multiplied by G3 is equal to zero.", - "OK, see how I got this? This is simply KCL,", - "but to get my currents, I simply take the differences", - "of voltages across elements, and divide by the element of", - "resistance, and I get the currents.", - "OK, so I can similarly write KCL at E2.", - "So, at KCL at E2, again, let me go outwards.", - "So, the current going up is E2 minus V nought multiplied by G4.", - "The current going left is E2 minus E1 divided by R3 or", - "multiplied by G3. The current going down is E2", - "minus zero multiplied by G5. And, the current going down is", - "-I1. OK, you've got to be careful", - "with your polarities here. So all the currents going out", - "sum to zero. And here are the currents that", - "are going out at this point. So what I do next is I can move", - "the constant terms to the left-hand side and collect my", - "unknowns. So, let me write them out here.", - "So, let's say I get E1 here, OK, and from this equation,", - "I have a V nought, G1, which comes out here.", - "So, minus V nought G1 comes over to the other side.", - "And, let me collect all the values that multiply E1.", - "So I get, G1 is one example. I have G2, and I have G3.", - "And then, for E2, I have minus G3.", - "OK, so I'll simply express this as the element voltages", - "multiplied by some terms in parentheses, and I put my", - "external sources on the right hand side.", - "Similarly, I go ahead and do the same thing here.", - "In this instance, let me move my sources to the", - "right. So, I get I1 coming out there,", - "and I get V nought G4 coming out there.", - "By the way, I just want to mention to you that if you're", - "looking to fall asleep, this is a good time to do so", - "because as soon as I write down these two equations,", - "OK, from now on it's nap time. There's nothing new that you're", - "going to learn from here on. It's just Anant Agarwal having", - "fun at the blackboard, pushing symbols around.", - "So, once you write down these two node equations,", - "the rest of it is just grubby math.", - "So, let me just have some fun. So let me just go ahead and do", - "that. So, I moved my voltages and", - "currents to the other side. And let me collect all the", - "coefficients for E1 here. So, E1 minus G3,", - "and that's it, I guess.", - "OK, and then I'll do the same for E2.", - "So, I get G4, and I get G3,", - "and I get G5. OK, so notice here that I have", - "two equations, and two unknowns.", - "OK, the two equations are on the right hand side,", - "I have some voltages and currents which are my dry", - "voltages and dry currents. OK, so actually this is getting", - "quite boring. I'm going to pause here,", - "and talk about something else. So, you can take this and you", - "can put it in matrix form, so I've done that for you on", - "page ten. It's all matrix form.", - "Yeah, I know that. You can use any technique to", - "solve it, use algebraic techniques, use linear algebraic", - "methods to solve it, use a computer,", - "whatever you want. And, computers,", - "when computers analyze circuits, they write down these", - "equations, and deal with solving matrices.", - "So, when you take the linear algebra across,", - "how many people here have taken a linear algebra class?", - "How many people here have heard of Gaussian elimination?", - "How can more people have heard of Gaussian elimination than", - "took a linear algebra class? Well anyway,", - "so now you know why you took those linear algebra classes.", - "And so, if I just collected these into matrix form --", - "OK, so I just simply expressed those two equations in linear", - "algebraic form, and here's my column vector of", - "unknowns, and you can apply any of the techniques you've learned", - "in linear algebra to solve for this.", - "Gaussian elimination works. OK, and in computer,", - "people doing research in computer techniques,", - "or solving such equations simply deals with huge equations", - "like this, building computer programs that,", - "given equations like this, can go ahead and solve them.", - "OK, so let me stop here and reemphasize that what you've", - "done is made a huge leap from Maxwell's equations to using the", - "lump matter discipline to KVL and KCL, which ended up giving a", - "simple algebraic equation to solve, and not having to worry", - "about partial differential equations that were the form of", - "Maxwell's equations." - ] -} \ No newline at end of file diff --git a/subs/2xJIfHLFdHA.srt.sjson b/subs/2xJIfHLFdHA.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/2xJIfHLFdHA.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/38euKuG1cUs.srt.sjson b/subs/38euKuG1cUs.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/38euKuG1cUs.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - 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Good morning.", - "Let's get going. As always, I will start with a", - "review. And today we embark on another", - "major milestone in our analysis of lumped circuits.", - "And it is called the \"Sinusoidal Steady-state\".", - "Again, I believe this will be the second and the last lecture", - "for which I will be using view graphs.", - "And the idea here is that, just like in the last lecture,", - "there is a bunch of mathematical grunge that needs", - "to be gone through. And I want to show you a", - "sequence in a little chart today that talks about the effort", - "level in doing some problems based on time domain", - "differential equations, as in the last lecture,", - "something slightly different today and something much better", - "on Thursday. And so, in some sense,", - "Thursday's lecture and today's lecture involve talking about", - "the foundations of the behavior of certain types of circuits.", - "And it is good for you to have this foundation as background,", - "but when you actually go to solve circuits you don't quite", - "use these methods. You use much easier techniques,", - "which I will talk about next Thursday.", - "Let's start with a quick review, and then we will go into", - "sinusoidal steady state. The last lecture we talked", - "about this circuit and we did the same two lectures ago on", - "Tuesday. We had one inverter driving", - "another inverter. And we said that the wire over", - "ground had some inductance. CGS is the capacitor of the", - "gate and R is the resistance at the drain of the first inverter.", - "And if you look at this circuit, that circuit formed an", - "RLC pattern. And what we did was we said", - "let's drive this with a one to zero transition at the input.", - "And the one to zero transition at the input would cause this", - "transistor to switch off, and this node would then go", - "from a very low value to a high value.", - "So it as if a 5 volt step was applied at this input.", - "We also saw that using time domain differential equations", - "that by applying a step input here the output looked like", - "this. The output would show some", - "oscillatory behavior when we have a capacitor and inductor.", - "I also gave you some insight as to why it oscillates like this.", - "And you also heard in recitation that the reason for", - "this oscillation was because of these two storage elements.", - "Each of these storage elements tries to hold onto its state", - "variable. For example,", - "the capacitor tries to maintain its voltage while the inductor", - "tries to maintain its current. And, much like a pendulum which", - "oscillates back and forth, it swaps potential energy", - "versus kinetic energy down here and swings back and forth.", - "In the same way, in an LC circuit like this,", - "energy swaps back and forth between a potential energy and a", - "kinetic energy equivalent, which swaps back and forth", - "between energy stored in the inductor and energy stored in", - "the capacitor and sloshes back and forth.", - "And because of this resistor the energy eventually dissipates", - "and you end up getting a final value which corresponds to the 5", - "volts appearing here. And why is that?", - "That is because remember the capacitor is a long-term open", - "for DC. It is a DC voltage.", - "After a long time this capacitor looks like an open", - "circuit and the inductor looks like a complete short circuit,", - "an ideal inductor as a complete short circuit for DC.", - "And so therefore in the long-term it is as if this guy", - "is a short, this guy is an open, so 5 volts simply appears here.", - "And this is the transient behavior.", - "Then we just switch the first transistor off.", - "In the last lecture, I left off with intuitive", - "analysis. Let me quickly cover that and", - "redo the intuitive analysis for you.", - "I left it the last time by having you think about whether", - "the transient response would begin by going down or begin by", - "going up. And I will cover that today.", - "This was the circuit that we analyzed.", - "A VI input with a step and an RLC out here.", - "And we were plotting the capacitor voltage.", - "And intuitively we can plot this in the following way.", - "I have also marked for you the section number in the course", - "notes which has a discussion of this intuitive analysis,", - "(Section 13.8). Let's do the easy stuff first.", - "Notice that the capacitor wants to hold its voltage.", - "And so given that we don't have any infinite impulse here,", - "I am going to start out with the capacitor voltage being", - "where it is. And the initial conditions are", - "given to you. You are given that the", - "capacitor voltage starts out being positive at v zero and the", - "current starts out being negative at time zero.", - "So I am telling you that there is a voltage v across the", - "capacitor at time t=0 and there is a current that is flowing.", - "Since i is negative there is a current initially that is", - "flowing in the opposite direction to this arrow here.", - "The i zero is negative. In light of that,", - "I can start plotting my curve here by intuition.", - "I start by saying at time t=0 I am told that the initial voltage", - "of the capacitor is at zero. This is about as simple as it", - "gets. Completely intuitive.", - "I also know that after a long time, can someone tell me after", - "a long time what the voltage will be at the end of the", - "capacitor? You should be able to get his", - "by observation? VI.", - "And why is it VI? It is vI because this is a DC", - "value VI. And after a long time this guy", - "behaves like an open circuit to DC.", - "This guy behaves like a short circuit to DC.", - "So since this is an open circuit, VI will appear here", - "after a long time. And so therefore,", - "after a long time, the capacitor voltage is going", - "to be at VI. And I just showed you that.", - "There you go. You already have the two", - "endpoints of your curve completely by observation,", - "intuition. No DEs, no nothing.", - "Just by staring at it and understanding the fundamentals", - "of how simple primitive circuit elements work.", - "Absolutely simple stuff. So you've nailed the two ends", - "now and you cannot go wrong with the stuff in the middle.", - "Let's see. As a next step what I do is I", - "need to understand what the dynamics of the circuit looks", - "like here. What I do is I develop the", - "characteristic equation. And initially you will write", - "the differential equation and then substitute e^st and get", - "this characteristic equation. But you could also remember it", - "as a pattern. For a series RLC circuit you", - "always get an equation of this form, always.", - "If this were R, L and C.", - "And whether you are looking at L up here or C up here,", - "as long as you're looking at the capacitor voltage,", - "the capacitor voltage is going to behave the same.", - "And for this circuit the characteristic equation remains", - "the same as well for a series RLC.", - "It is exactly this. And I write the standard", - "canonic form as s squared plus two alpha s + omega nought", - "squared. And omega nought is simply one", - "by square root of LC and alpha is simply R divided by L and I", - "have two in the denominator as well.", - "And then I get omega d which is my damped frequency given by", - "omega nought squared minus alpha squared.", - "And Q is simply called the quality factor.", - "And we will learn about Q in a lot more detail in about a", - "couple of lectures from today. That is given where omega", - "nought divided by two alpha. These parameters,", - "alpha, omega nought, Q and omega d pretty much", - "characterize everything else that I need to know about the", - "circuit. First of all,", - "omega d is the frequency of oscillation.", - "And so since omega d is a frequency of oscillation then I", - "know that the time period of oscillation is two pi by omega", - "d. Omega is in radians.", - "Notice that for typical values of circuits like this when R is", - "pretty small, alpha squared is going to be", - "very small. It's a common case for", - "underdamped circuit that omega d will more or less be equal to", - "omega nought. Commonly that is going to be", - "the case. This frequency is governed by", - "LC. And if R is large it is", - "governed by this omega d here. So I have the frequency of", - "oscillation. I also know that Q is related", - "to the frequency of oscillation divided by alpha.", - "It is a ratio of the frequency divided by how badly I am being", - "damped. So it is a fight between the", - "frequency of oscillation and now heavily I damp.", - "And the ratio of that is an indication of how many cycles I", - "ring. So Q tells me that the ringing", - "stops approximately after Q cycles.", - "These four values, omega d, Q, alpha and omega", - "nought are telling me more and more now.", - "So I have got these two factors.", - "So I know now, based on omega d and Q,", - "that it is going to look something like this.", - "Some ringing here and then I stop at this point.", - "The last thing that is left to do here for me for now is to", - "figure out whether I start out going down or I start out going", - "up. I start out going down or I", - "start out going up? I don't know that yet.", - "And I stopped at this point in the last lecture and let you", - "think about how you can stare at the circuit and intuitively", - "figure out whether this goes down or that goes up.", - "So here is the insight. Let's stare at this for a", - "minute purely through intuition. The capacitor has a voltage v", - "across it, right? And that is because I am", - "telling you that it has an initial voltage v.", - "Now, I want to find out at prime t equals zero plus,", - "in which direction does a capacitor voltage go?", - "Increase or decrease? What do I do?", - "Let me take a look at the inductor current.", - "I am told that the inductor current is negative which means", - "I am told that the inductor current is going in this", - "direction initially. The inductor current is pushing", - "in this direction. Now, remember,", - "just as the capacitor is one stubborn nut trying to hold its", - "voltage, the inductor is as stubborn.", - "It is trying to hold its current.", - "It is trying to maintain its current.", - "And its initial current i(0) is in this direction.", - "Capacitor has a voltage here, that is v(0),", - "and the inductor is yanking the current in that direction.", - "So what should happen to the capacitor voltage initially?", - "If I am at v(0) and someone is yanking current out,", - "at least initially in that direction, what should the", - "initial dynamics of the capacitor voltage look like?", - "Pardon? It should drop,", - "which means that if the initial current is being pulled in that", - "direction the capacitor voltage must droop to begin with.", - "Completely through intuition. No math here.", - "This means that i(0) is negative.", - "It is as if i(0) is being pulled out in this manner,", - "so the capacitor voltage must drop to begin life.", - "Therefore, the dynamics look somewhat like this.", - "Notice that this is very reminiscent of the ringing that", - "we saw at the gate node of the second inverter.", - "Let's stop here in terms of time domain analysis of RLC,", - "and today let's take another big step forward.", - "Today marks another transition in life here.", - "This is actually a huge transition so I want to just", - "pause and take like ten seconds of a breather just to clearly", - "demarcate the fact that we have a huge transition coming up.", - "The key to this transition is that I want to look at today the", - "steady-state response of networks to a sinusoidal drive.", - "We are going to do two things differently starting today on", - "this new journey of ours. In the past,", - "we looked at time domain behavior of circuits.", - "For RLC, for example, we looked at the transient", - "response. And what happened the instant I", - "turn something on? The transient response.", - "Today we are going to look at a steady-state response.", - "Steady-state response says that if I wait long enough,", - "for whatever the circuit wants to do in the beginning of life", - "to die out. If I wait long enough,", - "how is the circuit going to behave after a long time?", - "I will tell you why that is important in a second.", - "I look at the steady-state behavior.", - "Second, I am going to look today at sinusoidal drive.", - "Two things that are different from, say for example,", - "what I covered in the past ten minutes.", - "In the past ten minutes I covered two things which were", - "different. One is that I looked at the", - "transient response and then steady-state.", - "And remember for a DC input, for a DC voltage the", - "steady-state was a DC voltage across the capacitor,", - "correct? So the steady-state was pretty", - "boring, it was steady-state DC. But what we are going to do", - "today is instead of having DC inputs or step inputs which", - "settle to a DC value after some time, we are going to drive a", - "circuit through the sinusoidal input.", - "So you may ask me, Agarwal, are you nuts?", - "Why do you want to drive something with a sinusoidal", - "input? Why not just steps in DC and so", - "on? That was painful enough.", - "Why sinusoidal? Why not do triangular or why", - "not do some other exponentially decaying stuff or something", - "really cool like a whacko music signal?", - "What is special about sinusoidal stuff?", - "The key thing to realize is that, well, let me ask you a", - "question first. How many people here know about", - "Fourier series? Good.", - "It looks like some of you have taken the prerequisites.", - "Good. Need I say more as to why this", - "is important? Just that question should give", - "you the answer, right?", - "You've learned about Fourier series.", - "And when you learned about Fourier series you were", - "wondering why on earth are we learning about Fourier series?", - "Who cares that you can represent the periodic signals", - "as a summation of a series of sine waves?", - "Why is that interesting? Why are you telling me that I", - "can take a square wave and represent that as a summation of", - "periodic square waves and represent that as a summation of", - "sines? Who cares that I can take a", - "sequence of pulses with a fixed period and represent that as a", - "sum of sines? Who cares that I can take a", - "triangular wave and represent that as a sum of sines?", - "I am not sure what answer your math professors gave you when", - "they taught you Fourier series. But in math they are purists.", - "They don't care about applications.", - "The answer could well have been because it is aesthetically", - "pleasing. I mean isn't it cool that you", - "can represent a sequence of pulses as a sum of sines?", - "That is good enough for mathematicians.", - "But I am an engineer. If it I cannot see how it helps", - "humanity in the short-term then I probably don't care too much", - "about it. Let me give you some practical", - "significance of this. So it turns out that,", - "since we know that we can represent periodic signals with", - "sums of sines. What this means is that if I", - "can figure out the behavior of networks to a sinusoidal input,", - "if I can understand how to analyze a network for a", - "sinusoidal input that means that if the circuit is linear I can", - "then compute the response of the circuit to any periodic", - "waveform. Here is the argument.", - "I can represent any periodic waveform as a sum of sines.", - "The Fourier series, remember?", - "If I just figure out the response of my network for a", - "sine wave, then if this is a linear network,", - "I can compute the response to any sequence of scaled sum of", - "sines. A some sine,", - "B sine two, omega whatever, C sine something or the other.", - "I can simply take the response of the one sine.", - "And from there I can go ahead, and knowing the response of a", - "sine wave I can compute the response to a sum of sines.", - "That is pretty cool. Therefore, doing it for", - "sinusoidal drives is really important.", - "Why steady-state now? Hopefully, I have convinced you", - "that looking at the response of circuits to sinusoidal drive is", - "important and interesting because we can long ways from", - "there. What about steady-state?", - "Well, it turns out that, and I am going to show you,", - "when you listen to music, you have an amplifier and", - "listen to music, what you are observing by and", - "large is the steady-state behavior of the amplifier.", - "You are listening to something over many seconds or many hours.", - "And the transients used for most of our common circuits,", - "the transients die out pretty quickly.", - "And so the transients are quite complicated and they die out", - "quickly. We say we are engineers.", - "Let's focus on what is practically important.", - "And we focus on the steady-state behavior as a large", - "part of our analysis and just completely ignore the transient", - "response when we care about the response to sinusoidal input.", - "The transient response will die away, and I will show that", - "mathematically to you in a few seconds.", - "And let's focus on the steady-state because that what I", - "am going to hear most of the time.", - "I am going to listen to an average over long periods of", - "time. That's the motivation behind", - "this. And let me put this in", - "perspective for you. By now this should bring", - "memories to your mind. This is the playground that we", - "are in. This is the lumped circuit", - "playground here. Remember we came from the", - "playground of nature to the playground of EECS where we made", - "the big leap from Maxwell's equations to lumped circuits,", - "that's lumped circuit abstraction.", - "And within there we spent a large part of the last couple of", - "months doing linear circuits. We also analyzed nonlinear", - "circuits. Remember the amplifier circuit", - "of the MOSFET large signal analysis was nonlinear?", - "Well, there is linear and nonlinear.", - "Within linear we also showed that if you take a digital", - "circuit, at least as we understood them,", - "and draw the subcircuit for a given set of switch settings,", - "if I set the switches in a given way what I was left with", - "was another linear circuit for a given value of all the switch", - "settings. My small signal analysis was", - "also linear. If I focused on small signals I", - "also had linear analysis. Today what we are going to do", - "is this. We are going to articulate a", - "different part of the playground.", - "This was a big linear playground.", - "We've done this. We've done this.", - "We are going to explore this territory.", - "This is that territory of the playground in which we have", - "sinusoidal inputs to circuits. Furthermore,", - "we are going to look at a subcircuit of that region which", - "is steady-state. We will look at sinusoidal", - "input and in the steady-state. So that is going to be our", - "focus for the next two or three lectures just to give you a", - "perspective of where we are. To motivate this,", - "what I would like to do is consider your amplifier.", - "This is our friend the amplifier circuit,", - "this part here. And remember,", - "even though this is an amplifier, I am using a MOSFET", - "here. And a MOSFET,", - "as you know, has this gate capacitance CGS.", - "I am explicitly drawing it out for you here.", - "And I am going to drive this with a bias voltage plus some", - "small signal vI, the usual template for", - "amplifiers. And there is some Thevenin", - "resistance attached to that source.", - "I am going to model my source as a bias voltage,", - "a small signal plus some source resistance.", - "And I want to apply a sine wave here and I am going to look at", - "what this looks like. You may think,", - "look, this is a linear amplifier.", - "And so if I apply a sine wave here I should see some response", - "here, and that should be the same amplitude if I feed the", - "same amplitude here over any frequency.", - "But let's see what happens. Keep a look at,", - "switch over to that view graph while I show you a little", - "demonstration here. What you see here are three", - "sine waves, a yellow sine wave which is the input here,", - "you see a green sine wave which is the input vC at the gate of", - "the MOSFET, and then you see the blue which is the output here.", - "For now simply focus on the yellow and the blue.", - "The yellow is the input and the blue is the output.", - "So I apply some input and I get an output that looks more or", - "less some linear function of this input here.", - "It is a small signal. What I am going to do is I am", - "going to change the frequency of the input.", - "Remember, I want to look at the response of the circuit to a", - "sinusoid. I am feeding a sinusoid here.", - "I look at the response. I am going to change the", - "frequency. That is a big shift that we are", - "making in that the curve that we drew in the last lecture had to", - "do with varying time. Now I am going to focus on", - "sinusoids and vary their frequency.", - "I am going to change the frequency.", - "Stare at the blue curve as I increase the frequency and just", - "think of what you might expect. Based on the knowledge you have", - "so far you would expect that look, as I change the frequency,", - "the frequency should change but I should see the same amplitude.", - "OK but take a look. Let me increase the frequency", - "of the input. What do you see at the output?", - "I am increasing the frequency.", - "What do you see happening there?", - "If you don't see anything changing there you will need to", - "see an optometrist. What do we see here?", - "As I changed the frequency, as I increased the frequency", - "what happened to the blue? The blue kept decreasing in", - "amplitude. And you are saying whoa,", - "what is happening here? We don't have the tools to deal", - "with this. I expected that when I changed", - "my frequency, my frequency here should change", - "of course, but why is the amplitude changing?", - "What is happening here? That is weird.", - "I noticed that this amplitude became smaller because the", - "amplitude of the green became smaller.", - "And remember the green was the voltage across the capacitor.", - "So this is your RC. And here is my input.", - "My input has the amplitude, which I am holding more or less", - "constant. And notice that vC decreased in", - "value as I increased my frequency.", - "Just hold that thought. As I increased the frequency of", - "my input the amplitude of the output kept diminishing.", - "In other words, the gain of the system seemed", - "to have decreased as I increased by frequency.", - "And today we will look at why that is so and how we can", - "analyze that. The other thing that is not so", - "obvious here is there is a phase shift.", - "What I am going to do is try to see if we can observe the phase", - "shift here.", - "Notice here. What we have been used to is", - "for the amplifier we get a complete inversion at the", - "output. Inversion means a phase", - "difference of 180 degrees for a sine wave, right?", - "This peak should have been here, but notice that there is a", - "shifting of the peak. In other words,", - "if the yellow was my input my output should have had its", - "minimum when the input had its maximum.", - "But notice there is a shifting of the signal such that the", - "output is a maximum, not quite at the point where", - "the input is a minimum but a little bit after that.", - "Also weird. Not only has this little", - "circuit here lost its gain somehow, but also it seems to", - "have shifted the signal in phase.", - "That is weird. And today we will look at why", - "that is so and try to understand the frequency behavior of this", - "little subcomponent here. Notice that vC is exactly 180", - "out of phase with vO. So vO is faithfully an inverted", - "amplified form of the input vC. However, vC itself should have", - "been the same as vI but it looks quite different.", - "So let's understand why that is so.", - "The subcircuit to model is the subcircuit comprising the", - "source, resistor and the capacitor.", - "And I am just showing that to you here.", - "I have a vI, a resistor and capacitor.", - "And I am going to understand how this behaves.", - "And it is a first order circuit, single capacitor.", - "My input is a vI cosine of omega t.", - "vI is a real number for t greater than zero.", - "And I am telling you that the capacitor voltage starts out", - "being zero. And my vI is a sinusoid.", - "It's not a step this time. It's a sinusoid.", - "So vI is a sinusoid and I want to find out what vC looks like.", - "The behavior here tells me, I will give you the answer,", - "that when I feed a sinusoidal input as the frequency", - "increases, vC should be decreasing somehow and also be", - "shifting in phase. Let's do the derivation for", - "that and see what happens. To give you some insight as to", - "how to go about analyzing this let me draw a little graph as to", - "the effort level of doing this. To determine vC of t on the", - "y-axis here is our effort. How hard do we have to work to", - "solve this circuit for a sinusoidal input?", - "And on this graph, down here is easy and up here", - "is pure agony. Sheer agony up here.", - "So it's the scale of effort level ranging from easy to", - "complete agony. And this is the time axis.", - "And the time axis starts out at 11 o'clock, the early part of", - "today's lecture, and ends at roughly 12,", - "that is today's lecture and this is next lecture.", - "What I am going to show you today is a method that uses a", - "usual differential equation approach, and this is going to", - "be pure agony. If you thought last Thursday", - "was agony watch today. This is going to be sheer,", - "sheer, sheer hell. So I am going to grunge through", - "that, and I think I will sort of give up halfway because it's", - "just too painful even for me here.", - "Then what I am going to do is at the end of this lecture I am", - "going to show you an approach that I give a cutesy name.", - "I call it the \"sneaky approach\".", - "We are going to sneak something in there it is going to be a lot", - "easier. And then in the next lecture I", - "am going to show you an even sneakier approach that is just", - "going to be absolute bliss. So let's start here.", - "Indulge me as I go through the agony part.", - "I am going to blast through it because that is not of how we", - "are going to do things, but you just need to know that", - "that is agony. Let's do a usual differential", - "equation approach. Steps one, two,", - "three and four. Set up differential equation,", - "find the particular solution, find the homogenous solution,", - "add up the two and solve for the unknowns.", - "It's a mantra. The four-step manta.", - "Let's do it. Step one, write the DE.", - "That's easy. We have done this before the RC", - "circuit. It's RC dvc/dt+vc=vI.", - "This is no different from what you got from what you got from", - "your RC circuit with a step input, just that my input is VI", - "cosine of omega t in this case. It is not just a DC voltage VI.", - "Stare at that. Enjoy it while the going is", - "easy. It's like traversing rapids,", - "and before you come to a class five, you have calm and raging", - "waters there, you kind of sit there saying", - "oh, the scenery around here looks really good and so on.", - "All you are doing is stalling before you have dive down to", - "class five. We will get to class five", - "rapids in a few seconds here, so just enjoy this.", - "RC dvc/dt+vC=vI. You've seen this before.", - "Nothing fancy. Good old stuff.", - "VI cosine of omega t. You want to hold onto your", - "seatbelts? OK.", - "Let's find the particular solution to the cosine input.", - "Let's use our standard method. What I will do is just so,", - "there is going to be so much crapola up there,", - "so that I draw your attention to vP, which is what we are", - "trying to get, I am just going to put a box", - "around vP in red. If you see like all sorts of", - "garbage appear, just look for the red square.", - "That is what we are trying to get at.", - "That's the equation. Let's try.", - "First try, A worked before. A constant value A worked", - "before for DC inputs. Let's try that again.", - "If it worked then it may work now.", - "If I use A, a constant value, and I substitute it here,", - "I get dA/dt goes to zero, vP is A, but on the right-hand", - "side I have VI cosine omega t. So clearly A doesn't work.", - "Sorry. I struck out.", - "Well, cosine omega t here, let's try A cosine omega T as", - "my particular solution. Things are getting a little", - "harder now, a little more painful.", - "So substitute A cosine omega t here.", - "So I do get A cosine omega T for vP, but out here I get RCA", - "sine omega t times omega times minus one.", - "So I have a sine and a cosine, and I have a cosine on the", - "right-hand side. Sorry, it doesn't work.", - "Nope, doesn't work either. Well, let's try A cosine omega", - "t plus phi. We are now embarking into the", - "rapids here. You can begin feeling the", - "pressure. Just to refresh your memories", - "of sines and cosines. A is the amplitude of the", - "cosine. Omega is the frequency.", - "Phi is the phase. Remember the signal I showed", - "you earlier? If something happens to the", - "amplitude of the sine, something happens to the phase.", - "A cosine omega t plus phi. Let me plug it in here and go", - "by standard practice. Here is what I get.", - "I plug in A cosine omega t to this equation,", - "and this is what I get. I differentiate it.", - "I get omega out minus sine, sine of negative d plus phi,", - "A cosine omega t plus phi equals VI cosine omega t.", - "That might work. Now we get into the class six", - "part of the class five. All class fives have a little", - "bit of class six rapids. Remember, the rapids go up on", - "an exponential scale so it like earthquakes.", - "What I do now is expand out sine omega t plus phi,", - "blah, blah, blah, it goes on and on.", - "I could go on and on, but this is even tiring me.", - "This can be made to work, but I am not sure I want to put", - "all of us through this trig nightmare here.", - "If I am really, really nasty I could give this", - "to you as a homework assignment or something,", - "but I am not that nasty so you won't see that.", - "But if I go down this path it will get me to the answer,", - "but I would have to soon negotiate class six,", - "class seven rapids to get to where I want.", - "So let me punt on it, let me start from scratch.", - "I am at step two, let me start from scratch.", - "Instead what I would like to do is let's get sneaky here.", - "Rather than negotiating the class five rapids,", - "what we can say is ah-ha, we can take our canoes and jump", - "onto shore and run down and then get back onto the river.", - "Let's do that. That is called the sneaky", - "approach. So that all our friends who are", - "behind us think we are negotiating the rapids,", - "but what we are going to do is get sneaky and take the shore", - "path. Let's get sneaky,", - "just walk down the shore and see what is there.", - "I want to do something completely weird here.", - "I want to look at solving this equation through the shore", - "method. S stands for shore or S stands", - "for sneaky, whatever you want. What I am going to do is rather", - "than trying to solve for VI cosine omega t.", - "I am going to say let's try a different input all together.", - "And you will understand why in a second.", - "It's like I am the captain of my canoe and I tell my", - "teammates, hey, let's not negotiate the rapids,", - "let's go and explore the shore. Maybe down the shore we can", - "find a path that gets us across to the other side more easily.", - "So here is me and my colleagues carrying our canoe and getting", - "onto shore and taking a sneaky path.", - "This is not what I set out to solve.", - "I don't know where this will lead me.", - "But let's see where the shore path leads us.", - "I want to try solving this equation Vie^st.", - "S stands for shore or sneaky or whatever you want.", - "I don't know where I am going, but let's see where this leads", - "us. Let's explore.", - "Make believe you are Columbus or something.", - "I don't know. Let's use the usual techniques", - "and see how this works out. Let's try a particular", - "solution, Vpe^st. My input is Vie^st.", - "I am trying to solve the circuit for a different input.", - "And let me try solution Vpe^st and see if that works out", - "nicely. I substitute Vpe^st into my", - "equation here, so RCVpe^st blah blah blah.", - "What I get here is Vie^st, Vpe^st stays the same,", - "but here vP comes out, s comes out and e^st stays the", - "same. That is nice property of", - "exponentials. This is what I get.", - "A really cool property of exponentials is that when I", - "differentiate it I get the exponential back.", - "Unlike a cosine I got a sine, and for a sine I got a cosine.", - "Exponentials are very plain and simple, are straightforward.", - "What you see is what you get. You differentiate it.", - "You get the same thing, you get scaling vP,", - "S and so on, and some scaling here.", - "You get S scaling here, but the basic form stays the", - "same. This is quite nice.", - "I have e^st in all three places, so I can cancel those", - "out and I get this expression. And I get this.", - "Wow. So if I go down the shore I get", - "some place fast. I don't know where I am yet,", - "but whatever I did, it was easy.", - "I am just exploring this path, down the shore path.", - "I am making progress. I don't know where I have", - "gotten yet. We will see where we got to in", - "a second, but I got some place quickly, fast.", - "I was able to solve for this input Vie^st and get this", - "solution very quickly. So what happened here?", - "I assumed the solution of the form Vpe^st, substituted it", - "back, and found that if vP were equal to Vi/(1+sRC) then Vpe^st", - "is a solution. What I have done here is that", - "Vi/(1+sRC) is a particular solution to this equation for", - "the input Vie^st. I put a box around it because", - "this is important. This was easy.", - "We went down the shore, and said let's try this other", - "input. We made rapid progress on shore", - "and I got some place. I don't know where I am yet.", - "I got this. Let me pause here and let me", - "give you the final answer. I am going to show you over the", - "next five minutes that this is our answer.", - "You are staring at the answer already.", - "I am a party, I have taken a shore path and", - "we have gotten some place. We see the river there,", - "so it turns out we are exactly where we want to be,", - "just after the rapids. All I have to do now is get my", - "colleagues into the river with myself in the canoe and we are", - "done. You don't know that yet.", - "My colleagues and I are sitting on the shore looking at the", - "river. We've gotten some place.", - "There are no rapids there. We have gotten some place.", - "We don't quite know is this just after the rapids or not.", - "We don't know yet, but I got there very quickly.", - "And I will tell you right now, that is the place we wanted to", - "go to. The next five view graphs I am", - "going to blast through. There is going to be more pain", - "and agony to show you why that is the case.", - "It's me thinking I am Columbus and proving to my colleagues", - "that this is where we want to be.", - "And pulling out my sextant, and the compasses and so on", - "that cartographers and people use to prove to my colleagues", - "that this is where I want to be. This is the answer.", - "The next five view graphs will be demonstrating that this is", - "indeed the answer, or close enough to the answer", - "that we will be satisfied. Isn't this spectacular?", - "I am going to show you in about five minutes that this gives us", - "all the information we need to know to compute the sinusoidal", - "steady-state response to this differential equation.", - "Let me write that down here just so you know.", - "Just so you remember. I am going to put a marker on", - "the shore that says this is where we are right now.", - "Now let me prove to you. As I just said,", - "vPS is Vi, it's this stuff here multiplied by e^st is the", - "solution to Vie^st. This guy here is a solution for", - "Vie^st and vP is simply the coefficient that multiplies", - "e^st. Similarly, if I substitute S", - "equals j omega. I told you five view graphs of", - "more hell, but I am just going to prove to you that this is it.", - "I am substituting S equals j omega.", - "This is Columbus giving a big speech at the end convincing his", - "colleagues that we are where we want to be.", - "I substitute j omega for S and this is what I get.", - "This is a solution for e to the st, and so this is a solution", - "for e to the j omega t. And let me mark this for you as", - "something to remember. Vi/(1+j omega RC).", - "In terms of that, I am substituting j omega for", - "S. And this is a complex number.", - "It is a complex amplitude. It is a complex number because", - "of j here, and it multiplies e to the j omega t.", - "Just keep this in mind. So that was easy.", - "The steps were easy. I am still proving to you that", - "this is where we want to be. Now let me draw the connection", - "back to vP. And the first fact was that", - "finding the response to Vie^(j omega t) was easy.", - "We know that. Second was the following", - "observation that Vi cosine omega t is simply the real part of", - "this number here. So Vi cosine omega t is simply", - "the real part of Vie^(j omega t) from the Euler relation.", - "So cosine omega t is simply the real part of this guy.", - "Light bulbs beginning to go off?", - "The first fast was that finding the response to Vie^(j omega t)", - "was easy. And the response was this,", - "right? Times e to the j omega t.", - "That was easy. All right.", - "And the second part is that the real part of this is Vi cosine", - "omega t was our input. Draw the connection between two", - "steps. Finding the response to Vie^(j", - "omega t) was easy. The real part of that was the", - "input we cared about. Are light bulbs going off?", - "Let me draw you a little picture here to show you what is", - "happening. Response to vI is vP.", - "It's the particular response we are looking for.", - "Remember the red square? But we threw in a sneaky input", - "vIS and we formed the response vPS to that.", - "This step was easy. This step was hard.", - "vI to vP was hard, trig nightmare,", - "remember? But vIS to vPS was easy.", - "It was a simple Vpe^st thing. We also know that the real part", - "of vIS is vI. The real part of this is simply", - "vI. If you have a real circuit,", - "if you have a real linear circuit, for a linear circuit,", - "if the real part of this gives me vI then the real part of the", - "solution should give me vP. So computing vPS was easy.", - "If I take the real part of this, I take the corresponding", - "real part of this. This is sort of an inverse", - "superposition argument. Superposition,", - "I said, take the response for A, take the response for B,", - "add them up and you get the response for A plus B.", - "Here what we are saying is that get the response to A plus B,", - "or to A plus jB and the real part of the input will produce", - "the response given by the real part of the output.", - "So this is an inverse superposition argument.", - "If it is a linear circuit, then if vI is the real part of", - "this sneaky input then I find the response to the sneaky input", - "and take its real part I should get vP.", - "Here I am, Columbus, staring down at the entrance to", - "this part of the river. I just proved to my colleagues", - "that all we have to do is take the real part of what we have.", - "We can just jump right back into the river and get back to", - "vP. And what I am going to do next", - "is just grind through the math and just show you that.", - "I will just blast through it. It is not important,", - "but you have it in your notes. I am telling you that vP is", - "simply the real part of the sneaky output.", - "And I take the real part of vP e to the j omega t.", - "And I take the real part. And just a bunch of math here.", - "I am just taking the real part and doing a bunch of complex", - "math. Remember vP was given by this", - "quantity here. And I take the real part and I", - "end up with vP is simply this quantity multiplied by cosine", - "omega t plus phi, where phi is given by is given", - "by tan inverse of omega RC, and this is the coefficient", - "multiplying the cosine. So by taking the sneaky path", - "and then taking the real part of that output answer,", - "I was able to very quickly get to where I wanted to be.", - "So from here to here it is only math.", - "Recall, that vP, the thing in the red was what", - "we set out to find out, which was the particular", - "response to VI cosine of omega t.", - "And remember that two grunge is all of this stuff.", - "I am going to blast through two or three more view graphs that", - "just give you more insight and more math, nothing particular.", - "And remember to solve the equation we have to find a", - "homogenous solution, too.", - "But recall that the homogenous solution for an RC circuit is of", - "the form Ae^-t/RC. This means that as time becomes", - "very large this part goes to zero.", - "As time becomes large in the steady state,", - "remember I care about the steady state?", - "This goes to zero. I don't care about the", - "homogenous solution. Isn't that fantastic?", - "Most the circuits we will deal with, except for purely", - "oscillatory ones, the homogenous part dies away.", - "You have something like e to the -t whatever.", - "It just dies away. It's gone.", - "So the total solution has vH going away.", - "And what I end up with is just vP.", - "My total solution in the steady state is simply vP.", - "And A is given by this that we just calculated.", - "I just have a bunch more insight that I talk about that", - "you can look through in your notes.", - "And I just want to show you a very quick summary.", - "In summary, what we have is we computed vP.", - "It was a complex coefficient. And all these steps,", - "2 grunge, 3 and 4 were a waste of time.", - "And what I showed you was that for the input VI the coefficient", - "vP was complex. And I can take the ratio and", - "represent it in this manner as well.", - "And from vP, I can then compute the", - "multiplier for the cosine as follows.", - "I divide by vP here. Remember the cosine was", - "multiplied by, in the mathematical step that I", - "did, VI divided one plus, this stuff here,", - "so I could get the magnitude and phase of the transfer", - "function of this circuit in the following manner.", - "And to wrap up very quickly, I am going to cover this again", - "the next time and show you a magnitude plot.", - "Notice here that if I plot Vp/Vi.", - "Remember this was Vp here. That's the answer.", - "The magnitude looks like this. On a log scale Vp/Vi for small", - "frequencies omega is at one, but as omega increases Vp/Vi", - "keeps decreasing. That is the output.", - "Remember Vp was the amplitude of the output?", - "That keeps decreasing. And this is the reason why.", - "As I increase the frequency, the amplitude of my output", - "cosine kept decreasing. I could also plot the phase for", - "you. And the phase,", - "in the same manner as omega increased, my phase also kept", - "shifting from zero initially to pi/2 finally.", - "Let me stop here and start with this the next time and revisit", - "this. Unfortunately,", - "I won't have time for the demo. I will show it to you next", - "time." - ] -} \ No newline at end of file diff --git a/subs/3NIegrCmA5k.srt.sjson b/subs/3NIegrCmA5k.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/3NIegrCmA5k.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/3SaQtdKynIM.srt.sjson b/subs/3SaQtdKynIM.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/3SaQtdKynIM.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/3g8ZeZlpv8E.srt.sjson b/subs/3g8ZeZlpv8E.srt.sjson deleted file mode 100644 index 881fbe6b2e..0000000000 --- a/subs/3g8ZeZlpv8E.srt.sjson +++ /dev/null @@ -1,62 +0,0 @@ -{ - "start": [ - 0, - 610, - 6120, - 8860, - 9590, - 10640, - 12310, - 16329, - 22030, - 24350, - 25440, - 29110, - 31860, - 32910, - 35920, - 38720, - 41110, - 42210 - ], - "end": [ - 610, - 6120, - 8860, - 9590, - 10640, - 12310, - 16329, - 22030, - 24350, - 25440, - 29110, - 31860, - 32910, - 35920, - 38720, - 41110, - 42210, - 44680 - ], - "text": [ - "SPEAKER 1: All right.", - "So v1 here is simply the difference between v0 and e1.", - "So v1 is simply v0 minus e1.", - "That's it.", - "What about i1?", - "That is pretty simple, too.", - "i1 is simply v1 divide by r1.", - "And because v1 is v0 minus e1, I can replace v1 by v0 minus", - "e1 and divide by r1.", - "That gives me i1.", - "So in this manner, I can go ahead and find all the vi's", - "and ii's very straightforwardly from the", - "known voltages.", - "So most often when we analyze circuits, we just go ahead and", - "find the e's-- the known voltages--", - "because we know we can very quickly find all the branch", - "voltages and currents.", - "And so, we often stop at the known voltage step." - ] -} \ No newline at end of file diff --git a/subs/3nCyei-6rtk.srt.sjson b/subs/3nCyei-6rtk.srt.sjson deleted file mode 100644 index cffcf0c06e..0000000000 --- a/subs/3nCyei-6rtk.srt.sjson +++ /dev/null @@ -1,140 +0,0 @@ -{ - 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"voltage at this node is simply v0, because this node is", - "connected to ground by a voltage source.", - "And so the voltage source would hold the voltage of that", - "node at v0.", - "So I directly have the voltage of that node.", - "So right there I've done my second step.", - "So that's my step two of node analysis.", - "So let's move on and start off with step", - "three of node analysis.", - "All right?", - "Step three would be to write KCL for the nodes-- on each of", - "the nodes-- e1 and e2 here, which are my unknowns.", - "I'm going to write KCL for these nodes, and I am going to", - "substitute device laws and KVL in dividing the current that", - "leaves those nodes.", - "But also remember that as I work with currents, and sum", - "the currents for KCL, I'll simply use my usual", - "convention, which is sum the currents leaving a node always", - "so I don't make mistakes.", - "Now again, for another piece of convenience, I'm going to", - "use conductances.", - "So the variable I have is resistance.", - "1 by that resistance is the conductance, since I would", - "just use that to make my algebra a little simpler.", - "So let's get started.", - "Let's start with node e1.", - "And I'm going to write KCL at node e1.", - "Now, with KCL, notice that I'm going to follow my usual", - "convention to avoid mistakes.", - "I'm going to add up the currents that leave a node so", - "that I don't make mistakes.", - "So let's go ahead and start.", - "Let me start with KCL at e1.", - "So if you look at e1, what is the current that is going up", - "in that direction?", - "I know the node voltage here is e1.", - "I know the voltage of this node is v0.", - "So can you tell me what the current is going up?", - "Let me pause for a second so that you can think about it.", - "And then I'll go back and do it for you." - ] -} \ No newline at end of file diff --git a/subs/3sWKu1arHKE.srt.sjson b/subs/3sWKu1arHKE.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/3sWKu1arHKE.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/4TCnYYpZxEc.srt.sjson b/subs/4TCnYYpZxEc.srt.sjson deleted file mode 100644 index b0f54f840a..0000000000 --- a/subs/4TCnYYpZxEc.srt.sjson +++ /dev/null @@ -1,1913 +0,0 @@ -{ - "start": [ - 0, - 9067, - 16945, - 24675, - 30770, - 36145, - 41491, - 46000, - 51870, - 57846, - 61019, - 64902, - 69407, - 73679, - 82000, - 88237, - 93197, - 99487, - 105776, - 111959, - 116649, - 119954, - 124644, - 132000, - 135431, - 139411, - 141676, - 144627, - 147372, - 150186, - 154746, - 159349, - 162126, - 166492, - 169428, - 174031, - 178238, - 183000, - 186881, - 189681, - 192800, - 195154, - 197699, - 200563, - 204254, - 206227, - 209472, - 212590, - 225000, - 227611, - 242000, - 255000, - 259230, - 261883, - 265898, - 269913, - 274000, - 279336, - 284396, - 287800, - 291204, - 295160, - 300118, - 306471, - 313285, - 320100, - 325528, - 331881, - 336811, - 340692, - 344121, - 346773, - 350719, - 353889, - 357835, - 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2535285, - 2539285, - 2542142, - 2544857, - 2551141, - 2556378, - 2560101, - 2566967, - 2572320, - 2580000, - 2584468, - 2588571, - 2593677, - 2596686, - 2600060, - 2604072, - 2607446, - 2613199, - 2618153, - 2621765, - 2627957, - 2634459, - 2639000, - 2643047, - 2647391, - 2652821, - 2657757, - 2661114, - 2665162, - 2670000, - 2676179, - 2680066, - 2686146, - 2691827, - 2697408, - 2703138, - 2709414, - 2715906, - 2721208, - 2723805, - 2729000, - 2731416, - 2735766, - 2739770, - 2743153, - 2747572, - 2750403, - 2752957, - 2755581, - 2760000, - 2865697, - 2869521, - 2872199, - 2876215, - 2880140, - 2884778, - 2890040, - 2893875, - 2897354, - 2902527, - 2906540, - 2911000, - 2915891, - 2920072, - 2925052, - 2928610, - 2931456, - 2936000 - ], - "text": [ - "So today we are going to talk about another process of lumping", - "or another process of discretization what will lead to", - "the digital abstraction. So today's lecture is titled", - "\"Go Digital\". So let me begin with a usual", - "review. And so in the first lecture we", - "started out by looking at elements and lumping them.", - "For example, we took an element and said for", - "the purpose of analyzing electrical properties let's lump", - "this element into a single lumped value called a resistor,", - "R. And this led to the lumped", - "circuit abstraction. The lumped circuit abstraction", - "says let's take these elements, connect them with wires and", - "analyze the properties of these using a sort of analysis", - "technique.", - "So a set of a methods. We've looked at the KVL,", - "KCL method. Another example of a method we", - "looked at was the node method. And of this category there is", - "one method you should remember, which you can apply to every", - "single circuit and it will simply work, is the node method.", - "For linear circuits other methods also apply,", - "and these include superposition,", - "Thevenin method, and in recitation or in your", - "course notes you would have looked at the Norton method.", - "So that's what we did so far. So this is a toolkit.", - "So now you have a utility belt with a bunch of tools in it,", - "and you can draw from those tools.", - "And, just like any good carpenter, you know,", - "the carpenter has to cut a piece of wood.", - "He could use a chisel. He could use a saw.", - "He could use an electric saw. And the reason you pay", - "carpenters $80 an hour in the Boston region is because they", - "know which tool to use for what job.", - "So what we'll learn today is, so this was one process of", - "discretization. We discretized matter.", - "This gave us the discipline here that we decided to follow,", - "lumped matter discipline, that moved us from Maxwell's", - "equations into this new playground called EECS.", - "Where all elements looked like these rinky-dinky little values", - "like resistors and voltage sources and so on.", - "What we'll do today, if that wasn't simple enough,", - "let's simplify our lives even further.", - "What we're going to do is lump some more.", - "So what else can we lump? We've lumped matter,", - "so all matter is taken care of. So what can we lump to make", - "life even easier? When in doubt,", - "if things are complicated, discretize it or lump it,", - "right? So what do you think?", - "What we will do today is lump signal values.", - "So we'll just deal with lumped values.", - "And this will lead to the digital abstraction.", - "And the related reading is Chapter 5 of the course notes.", - "So before we do this kind of lumping, let me motivate why we", - "do this. One reason is to simplify our", - "lives, but there is no need to just go around simplifying", - "things just because we can. Let's try to see if there are", - "other reasons motivating the digital abstraction.", - "So what I would like to start with is a simple example of a", - "analog processing circuit that you should now be able to", - "analyze. So I'm going to be motivating", - "digital. So let's start with an analog", - "circuit that looks like this, two resistors,", - "R1 and R2. And what I'm going to do is", - "apply a voltage source here, V1, apply another one here,", - "V2, and make this connection. And let me call this voltage V", - "nought and call this my output. This voltage with respect to", - "ground node, rather than drawing this wire here,", - "I often times draw a ground here and simply throw ground", - "wherever I want. This symbol simply refers to", - "the fact that the other terminal is taken at the ground node.", - "So here is my V nought. Now, let's go and analyze this", - "and see what it gives us. In this example,", - "V1 and V2 may be outputs of two sensors, maybe heat sensors or", - "something like that. This is a heat sensor on that", - "side of the room and this is a heat sensor on this side of the", - "room. And I pass their signals", - "through two resistors and I look at the voltage there.", - "So by now you should be able to write the answer V nought,", - "or the value V nought almost by inspection.", - "Just to show you, let me use superposition.", - "When you see multiple sources, the first thing you should", - "think about is can I use superposition to simplify my", - "life? And let me do that.", - "V nought here is the sum of two voltages, one due to V1 acting", - "alone and one due to V2 acting alone.", - "So what's the voltage here due to V1 acting alone?", - "To find out that I short this voltage, I zero out this voltage", - "and look at the effect of V1. So the effect of V1,", - "if this were shorted out, is simply V1 x R2 / R1 + R2.", - "This is now a voltage divider, right?", - "A voltage V applied across two resistors and the output taken", - "across one resistor. So that's this value.", - "Then I could do the second part.", - "To look at the effect of V2, what I will do is short this", - "voltage and look at the effect of this.", - "Now, this voltage is across this resistor divider.", - "And so I get R1 / (R1 + R2) here.", - "So you'll notice that for something like this,", - "if I had applied KVL and KCL of the node method I would have", - "gotten a bunch of equations, but here I wrote it just by", - "inspection. You should be able to look at", - "circuit patterns like this and write the answers down very", - "quickly. Let's say if I chose R1 to be", - "equal to R2 then V nought would simply be (V1 + V2) / 2.", - "So if these two values were equal, I simply get the output,", - "the average of the two voltages.", - "So this guy is an adder circuit.", - "It adds up these two voltages. But more precisely it's an", - "averaging circuit. It takes two voltages and gives", - "me the average value. Now, if you have two sensors in", - "the room, you might think of why you want to take that average", - "value to control the temperature of the room.", - "But suffice it to say that V nought is the average of the two", - "values. So let me show you a quick demo", - "of this example and then look at what the problems are with this", - "example. So let's say,", - "as one example, I applied a square wave at V1,", - "which is the top curve, the green curve,", - "and I applied a triangular wave at V2, that's the second one.", - "As you expect, the output is going to be the", - "sum of the two voltages scaled appropriately.", - "So notice that I have a square wave with a superimposed", - "triangular wave on top. And I can play around.", - "What I could do is change the amplitude of my wave form here.", - "And, as you notice, the amplitude of the output", - "component also changes accordingly.", - "So this is one simple example of an adder circuit,", - "and the two wave forms get summed up and I get the output.", - "So I'll switch to Page 3. Let me just draw a little", - "sketch for you here. Here, what I showed you was I", - "had a triangular wave coming on one of these inputs and I had a", - "square wave on the other one, and the output looks something", - "like this.", - "OK? No surprise here.", - "This is a simple analog signal processing circuit which gives", - "me the average of two wave forms.", - "Now, let me do the following. Often times I may need to look", - "at this value some distance away.", - "So let's say this person here wants to look at the value.", - "So I bring this wire here. And I also bring the ground", - "connection and I look at it. I look at this value here.", - "And when I have a long wire I can get noise added onto the", - "circuit. So let's say a bunch of noise", - "gets added into the signal there.", - "And what I end up seeing here is not something that looks like", - "this but something that looks like that.", - "That's not unusual. And the problem with this is", - "now when I look at this, if I'm looking to distinguish", - "between, say, a 3.9 and a 3.8,", - "it's really hard to do that because my noise is overwhelming", - "my signal. I have a real problem,", - "a real problem here. Noise is a fact of life.", - "So what do we do? This is so fundamental.", - "Large bodies of courses in electrical engineering are", - "devoted to how do I carefully analyze signals in the presence", - "of noise? You'll take courses in speech", - "processing that look at clever techniques to recognize speech", - "in the presence of noise and so on and so forth.", - "One technique we adopt that we'll talk about here,", - "which is fundamental to EECS, is using the digital", - "abstraction. Let me show you how it can", - "really help with the noise problem.", - "So the idea is value lumping or value discretization.", - "Much like we lumped matter, we've discretized matter into", - "discrete chunks, let's discretize value into two", - "chunks. Let's simply say that now I'm", - "going to deal with two values and I can, say,", - "call them high, low.", - "I have a bunch of choices here. I may call it 5 volts and 0", - "volts. I may call it true and false.", - "What I'm doing is I'm just restricting my universe to deal", - "with just two values, zero and one.", - "This is like dealing with a number system with only two", - "digits. And these are zero and one.", - "So what I've now done is I'm saying that rather than dealing", - "with all possible continuous values, 0.1, 3.9999 recurring", - "and so on and so forth, what I'm going to do is simply", - "deal with a high and a low. Dealing with this whole", - "continuum of numbers is really complicated.", - "Let me simplify my life and just postulate that I am going", - "to be looking at high and low. Whenever I see something I'll", - "look at it and say high or low, is it black or white,", - "period. There's no choice here,", - "just two individual values. So that sounds simple,", - "and nice and so on, but what's the point?", - "What do we get by doing that? Let's take our example.", - "Let's take what might be a digital system.", - "Let's take a digital system and let's say I have a sender.", - "Much like I sent a signal value a long distance,", - "let me have a sender, and I have a ground as well and", - "here is a receiver. This symbol simply says that", - "both of them share a ground wire.", - "So the sender and a receiver. And what I'm interested in", - "doing, the sender is interested in sending a signal to the", - "receiver. And in the digital system,", - "the way I would send a digital signal is all I can use is ones", - "and zeros, OK? So let's say the sender sends", - "something like this. The sender wants to send a", - "value. This is my time axis and this", - "is 2.5 volts, this is 0 volts and this is 5", - "volts. My sender has some agreement", - "with the receiver and says I'm just going to be sending to you", - "low values and high values. And this signal here would", - "correspond to \"0\" \"1\" \"0\". It's a symbol.", - "That's why I have input zero in quotes there.", - "We'll go into this in much more detail later,", - "but for now suffice it to say that I'm sending a set of", - "signals here \"0\" \"1\" \"0\". This simplistic scheme will not", - "work in many situations but go along with this for a few", - "seconds. So I send the signal sequence", - "\"0\" \"1\" \"0\" out here. And notice that there is a high", - "and a low. And the agreement the sender", - "and the receiver have is that, look, if you see a value that's", - "higher than 2.5 volts that's a high.", - "If you see a value below 2.5 volts in the wire that's a low.", - "And I'm going to send a 0 volt and a 5 volt from here.", - "So now at the sending site let's say I don't have any noise", - "in this system. Let's say this is my Vn,", - "some noise being added. And let's say Vn is 0.", - "Then in that case I will receive exactly what is sent \"0\"", - "\"0\" 5, 2.5, 0 volts. And this is time.", - "Nothing fancy here, right?", - "My receiver receives a \"0\" \"1\" \"0\".", - "Now, the beauty of this is that now suppose I were to impose", - "noise much like I had noise out there and Vn was not 0.", - "Rather Vn was some noise voltage, let's say 0.2 volts", - "peak to peak. Let's say that simply got", - "superposed on the signal. In which case what do I get?", - "What I end up here with is a signal that looks like this.", - "So the receiver gets that signal because a noise is added", - "into my signal and that's what I get.", - "But guess what? No problem.", - "The receiver says oh, yeah, this is a 0 because the", - "values are less than 2.5, this is a 1 and this is a 0.", - "\"0\" \"1\" \"0\". So here my receiver was able to", - "receive the signal and correctly interpret it without any", - "problems. So because I used this value", - "discretization and because I had this agreement with the", - "receiver, I had better noise immunity.", - "Consequently, I had what is called a noise", - "margin. Noise margin says how much", - "noise can I tolerate? And in this situation,", - "because the sender sends 5 volts and 0 volts,", - "the 5 volts can creep all the way down to 2.5,", - "I'll still be OK. Similarly, 0 could go all the", - "way up to 2.5, I'd still be OK.", - "So in this case I have a noise margin of 2.5 volts for a 1 and", - "similarly 2.5 volts for a 0, because there are 2.5 volts", - "between a 0 volt and 2.5. So notice that I have a nice", - "little noise margin here, which simply is the English", - "meaning of the term there is a margin for noise.", - "And even though I can change the signal value by up to 2.5", - "volts, the receiver will still correctly interpret the signal.", - "So I've decided to discretize values into highs and lows.", - "And because of that, if all I wanted to do in life", - "is send highs and lows I can send them very effectively.", - "There are many complications, but if all I care about is", - "sending highs and lows I can send it with a lot of tolerance", - "to noise. So many of you are saying but", - "what about this, but what about that?", - "There are lots of buts here. And let's take a look at some", - "of them. If you look up there.", - "What I ended up doing was creating a design space that", - "looked like this. This is on Page 6.", - "What I did was I said with a range of values from 0 to 5,", - "what I'm going to do is at 2.5 I drew a line and I said as a", - "sender if you wanted to send a 0 then you would send a value", - "here. And if you wanted to send a 1", - "you would send a value here. Similarly, for a receiver.", - "And if the sender sent a value all the way up in 5 volts that", - "was the best thing, but technically the sender", - "could send any value between 2.5 and 5.", - "And if there was no noise then the receiver could correctly", - "interpret a 1 if it was above this and 0 if it was below this.", - "The problem with this approach really is that if I allow the", - "sender to send any value above 2.5 all the way to 5 then there", - "really is no noise margin in this situation.", - "OK? Because if I allowed the sender", - "to send any value between 2.5 and 5 then what if I have a", - "value 2.5 for a 1? Then I may end up getting very", - "little noise margin on the other side.", - "Worse yet, what if I get a value 2.5?", - "That's a much worse situation. What if the receiver receives a", - "value of 2.5? Now what?", - "What does the receiver do? The receiver cannot tell", - "whether it's a 1 or a 0. The receiver gets hopelessly", - "confused. So to deal with that,", - "I'm going to fix this, what I'm going to do is the", - "following. Switch to Page 7.", - "What I'll do here is to prevent the receiver from getting", - "confused, if the receiver saw 2.5, what I'm going to do is", - "define what is called \"no man's land\".", - "I'm going to define the region of my voltage space called the", - "forbidden region. And what I'm going to do is,", - "say, let's say I defined it as 2 volts, 3 volts and 5 volts,", - "0, 2, 3 and 5. With my forbidden region,", - "if I have a sender then I tell the sender you can send any", - "value between 3 and 5 for a 1. And you can send any value", - "between 2 and 0 for a 0. To send the symbol 0,", - "I can send any voltage between 0 and 2, and similarly for 1.", - "At the receiving side, if I see any value between 3", - "and 5, I read that as a 0, and any value between 0 and 2 I", - "read that as 2 volts. So I may label this value VH", - "and label this threshold VL, so there's a high threshold and", - "a low threshold. So this solves one problem.", - "Now the receiver can never see a value in the forbidden region.", - "Now, I can stand her and pontificate and say,", - "oops, that's a forbidden region, thou shalt not go there.", - "But what if I get some noise and a value goes in there?", - "In real systems values may enter there.", - "But what I'm saying, so this is the beauty of using", - "a discipline. Let me use my playground", - "analogy. This is my playground.", - "We got into this playground using the discrete matter of", - "discipline, the playground of EECS, but in that playground", - "some region of that playground deals with just high and low", - "values. I further restrict the", - "playground and I say I'm only going to focus on that", - "playground in which all signal values have a forbidden region.", - "All senders and receivers adhere to a forbidden region.", - "And if there is any signal in this space, in the forbidden", - "space then my behavior is undefined.", - "I don't care. You want to go there?", - "Sure. I don't know what's going to", - "happen to you. Now, we're engineers,", - "right? So we've disciplined ourselves", - "to play in this playground. It's like I tell my 9-year-old,", - "don't go there, right?", - "And of course he wants to go there.", - "He says what will happen if I go there?", - "And the answer here will be undefined, OK?", - "Something really bad could happen to you.", - "I don't know what it is but something really bad,", - "you know, a lightening bolt or who knows what,", - "but something really bad. And you as a designer of a", - "circuit can, let's say you were Intel.", - "Intel designs its chips. And let's say Intel decides to", - "play in this playground and there is a forbidden region.", - "So Intel says oh, it's really easy for me if in", - "the forbidden region the chip simply burns up and catches", - "fire, we'll sell more chips. That's fine.", - "Whatever you want. The key here is that all I'm", - "saying is that I am going to discipline myself into playing", - "in this playground and that's where I will define my rules,", - "and you stay within the boundaries and all the rules", - "will apply. It's called a \"discipline.\"", - "You're disciplining yourselves to stay within it.", - "There's no logic to it. It's just a discipline.", - "Just do it and you'll be OK. When we look at practical", - "circuits and so on, we have to address the issue of", - "what happens when things go in there.", - "But let's postpone that discussion.", - "For now I've solved one of my problems, which is,", - "the previous problem was what does a receiver do if it saw a", - "2.5? Now it can't see a 2.5.", - "But then the receiver asks, Agarwal, but what if I see a", - "2.5? I can tell the receiver you can", - "do whatever you want to do. You can stomp it.", - "You can squish it. You can burn it.", - "You can chuck it. Whatever you want.", - "It's up to you. Do whatever you want.", - "You won't see a value. If you do, do whatever you", - "want. It's undefined.", - "That works. So you, as the receiver", - "designer can do whatever you want when you see a 2.5.", - "You can say yeah, I'll just put out a 1 if I see", - "a 2.5 or a 2.6. I'll just do something.", - "No one cares. So this is pretty good.", - "This is pretty good. We still have a problem,", - "though. Do people see the problem here?", - "This still doesn't quite work. If Intel did this,", - "instead of your laptops failing and blue-screening every hour", - "they'd be doing it every millisecond.", - "So the problem is this discipline have allowed the", - "sender to send any value between 3 and 5 as a 1.", - "And any value between 3 and 5 at the receiver is treated as a", - "1. Do you see where the problem", - "is? Yes?", - "The sender sends a 1.99 and the noise pumps it into forbidden", - "region. Exactly.", - "So the sender says it's legitimate, I'm Intel.", - "They've told me stick to 0 and 2.", - "And Intel parts will be sending to values between 0 and 2.", - "And Motorola parts, which are receivers,", - "you know they have to receive 0 and 2.", - "So Intel can send the value, 2.", - "They can because it's 1.9 out of 2.", - "It's legal. This way I can make really", - "cheap parts. But now the problem is that", - "even the smallest amount of noise will bump it into the", - "forbidden region, and so therefore this one has a", - "problem. And the problem is that this", - "one offers zero noise margin. There is no noise margin.", - "There is no margin for noise in the discipline.", - "All right, back to the drawing board, folks.", - "Switch to Page 8. Let's get rid of all this stuff", - "and go back to the drawing board.", - "OK, so what do we do now? How about the following?", - "How, about as before I say, as a receiver,", - "if you see a value between 3 and 5 you treat that as a 1 and", - "a value between 0 and 2 you treat that as a 0.", - "No difference. So as a receiver same as", - "before. But now what I do is I hold the", - "sender to tougher standards. I hold the feet of the sender", - "to the fire and say you have to adhere to tougher standards.", - "So what I'm going to do is hold the sender to tougher standards,", - "maybe four walls. That is tell the sender that if", - "you want to send to 0 or a 1, for a 1 you have to send a", - "value between 4 and 5, and for a 0 a value between 0", - "and 1. Sender is now held to tougher", - "standards. This is what my chart looks", - "like. So now I do have some noise", - "margin. Can someone tell me what is the", - "noise margin here for a 1? 1 volt.", - "And the reason is that the lowest voltage a sender can send", - "is 4 volts, OK? If the 4 leaks down to 2.99", - "that's in the forbidden region, I'm in trouble.", - "2.99. This is my forbidden region", - "here. And 2.99 is in the forbidden", - "region. I'm in trouble.", - "So notice that the lowest value that the receiver can receive is", - "3 volts. So if I sent the 4 and sent", - "this over a long cable to you, the value can be beaten up by", - "noise to such an extent that you may begin receiving 3s but", - "nothing lower than a 3. So this is a noise margin,", - "1 volt. Similarly, for a 0 the noise", - "margin is also 1 volt. So let me label these.", - "There are four important thresholds here.", - "This threshold is called VOL. V output low.", - "These have special meanings. This threshold here is called", - "VOH, V output high. This threshold here is called V", - "input high and this threshold here is called V input low.", - "So VOH simply says that senders must send voltages higher than", - "VOH. Receivers must receive values", - "higher than VIH as a 1. So these four thresholds", - "together give you your threshold.", - "For the sender gets 2.5, what does sender do?", - "It could do that. So, in that case,", - "you can do that. If all you want to do is have", - "one value here then what you have is an infinitesimal value", - "here for the forbidden region. That's fine.", - "It's up to you to design it that way.", - "You can. But it turns out that when you", - "design circuits, when we see some examples in", - "the next lecture it turns out to be fairly practical and easy to", - "do it this way. But, again, these are design", - "choices. If I'm Intel,", - "Intel wants all its parts to work together.", - "So parts that follow a common discipline can work together,", - "right? Because senders will send", - "values, receivers will receive these values here,", - "so it will simply work. So the noise margin for a 1", - "here is simply VOH minus VIH and the noise margin for a 0 is VIL", - "minus VOL. VIL minus VOL is the noise", - "margin for a 0. So what do we have here?", - "What we have here is a discipline that we've agreed to", - "follow where senders are held to a tough standard and receivers", - "are held to a different standard so that I allow myself some", - "margin for error. And it's up to you as a", - "designer to choose ranges for the forbidden region.", - "Now, you may say that I want to make my forbidden region as", - "small as possible. But you will see in practical", - "circuits it's very hard to achieve that.", - "Practical devices that you get, they have a natural region that", - "gets very, very hard to break apart, and that tends to", - "establish what that region looks like.", - "So to continue with an example here, I may have the following", - "voltage wave form for a sender. So I have some sender,", - "I have a sender here.", - "I have VOL, VIL, VIH, VOH and some other high", - "voltage. And then, as a sender,", - "if I want to send a \"0\" \"1\" \"0\" then I send a 0.", - "I have to be within this band. And then for a 1 I have to be", - "within this band. So this is an example of,", - "say, \"0\" \"1\" \"0\" \"1\". And at the receiver --", - "Let's have VOL, VIL, VIH, VOH.", - "So at the receiver, I interpret any signal below", - "VIL as a 0. So I may get some signal that", - "looks like this.", - "And I'll still interpret that as a \"0\" \"1\" \"0\" \"1\".", - "So to summarize here, this discipline that forms the", - "foundations of digital systems is called \"a static discipline\".", - "The static discipline says if inputs meet input thresholds --", - "So if an input to a digital system meets the input", - "thresholds then outputs will meet, or the digital system", - "should ensure that the outputs --", - "Output thresholds. So this means that if I have a", - "system like this then if I give it good inputs.", - "And by giving it good inputs I mean for 1s I have signal values", - "that are greater than VIH and for 0s signal values which are", - "less than VIL. These are valid inputs.", - "So if my inputs are valid, that is below VIL for a 0 and", - "above VIH for a 1 then this digital system D will produce", - "corresponding outputs that follow output thresholds.", - "For a 1 it will produce outputs that are greater than VOH and if", - "it needs to produce a 0 it will produce outputs that are less", - "than VOL. So notice that there is this", - "tough requirement in digital systems that for the inputs,", - "I should recognize as a 1 anything higher than a VIH.", - "But if I want to produce a 1, I have to produce a tough 1", - "like a 4-volt 1. So there is a discipline that", - "all my digital systems must follow, and that discipline is", - "called a static discipline. So static discipline encodes", - "the thresholds, encodes four thresholds that", - "all digital systems must follow so that they can talk to each", - "other. So if Intel and Motorola want", - "to make parts that are compatible with,", - "say, Pentium 4 devices then they will all talk over the", - "phone or something and agree on a static discipline.", - "We will say that, all right, all my peripherals", - "will follow a static discipline with the following volted", - "thresholds. And this way parts made by", - "different manufacturers can interoperate and still provide", - "immunity to noise. Yes.", - "Question?", - "Absolutely. There are many constraints on", - "how you as a designer choose the noise margin.", - "As a designer you want to make your noise margin as large as", - "possible. The larger the noise margin the", - "better you can tolerate noise which is why,", - "how many people have heard of some devices called rad hard", - "devices, radiation hard devices? Some of you have.", - "There are a bunch of devices. Different manufacturers make", - "different kinds of devices for different markets.", - "For consumer markets they use parts which may have relatively", - "poor noise margins because consumers can tolerate more", - "faults. But if you're building devices", - "for, say, the medical industry or for spaceships and so on,", - "you need to be held to a much, much tougher standard.", - "So for those devices you may end up having much,", - "much tighter bands in which you have to operate so you have a", - "tougher noise margin. So that leads us to,", - "given these sort of voltage thresholds, we now move into the", - "digital world. And in the digital world we can", - "build a bunch of digital devices.", - "The first device we will look at is called a combinational", - "gate.", - "A combinational gate is a device that adheres to the", - "static discipline, Page 11, and this is a device", - "whose outputs are a function of inputs alone.", - "So I can build little boxes which take some inputs,", - "produces an output where the outputs are a function of the", - "existing inputs. And this kind of a device is", - "called a combinational gate. And I can analyze such devices", - "for the kinds of things that I would like to do.", - "Before I go into the kinds of devices I'd like to build,", - "let's spend a few minutes talking about how to process", - "signals. How to process digital signals,", - "Page 10. So notice that you have two", - "values, 0 and a 1. So devices like my", - "combinational gate, for example,", - "can only deal with 0s and 1s. So I have to come up with some", - "kind of a mathematics or some kind of a set of processing that", - "can work with 0,1 values. So 0,1 map completely natural", - "to the logic true and false. So I can borrow from logic and", - "use true and false to do my processing of signals.", - "So if all I care about is processing logic values,", - "0s and 1s, trues and falses then that's all I need.", - "I can also use numbers. How do I represent a number?", - "3.9 which is 0s and 1s. It turns out that this is a", - "whole field in itself. You'll hear more about this in", - "recitation. Let me also point you to the", - "last section of the course notes, Chapter 5.6 I believe,", - "that talks about how to represent numbers.", - "The basic insight is much like you can represent arbitrary long", - "numbers with the digits 0 through 9 in the same way,", - "but concatenating digits you can represent arbitrary long", - "numbers with 0-1-1-1-0-0 and so on.", - "So you can have a whole sequence of digits and you can", - "build a binary number system. So you can read A&L Section", - "5.6, I believe. It's the last section for", - "numbers. And you will also discuss this", - "in your recitation tomorrow. Let me spend some more time", - "talking about Boolean logic, two-valued logic,", - "and how to process these systems.", - "So one way of processing it is using logic statements of the", - "following form. If X is true and Y is true then", - "Z is true, else is Z false. So this is a logic statement.", - "It says if X is true and Y is true then Z is true,", - "else Z is false. So I can process this with 0s", - "and 1s, trues and falses. And I do this all the time so I", - "have a succinct notation for this.", - "I express this as Z is X anded with Y.", - "X and Y is Z. So Z is true if X is true and Y", - "is true. A shorthand notation for this", - "is just a dot. And a circuit notation for this", - "is called an \"AND gate\". That's a little circuit.", - "I haven't told you what's inside it.", - "It's an abstract little device called an AND gate which takes", - "two inputs, produces one output Z where the output is related to", - "the inputs in the following manner.", - "That's a little device called an AND gate.", - "I could also represent logic in truth tables.", - "And truth tables simply enumerate all the values and the", - "corresponding outputs. Inputs can be 0-0-0-1-1-0 or", - "1-1. For an AND system output is 1,", - "only if both are ones, it's a 0 otherwise.", - "So that's a truth table for AND gate.", - "So from 0s and 1s we deal with logic and we create devices like", - "the AND gate to process digital signals.", - "And what we will do is look at a whole bunch of little symbols", - "like this, like the AND gate to process our input signals.", - "And these devices might look like other functions like OR", - "gates and so on. Let me show you a quick demo.", - "What I'm going to show you is a signal feeding an AND gate.", - "And one signal is going to look like this, and my signal Y is", - "going to look like this. So you expect a processed", - "output. So 1-0-1-0-1-0-1.", - "And the output is simply going to be --", - "This is my time axis going this way.", - "It is going to be an AND-ing of these two signal values like so.", - "What I'm also going to show you is I'm going to superimpose", - "noise on this wire. I'm going to superimpose noise", - "on the wire, and what I want you to observe is the output of this", - "digital gate. The output will stay exactly", - "like this, even though I impose noise.", - "The ultimate test. So stay right there.", - "Let's do this demo. Give me a couple of seconds.", - "If you look at the signal up there, look at the middle wave", - "form, and I'm imposing let's have a digital system in a noisy", - "environment like a lumberyard, for example,", - "or chopping a bunch of trees in my backyard and building digital", - "systems on the side. And if I have my buddies", - "revving up chainsaws superimposing noise on my second", - "input, but look at the output. And just to show that I'm not", - "bluffing here, what I'll do is I'll pass the", - "noise through and make the noise larger.", - "And you'll notice that when the noise begins to surpass the", - "noise margins the output begins to go berserk.", - "Watch. Can you increase it gradually?", - "Notice that as I put in a lot more noise then the output", - "begins to go berserk, but as long as my input is", - "within the noise margin my output stays perfectly stable.", - "So that's the \"Intro to Digital Systems\".", - "You'll see numbers in recitation.", - "And we'll see you at lecture on Tuesday." - ] -} \ No newline at end of file diff --git a/subs/4cLA-IME32w.srt.sjson b/subs/4cLA-IME32w.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/4cLA-IME32w.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/4rpg8Bq6hb4.srt.sjson b/subs/4rpg8Bq6hb4.srt.sjson deleted file mode 100644 index fec1906009..0000000000 --- a/subs/4rpg8Bq6hb4.srt.sjson +++ /dev/null @@ -1,71 +0,0 @@ -{ - "start": [ - 0, - 3440, - 7050, - 8640, - 11130, - 13800, - 15470, - 16460, - 19880, - 21220, - 23670, - 27040, - 28360, - 31280, - 34840, - 37870, - 40670, - 41980, - 44180, - 46220, - 49980 - ], - "end": [ - 3440, - 7050, - 8640, - 11130, - 13800, - 15470, - 16460, - 19880, - 21220, - 23670, - 27040, - 28360, - 31280, - 34840, - 37870, - 40670, - 41980, - 44180, - 46220, - 49980, - 53130 - ], - "text": [ - "SPEAKER 1: 6.002x is an extraordinarily fun course.", - "This course is the first course in an EE or an EECS", - "curriculum at MIT.", - "This course will help you make the big jump", - "from physics to EECS.", - "You will learn, what, all kinds of fun", - "things in this course.", - "So, for example, you will learn what's behind this.", - "What's behind the iPhone.", - "What are some of the foundational technologies and", - "cool ideas that drive this and many other fun", - "things in our lives?", - "Very useful things in our lives as well, that have", - "really been able to improve the productivity of all of", - "humankind over the past many, many decades.", - "This course also forms the foundations of", - "devices like this.", - "This is a chip photo of Intel's 22", - "nanometer multicore processor.", - "And you will learn about some basic technologies that are", - "used in building devices such as this as well." - ] -} \ No newline at end of file diff --git a/subs/6nj1OCvSRI8.srt.sjson b/subs/6nj1OCvSRI8.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/6nj1OCvSRI8.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/7ssVrey04Pw.srt.sjson b/subs/7ssVrey04Pw.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/7ssVrey04Pw.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/8QEfTdAsUcA.srt.sjson b/subs/8QEfTdAsUcA.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/8QEfTdAsUcA.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/8fhUjsUUJYU.srt.sjson b/subs/8fhUjsUUJYU.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/8fhUjsUUJYU.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - 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Good morning. I hope you guys did", - "not spend all of last night celebrating the Red Sox victory,", - "but there is one more tonight. OK. Let's see. I trust the quiz went", - "OK. What I will do today is take off from where we left", - "off on Tuesday. And continue our discussion of the", - "large signal and small signal analysis of our amplifier.", - "Today the focus will be on \"Small Signal Analysis\".", - "So let me start by reviewing some of", - "the material. And, as you know, our MOSFET amplifier", - "looks like this.", - "One of the things you will notice in circuits, as I have been mentioning", - "all along in this course, is that certain kinds of patterns", - "keep repeating time and time again. And this is one such pattern. A", - "three terminal device like the MOSFET with an input and the drain", - "to source port connected to RL and VS in series in the following manner,", - "this is a very common pattern. There are several other common", - "patterns. The voltage divider is a common pattern.", - "We keep running into that again and again and again.", - "The Thevenin form, a voltage source in series with the", - "resistor is another very common form. The Norton equivalent form,", - "which is a current source in parallel with a resistor is also", - "very common. And it behooves all of us to be very familiar with the", - "analyses of these things. Voltage dividers in particular are", - "just so common that you need to be able to look at it and boom,", - "be able to write down the expression for voltage dividers.", - "I would also encourage you to go and look at current dividers.", - "When you have two resistors in parallel and you have some current", - "flowing into the resistors to find out the current in one branch versus", - "the other very quickly. The expression is very analogous to", - "the voltage divider expression. And some of these very common", - "patterns are highlighted in the summary pages in the course notes,", - "so it is good to keep track of those and be extremely familiar with those", - "patterns to the point where if you see it you should be able to jump up", - "and shout out the answer just by looking at it without having to do", - "any math. So here was an amplifier. And then we noticed that when the", - "MOSFET was in saturation it behaved like a current source.", - "And this circuit would give us amplification while the MOSFET was", - "in saturation. So we agreed to adhere to the", - "saturation discipline which simply said that I was going to use my", - "circuit in a way that the MOSFET would always remain in saturation in", - "building things like amplifiers and so on. And by doing that throughout", - "the analysis I could make the assumption that the MOSFET was in", - "saturation. I didn't have to go through --", - "Analysis became easier. I didn't have to figure out now,", - "what region is the MOSFET in? Well, because of my discipline it is", - "always going to be in saturation. But in turn what we had to do was", - "conduct a large signal analysis.", - "Again, in follow on courses you will be given circuits like this.", - "In fact, this very circuit with a very high likelihood.", - "And you will be looking at more complicated models of the MOSFET.", - "Or you will be given the MOSFET like this and,", - "let's say in that course the designers do not adhere to the", - "saturation discipline, in which case you have to first", - "figure out is my MOSFET in its triode region or in the saturation", - "region? And depending on the region it is in you have to apply different", - "equations. So it is one step more complicated than in 002.", - "In 002 we simplified our lives by following a discipline.", - "And let me tell you that following a discipline is quite OK.", - "When it simplifies our lives and we can do good things with it,", - "it is quite OK to do that. We are not wimps or anything like that.", - "It is quite OK to have a discipline and agree that we are going to play", - "in this region of the playground and build circuits in that manner.", - "By doing so, we could assume the MOSFET was in saturation all the", - "time. And analysis simply used a current source model.", - "By the same token, what becomes important is to figure", - "out what are the boundaries of valid operation of the MOSFET in", - "saturation? To do that we conducted a large signal analysis.", - "And it had two components to it. One of course was to figure out the", - "output versus input response. And what this usually does is that", - "it does a nonlinear analysis of this circuit.", - "If it is a linear circuit it is a linear analysis.", - "And figures out what the values of the various voltages and currents", - "are in the circuit as a function of the applied inputs and chosen", - "parameters. And the second step we said was to figure out valid", - "operating ranges --", - "-- for input and corresponding ranges for the other dependent", - "parameters such as VO. You could also find out the", - "corresponding operating range for the current IDS and so on.", - "So by doing this you could first analyze the circuit,", - "find out the \"bias\" parameters, find out the values of VI and VO and", - "so on. And then you could say all right,", - "provided, as long as VI stays within these bounds my assumption that this", - "is in saturation will hold and everything will be fine.", - "The reading for this is Chapter 8. And today we will take the next", - "step and revisit small signal analysis. In the demo that I showed", - "you at the end of last lecture, I showed you an input triangular", - "wave. And the input triangular wave gave", - "rise to an output. And we noticed that we did have", - "amplification, I had a small input and a much", - "bigger output. I did have amplification when the", - "MOSFET was in saturation but it was highly nonlinear.", - "The input was a triangular wave and the output was some funny,", - "it kind of looked like a sinusoid whose extremities had been whacked", - "down and kind of flattened. And its upward going peak had been", - "shrunk. So it was a kind of weird nonlinear behavior.", - "I will show that to you again later on. And so it amplified but it was", - "nonlinear. And remember our goal of two weeks ago?", - "We set out to build a linear amplifier. So today we will walk", - "down that path and talk about building a linear amplifier.", - "So to very quickly revisit the input versus output characteristic,", - "VI versus VO, this is VT and this is VS, this is what things looked like.", - "Also to quickly review the valid ranges, until some point here the", - "amplifier was in saturation, the MOSFET was in saturation and", - "somewhere here I had VO being equal to VI minus a threshold drop.", - "At that point the MOSFET went into its triode region and I no longer", - "was following the saturation discipline. So therefore this is my", - "valid region of operation. We also know that the output was", - "given by VS minus K (VI-VT) all squared RL over 2.", - "Again assuming the MOSFET is in saturation. It is very important to", - "keep stating this because this is true only when the MOSFET is in", - "saturation, when I am following the discipline. Notice that this is a", - "nonlinear relationship. So VO depends on some funny square", - "law dependence on VI. The key here is how do we go about", - "building our amplifier? Take a look at this point here.", - "At this point here let's say I have a VI input. Corresponding output is", - "VO. Focus is this point. And left to itself this was a", - "nonlinear curve. Remember the trick that we used in", - "our nonlinear Expo Dweeb example? We used the Zen Method.", - "Remember the Zen Method? We said look, this is nonlinear,", - "but if you can focus your mind on this little piece of the curve here", - "this looks more or less linear. If I look at a small itty-bitty", - "portion of the curve and I do the Zen thing, and kind of zoom in on", - "here. This looked more or less linear. This means that if I could", - "work with very small signals and apply the signal in a way that I", - "also had a DC offset of some sort. Then I would be in a region of the", - "curve, I would be delineating a small region of the curve which", - "would be more or less linear. This was a small signal trick.", - "And what we will do here is simply revisit the small signal model.", - "Most of what I am going to do from here on will be more or less a", - "repeat of what you saw for the light emitting expo dweeb.", - "Just that here I have a three terminal device,", - "with a little bit more complication. The equation is different. I don't", - "have to resort to a Taylor series expansion. I will just do a", - "complete expansion of this expression and develop the small", - "signal values for you. Recall the small signal model.", - "It had the following steps. The first step will operate at some", - "bias point, VI, VO, and of course some corresponding", - "point IDS. This is Page 3. And then superimpose a small signal", - "VI on top of the big fat bias. Remember the \"boost\"?", - "So VI is the boost. Boom. And above VI,", - "I have small signal VI that I apply. And our claim is that response of", - "the amplifier to VI is approximately linear.", - "The key trick with this is that for", - "my small signal model here, this is Page 3 here, and Page 2.", - "The key trick here is that with the small signal model,", - "I operate my amplifier at some operating point,", - "VO, VI. I superimpose a small signal VI on top of small VI on top", - "of big VI. And then I claim that the response to VI is", - "approximately linear. And let me just embellish that curve", - "a little bit more.", - "Notice that in this situation this was my VI, which is my bias voltage,", - "this is VO, which is the output bias, and of course not shown on this", - "graph is the output operating current which is IDS.", - "One nice way of thinking about this is to redraw this and think that", - "your coordinate axes have kind of shifted in the following manner.", - "This is VI. This is also on your Page 3. This is VT.", - "Remember this was the operating point, VO and VI.", - "And notice that we were operating in this small regime of our", - "transfer curve here. And in effect what we are saying is", - "that I am going to apply small variations about VI and call those", - "variations delta VI or small VI. And the resulting variations are", - "going to look like delta VO. Also referred to as small V,", - "small O. So I will have small variations here.", - "And they give rise to corresponding small variations there.", - "One way to view this is as if we are working with a new coordinate", - "system. Another way to view this is that so the capital VI and capital", - "VO correspond to my VI and VO as the total voltages in my circuit,", - "but at this bias point I can think of another coordinate system here", - "with small VI and VO out there. And for small changes to VI,", - "I can figure out the corresponding small changes to VO.", - "Just that all the analysis I perform here is going to be linear.", - "And I will prove it to you in a couple of different ways in the next", - "few seconds. When I am doing small signal analysis I am operating here", - "in this regime at some bias point. You have also seen this before.", - "How do I get a bias? This is my amplifier RL and VS.", - "This is Page 4. VO. The way I get a bias is I apply", - "some DC voltage VI and superimpose on top of that my small signal small", - "VI. This is my DC bias that has boosted up the signal to", - "an interesting value. And because of that what I can get", - "is by varying VI as a small signal with a very small amplitude,", - "I am going to get a linear response here. And I can draw", - "that for you as well.", - "This is my bias point here. And if I vary my signal like so then", - "my output should look like this. This is point VI, this is point VO,", - "and this is my small signal VI and this is my small signal VO and this", - "is capital VO. So this small thing here is VI.", - "I would like to show you a little demo.", - "I will start with the same demo I showed you the last time.", - "I showed you the amplifier. In the demo I am going to apply a", - "triangular wave. And initially I start with a large", - "signal. And you will see that the output looks really corny,", - "is going to look something like this. That's large signal response.", - "And then I will begin playing with the input making it smaller,", - "and you can see how it looks yourselves.", - "There you go. So this is where I stopped the last time.", - "The last lecture I applied this input, time is going to the right,", - "and the purple curve in the background is the output.", - "It looks much more like a sinusoid with some flattening of its tips.", - "Nothing like an interesting triangular wave.", - "What I will do next is that let me make sure I have enough of a boost", - "here, enough of a DC voltage so that I am operating at some point here.", - "I believe I already have that. Notice that I can shift up the", - "triangular wave input, or I can shift it down.", - "So let me bias it here. I have chosen a VI that's about,", - "I forget how many volts per division it is, but I have chosen", - "some VI here. And I biased it such that this is", - "the input. You get a nonlinear response. It is amplified.", - "It is much bigger. What I will do next is make VI that I apply smaller", - "and smaller. I have already done the boosting. Boom,", - "that's a boost. So I have boosted up your VI already.", - "Next is I am going to shrink it, and hopefully you will see that if", - "all that I am saying is truthful here you will see a triangular", - "response. Let's go try it out.", - "Watch the yellow. I am going to shrink the yellow and make it", - "smaller and smaller. There you go. It is great when", - "nature works like you expect it to. I have never seen a triangular wave", - "looks so pretty in my life. It is awesome. Look at this.", - "Here is a tiny triangular wave. And the output is also a triangular", - "wave but it is much more linear. Yes. Question? What's that? The", - "question is that the output here is only as big as the input used to be", - "before. That's a good question. What I have done here is I am", - "showing you a laboratory experiment. And let's assume that this input is", - "the input I am getting from some sensor in the field.", - "Assume that this is my input, not what I had before. Assume that", - "this is my input to begin with and this is the amplified output.", - "What I can also do is I can also change the bias.", - "And we will see this at the end of the lecture, in the last ten minutes", - "of lecture. How do you select a bias point? By changing your bias", - "point you can change the properties of an amplifier to give you a", - "preview of upcoming attractions. Let me ask you,", - "what do you think should happen if I change the bias point?", - "I have not shown you the math yet, so intuitively what do you think", - "should happen? If I increase the bias what do you", - "think is going to happen? Yes. Good insight. Higher bias", - "will be more amplification. Let's see if our friend is correct.", - "Let me set a higher bias.", - "Not necessarily,", - "I guess. You're actually right, by the way. I am playing a trick on", - "everybody here.", - "As I change my input bias. Notice that under certain", - "conditions my output becomes smaller and gets more distorted.", - "Under other conditions what is going to happen to my output is that", - "it is becoming smaller and is going to get distorted again.", - "So there are a bunch of funny effects happening that reflect on", - "the bias point, but for an appropriate choice of", - "bias point as I increase the bias the amplification should increase.", - "And I will show you that in a few minutes. But it is a complicated", - "relationship. Yes.", - "This is finally getting fun. Here is the question. Professor", - "Agarwal, we love your song and dance, but if you really want to get a high", - "signal at the output and you want to amplify your big input signal", - "how do you do it? So the question is let's say I have", - "an input that is this big here, if it is this big, I have shown you", - "how I can get things that are this big, but what if my input was this", - "big? How do I get an output that is this big? Well,", - "I will use one of those learned by questioning methods and have you", - "tell me the answer. Someone tell me the answer.", - "How do I do that? Yes. Use another amplifier.", - "So the answer is I will use one amplifier to go from here to here.", - "And the suggestion is use another amplifier to go from here to here.", - "And, in fact, I believe that you may have a problem in your problem", - "set where you will do that. And so you have only yourselves to", - "blame. So how do you make this work?", - "What you have to do is this VI has to be much smaller than the bias", - "point VI on this one. I have to build a different", - "amplifier, choose a different set of parameters such that VI prime,", - "which is the VI for this guy, is much less than V capital I prime for", - "this guy. It's a design question. You need to design it in a way that", - "the signals of interest need to be much smaller than the bias voltage", - "of this amplifier. So you may have to use much higher", - "supply voltages. My amplifier, I believe,", - "has a 4 volt supply or 5 volt supply. You might have to use an amplifier", - "with a much bigger supply, different values of RL and so on.", - "And I know that the course notes also have some exercises and problem", - "sets that discuss that in more detail. Yes. This is even more fun.", - "The question is, good question. The question is why do you need this", - "guy here? Just use this guy, right? Why do you need this guy?", - "Big guys rule, right? Who needs the little guys?", - "Well, let me use the Socratic method again. Why don't you give me", - "the answer? You guys are smart. Why do you need little guys? Why", - "do you need the small guy here? Anybody with the answer?", - "Yeah. The big guy may not be as sensitive. I like that.", - "You know what? He is almost correct. I will show you why in a", - "second. Anything else? Any other reason? Yes.", - "Bingo. That is another good answer.", - "So let me address both the answers. The answer given was that look,", - "this amplifier is amplifying the signal by a certain amount,", - "by a factor of 7. And I have designed this such that this", - "amplifies a signal by a factor of maybe 10.", - "So in all I am getting an amplification of 70.", - "This would be a great design question for lab next year.", - "I give you a bunch of components and ask you to design an amplifier", - "given the constraints with the highest amount of amplification.", - "It turns out that when you design your amplifier,", - "in order to meet the saturation discipline and so on,", - "you have to choose values of RL and VS and stuff like that and be within", - "power constraints so the amplifier doesn't blow up and stuff.", - "And by the end of it all you are going to get a measly 7X gain out of", - "it. The same way here, to be able to deal with a very small", - "signal here and get some amplification,", - "another set of values and you get 10X. So they multiply.", - "It is much harder to build one amplifier with a much larger gain.", - "You know what? I just realized that we will be looking at this in", - "the last five or seven minutes of lecture. I am going to show you", - "what the amplification depends upon. It depends upon K. It depends upon", - "RL. It depends upon VI. Now the question is I have had all", - "this time to think about how to stitch in sensitive into this,", - "and I believe I can. It turns out that when you have large voltages", - "and so on and you have practical devices, it turns out that the more", - "current you pump through devices they tend to produce noise of", - "various kinds. So very powerful amplifiers are not", - "very good at dealing with really tiny signals because they have some", - "inherent noise capabilities. And so I guess that is sensitive.", - "It is sensitive to noise. Another question? Yes.", - "Ask me the question again.", - "I didn't follow.", - "Let me just explain it. It turns out that I will not be", - "able to pass this through the big amplifier to begin with because it", - "is just going to give me a gain of just a factor of 7.", - "However, if I have a signal that is this big to begin with then I may", - "just need this amplifier. I don't need the smaller guy.", - "If my signal was this big to begin with, if I had a strong sensor that", - "produced a strong signal to begin with, yeah, I can deal with", - "just a single stage. I don't need to two stages.", - "It is all a matter of design. And it is actually a fun design", - "exercise. Given a budget, dollars, right? You go to your", - "supply room and look at the parts that you have and you go to build", - "what you have to build with the parts that you have.", - "And so sometimes you need to build two amplifiers to get the gain or", - "build a signal amplifier. It's all a design thing.", - "All right. Moving on to Page 7. That brings us to the small signal", - "model.", - "Page 5. What I showed you up on the little", - "demo was that provided the signal input in this example VI was much", - "smaller than capital VI out there as I shrank my input,", - "I was able to get a more or less linear response at the output.", - "And so to repeat my notation at the input, the total input is a sum of", - "the operating point input plus a small signal input.", - "This is called the total variable. This is called the DC bias. It is", - "also called the operating point voltage. And this is called my", - "small signal input. It is also variously called", - "incremental input. This is more a mathematical term", - "relating to incremental analysis or perturbation analysis.", - "So VI, call it small signal, call it small perturbation, call it", - "increment, whatever you want. Similarly, at the output I have my", - "total variable at the output a sum of the output operating voltage and", - "the small signal voltage. I do not like using Os in symbols", - "because big O and small O is simply a function of how big you write them.", - "It is not super clear. And in terms of a graph,", - "let me plot the input and output for you. Let's say this is the total", - "input and that is the total output. I may have some bias VI.", - "And corresponding to that I may have some bias VO. Hold that thought for", - "a second while I give you a preview of something that we will be", - "covering in about three or four weeks. Notice that as I couple", - "amplifiers together, the output operating point voltage", - "of this amplifier in this connection becomes the input operating point", - "voltage of this amplifier, right? So when they connect this output to", - "this input, the output operating point voltage becomes coupled to the", - "input here so it becomes the input operating point voltage here.", - "Now I have a nightmare on my hands. As I adjust the bias of this guy,", - "the bias of this guy changes, too. The two are dependent. It is", - "a pain in the neck. And we being engineers find ways to", - "simplify our lives. And you will learn another trick in", - "about three or four weeks. And that trick will let you decouple", - "these two stages in a way that you can design this stage in isolation,", - "go have a cup of coffee and then come back to this stage and design", - "this stage in isolation. For those of you who want to run", - "ahead and think about how to do it, think about it. What trick can you", - "use to get them in isolation? Moving on.", - "What I would like to do next is address this from a mathematical", - "point of view. And much as I did for the light", - "emitting expo dweeb analyze this mathematically and show you that if", - "VI is much smaller than capital VI, I indeed get a linear response.", - "This time around I won't use Taylor series because it turns out that", - "this expression can be expanded fully.", - "So you don't have to buy into Taylor series and so on.", - "I am going to list everything down for you. We know,", - "to begin with, that VO for the amplifier is VS-RLK/2 (VI-VT)^2.", - "What I am going to do for this, much as I did for the LED,", - "what I'm going to do is derive for you the output as a function of the", - "input when the input VI is very small.", - "In other words, when I substitute for VI,", - "V capital I squared plus small VI. Much as I did for the expo dweeb, I", - "want to substitute for VI a big DC VI. So VI is much smaller than VI.", - "And show you for yourselves that the output response,", - "V small O is going to be linearly connected to VI.", - "Notice that, let me write another equation here.", - "This is a total variable. This simply says that if the input", - "is VI then the output is going to be VO, which means that the operating", - "point input voltage should satisfy this equation,", - "correct? In other words, the operating point output voltage V", - "capital O should equal VS-RLK/2 (VI-VT)^2.", - "This is at VI equals capital VI. This is very simple but may seem", - "confusing. All this is saying is that look, this equation gives me", - "the relationship between VI and VO. Therefore, if I apply capital VI as", - "the input, I'm given that my corresponding output is capital VO,", - "so they must satisfy this equation, right?", - "Those are bias point values and that must satisfy this equation.", - "Simple. I know that. So hold that thought. Stash it away in the back", - "of your minds. Now let me go through a bunch of", - "grubby math and substitute for VI in this expression here.", - "Let me go ahead and do that. VS-RLK/2((VI+vi)-VT)^2. When I do", - "something that is other than math I will wake you up.", - "I will just keep doing a bunch of steps that are pure math.", - "No cheating. No nothing. Watch my fingers. When I do", - "anything that is not obvious math I will wake you up.", - "Next I am going to simply move VT over and rewrite this as follows,", - "RLK/2((VI-VT)+vi)^2. Again, I haven't done anything interesting so", - "far. I have just substituted this. I am just juggling things around", - "just to pass away some time, I guess. All right.", - "Next what I am going to do is simply expand this out and write it this", - "way RLK/2, expand that out and treat this as one unit VS -", - "RLK/2((VI-VT)^2+2(VI-VT)vi+vi^2). Nothing fancy here.", - "This is like the honest board. Nothing fancy here. Standard stuff.", - "Only math. I will move to this blackboard here where I do some fun", - "EE stuff. Yes.", - "Good. At least one person isn't asleep here.", - "Thank you. So just math here. Nothing fancy. Plain old simple", - "math. I have not done any trickery. I still have all my ten fingers.", - "Now what I am going to do, now watch me. I am not using Taylor", - "series here because this expression lends itself to this analysis.", - "Notice VI squared here. I made the assumption that VI is", - "much smaller than capital VI, so what I can do is assuming that VT", - "is small enough that VI minus VT is still a big number compared to small", - "VI, what I can do is ignore this in comparison to the capital VI terms.", - "So I have a capital VI term here. I am going to ignore VI squared.", - "So, for example, if capital VI was 5 volts and small", - "VI was 100 millivolts 0. , so 0.1 squared is 0.01.", - "So it is comparing 0.01 to 5. So I am off by a factor of 500.", - "So now watch me. Now I begin playing some fun and games here.", - "I eliminate this, and because I eliminate that it now becomes", - "approximately equal. What I do in addition is let me", - "write down the output. The total variable is the sum of", - "the DC bias and some variation of the output. And let me simply", - "expand that term and write it down again. VS-RLK/2(VI-VT)^2-RLK/2.", - "I get a two here. And I get VI-VT. I won't forget", - "the VI this time. Again, from here to there nothing", - "fancy. This is the one step where I have used a trick.", - "I have said small VI is much smaller than capital VI,", - "and so I have simply expanded this out and written it here.", - "So do you see the obvious next trick here?", - "From star look at this guy.", - "I can cancel this out from star because I know that at the operating", - "point these two expressions are equal, and so therefore I can cancel", - "out the operating point voltage and this.", - "What I am left with is small VO is simply minus RLK(VI-VT) times vi.", - "Only one place where I did something funny.", - "Other than that it is purely math. So this is what I get.", - "Notice that this whole thing is a constant, minus RLK(VI-VT).", - "This whole thing is a constant. And so VO is equal to some constant", - "times VI. Let me just define some terms for you that you will use", - "again and again. For reasons that will be obvious", - "next lecture, I am going to call this term here GM.", - "I am going to call this term a", - "constant, K(VI - VT). It is a constant for a given bias", - "point voltage. So I am going to call that GM.", - "And then I am going to call this whole thing A.", - "And of course this is VI. There you go.", - "I have my linear amplifier. A is the gain times small VI.", - "And the gain has these terms in it. I just call this GM. You will see", - "why later. But notice that the gain relates to RL.", - "The size of the load resistor RL, how big it is, 1K, 10K, whatever. K,", - "this is a MOSFET parameter, and VI minus VT.", - "That is a constant for a given bias point voltage and small VI.", - "So VO equals small VI.", - "I won't give you a graphical interpretation,", - "but I encourage you to go and look at Figure 8.9 in the course notes.", - "And it gives you a graphical interpretation of that expression.", - "Move to Page 7. Another way of looking at this,", - "another way of mathematically analyzing it, here I went through a", - "full blown expansion and pretty much deriving the small signal response.", - "What I can also do is take a shortcut here.", - "So let me just give you the shortcut. You might find this handy.", - "VO=VS-KRL/2(VI-VT)^2. And my shortcut is as follows.", - "My small signal response is simply this relationship.", - "I find the slope at the point capital VI and multiply by the", - "increment. Slope times the increment gives me the incremental", - "change in VO as follows. d/dI (VS-KRL/2(VI-VT)^2) evaluated", - "at vI=VI times vi. This is math again.", - "I want to find out the change in VO for a small change in VI,", - "and I do that by taking the first derivative of this with respect to", - "VI substituting V capital I and multiplying by the small change", - "delta VI or small VI. So this is simply the slope of the", - "VO versus VI curve at VI. And so therefore taking the", - "derivative here of this. This is a constant so it vanishes.", - "But twice 2 to cancel out, so I get KRL(VI-VT) times small vi", - "evaluated at capital VI. So I get twice KRL,", - "VI evaluated at capital VI, so it is VI minus VT times small VI.", - "Same thing. Oh, and I have a minus sign here.", - "I get the same expression that I derived for you up there,", - "and this is just taking the slope and going with it.", - "And this, as I mentioned before, this is A. The last few minutes let", - "me kind of pull everything together and also hit upon something that", - "many of your questions are touched upon.", - "And that all relates to how to choose the bias point.", - "So here I have taken an analysis approach. When teaching we often", - "teach you are given something, you analyze it, but as you begin to", - "master it you can begin to design things where you can ask a lot of", - "questions and so on. And here what we have is an", - "analysis given a value of RLK, VI and so on.", - "How to choose the bias point becomes more of a design issue.", - "If you are designing an amplifier, you asked me the question, how do I", - "choose two small amplifiers versus one big amplifier,", - "that sort of stuff? It boils down to how do you choose", - "the bias point? How do you choose VI?", - "How do you choose RL and so on? What I would like to do is touch", - "upon some of these things. First of all, gain or the", - "amplification. One of the most important design", - "perimeters for an amplifier is what is the gain? Let's say you get a", - "job at Maxim Integrated Technologies, and they say we would like you to", - "build a linear power amplifier for cell phones. You can say I know how", - "to do that. And then they say the next stage needs a 100", - "millivolt input. While this thing coming from the", - "antenna is only a few tens or a few hundreds of a microvolt.", - "So you sit down and say oh, my gosh, I need an amplification of", - "so much, and you go design an amplifier. So gain tends to be a", - "key parameter. And notice that gain is", - "proportional to RL. It relates to VI minus VT,", - "so proportional to VI. It is also related to RL.", - "The second point is the gain point determines where I bias something.", - "If I choose my bias too high I get distortion, or if I choose my bias", - "too low I get distortion.", - "So depending on how I choose my bias point, as a signal goes up it may", - "begin clipping or begin distorting. And I will show you a demo the next", - "time on that particular example. So bias point will determine how", - "big of a signal you can send without getting too much distortion.", - "And the other thing is that, relates to how big of an input,", - "what is a valid input range? So let's say you have a signal.", - "And you want that signal to have both positive and negative", - "excursions of the same value. Then, depending on where you choose", - "a bias point, your input range may become smaller or larger.", - "And we will go through these in the context of and amplifier and look at", - "some design issues in the next lecture." - ] -} \ No newline at end of file diff --git a/subs/9WOY2dHz5i4.srt.sjson b/subs/9WOY2dHz5i4.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/9WOY2dHz5i4.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/9bAUDWtsUkE.srt.sjson b/subs/9bAUDWtsUkE.srt.sjson deleted file mode 100644 index ee71e27a5d..0000000000 --- a/subs/9bAUDWtsUkE.srt.sjson +++ /dev/null @@ -1,398 +0,0 @@ -{ - "start": [ - 210, - 2420, - 5570, - 8930, - 12530, - 15130, - 18320, - 21090, - 22930, - 27010, - 27710, - 32770, - 37620, - 40130, - 41820, - 43850, - 48330, - 50890, - 52750, - 55680, - 57920, - 62680, - 65880, - 69760, - 71690, - 73260, - 76960, - 79730, - 82400, - 84210, - 88000, - 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2420, - 5570, - 8930, - 12530, - 15130, - 18320, - 21090, - 22930, - 27010, - 27710, - 32770, - 37620, - 40130, - 41820, - 43850, - 48330, - 50890, - 52750, - 55680, - 57920, - 62680, - 65880, - 69760, - 71690, - 73260, - 76960, - 79730, - 82400, - 84210, - 88000, - 89370, - 91940, - 95090, - 98650, - 100600, - 101680, - 107170, - 108370, - 113180, - 116660, - 119100, - 122830, - 125730, - 130509, - 131910, - 135140, - 138390, - 140890, - 143820, - 146880, - 149460, - 151750, - 155890, - 156540, - 159790, - 161890, - 167170, - 171160, - 177815, - 179510, - 182280, - 183920, - 188130, - 189530, - 193470, - 197510, - 201245, - 204430, - 208956, - 213830, - 214780, - 217640, - 219770, - 224350, - 226850, - 230110, - 232610, - 235270, - 236520, - 241170, - 244200, - 247150, - 249260, - 252150, - 256800, - 260240, - 262470, - 266330, - 267860, - 271280, - 274920, - 277880, - 279710, - 281760, - 285160, - 289220, - 292680, - 296890, - 298490, - 303230, - 306510, - 308777, - 311650, - 315870, - 320940, - 324050, - 326490, - 328780, - 331280, - 332820, - 335400, - 338620, - 341430, - 345500, - 348630, - 352335, - 355910, - 359730, - 363180, - 365400, - 369220, - 372480, - 377750, - 381520, - 384570, - 388780, - 391360, - 392440, - 396330, - 397580 - ], - "text": [ - "PROFESSOR: In the previous segment, we saw that circuits", - "composed of linear elements were, themselves, linear.", - "In this segment, we will see that linear circuits or linear", - "systems can be analyzed with extremely powerful techniques.", - "We will study two of these properties of circuits,", - "homogeneity and superposition, in this segment.", - "Let's start by studying the property of homogeneity.", - "So what does homogeneity mean?", - "Supposing we have a system with a bunch of inputs one", - "output here.", - "And let's say the inputs are x1, x2, and so on.", - "And for these xes let's say the corresponding output is y.", - "Let me add a little cartoon here, just to", - "make it easy to follow.", - "As they say, a picture is worth 1,000 words.", - "So let's say, if you have apple as an input and you get", - "a different kind of apple as an output, then let's look at", - "what the property of homogeneity says.", - "If I take the same system and if I", - "multiply each of the inputs--", - "x1, x2, and the old output, y-- if I multiply each of the", - "inputs with some constant, alpha, then the property of", - "homogeneity says that the output will also be multiplied", - "by the same value, alpha.", - "So this is the homogeneity property.", - "And in terms of our picture, if you have an Apple and you", - "took a fraction of the apple out, then your output would", - "also have the same fraction of the apple out.", - "So this is the homogeneity property.", - "Next let's look at another extremely powerful technique,", - "superposition.", - "Now superposition is a property of linear circuits,", - "and let's first understand what this property means.", - "So supposing I have a system here.", - "And what I'll do is I'll apply two sets of", - "inputs to the system.", - "So in the first set, let's say I apply the a set of inputs,", - "x1a, x2a, and so on.", - "And let's say that that gives rise to the a set of outputs.", - "And then if I take the same system--", - "just to make it clear, let me mark it as s.", - "If I take the same system and I apply a b set of inputs--", - "so x1b, x2b, and so on--", - "and if I get a corresponding output, yb, then what can we", - "say about the resulting system?", - "And just to make it very clear, going back to our", - "pictures and cartoons here, let's say the a set of inputs", - "corresponds to apples, a for apples.", - "And the b set of inputs goes on to blueberries.", - "So jokingly here, if I feed a bunch of apples to the system", - "and I get applesauce at the output, and on the other hand,", - "if I feed a bunch of blueberries to the system and", - "I get blueberry sauce at the output, then let's do some fun", - "stuff here.", - "Suppose I take the same system and I feed through the system", - "the sum of both of these inputs.", - "In other words, if I feed it x1a, x2a, and so on, and I add", - "to each corresponding input the b set of inputs, so I get", - "x1b here and x2b here-- so notice that this is here, and", - "the b set of inputs is here.", - "So notice that all I've done is I've added up", - "corresponding inputs.", - "What superposition tells me is that my outputs will be a sum", - "of the corresponding inputs.", - "In other words, if I had ya with the a set of inputs", - "alone, and I had yb with the b set of inputs alone, then if I", - "sum the corresponding inputs, the a and the b inputs, then", - "my output will be a sum of the corresponding outputs as well.", - "And again, jokingly, if I feed apples and blueberries to the", - "input, then in this case, jokingly again, maybe I get", - "mixed fruit jam.", - "How does this yield something interesting for us?", - "Let me do a specific example of the property of", - "superposition and see how this will yield a very interesting", - "technique to analyze linear circuits.", - "Again, remember, both the homogeneity and superposition", - "property applies to linear circuits.", - "So let me take a specific instance of", - "superposition here.", - "And so I take some system, a linear system, and let's say I", - "have two inputs that I apply, v1 and v2.", - "And let's say my goal is to find out what the output is.", - "What I want to show you is that, by the method of", - "superposition, I can use a divide and conquer technique.", - "What I can do is I can take the same system and I can set", - "the v2 output to 0 and apply just the v1.", - "And I measure the corresponding output, y1.", - "So y1 here is the partial output, given that I have", - "applied a v1 alone.", - "Similarly, I take the same system and in this case,", - "second time around, I set v1 to 0, and I apply v2 alone.", - "And then let's say I get y2 as my output", - "with v2 acting alone.", - "Then here is something very interesting.", - "So by superposition from a previous example, recall that", - "if I took one set of inputs and a second set of inputs and", - "I summed up the corresponding values, then superposition", - "said my output would be a sum of the individual outputs with", - "just each of those applied alone.", - "In other words, if I show the v1 as 0 and then if I sum to", - "that the second set of inputs, 0 and v2 from here, so that", - "this got applied here and the first set of inputs got", - "applied here, then what superposition would say is", - "that my output would be a sum of the two partial outputs.", - "In other words, y1 would come from here and y2 would be the", - "same as the y2 with the v2 applied alone.", - "So this is an extremely powerful idea.", - "So to recap, what have I done here?", - "I have used a method of superposition to apply a set", - "of inputs in the following way.", - "I started by saying that I have a circuit and I want to", - "apply v1 and v2 to it and compute the output.", - "Now rather than trying to solve the circuit by applying", - "both v1 and v2, what I did was I broke it up into two", - "sub-problems. In the first sub-problem, what I did was I", - "applied v1 alone and set v2 to 0, and then in the second", - "sub-problem, I applied v2 alone and I set v1 to be 0.", - "And I computed the two partial outputs, y1 and y2.", - "The method of superposition then says that if I took the", - "two corresponding sets of inputs and summed them up,", - "then my output would be a sum of the two partial outputs.", - "Notice that at the input here, if you look at these two", - "inputs, the v1 plus 0 is simply the v1, v2 plus 0 is", - "simply v2, which is the same as what I have here.", - "So in other words, I was able to solve the circuit that", - "contained v1 and v2 as inputs by applying just v1 alone and", - "then v2 alone, and then by summing up the two", - "corresponding outputs.", - "This will yield an incredibly powerful method for us called", - "the method of superposition." - ] -} \ No newline at end of file diff --git a/subs/9hfDCIJtT-4.srt.sjson b/subs/9hfDCIJtT-4.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/9hfDCIJtT-4.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/AEwvgztBf44.srt.sjson b/subs/AEwvgztBf44.srt.sjson deleted file mode 100644 index 2adde89104..0000000000 --- a/subs/AEwvgztBf44.srt.sjson +++ /dev/null @@ -1,533 +0,0 @@ -{ - "start": [ - 720, - 2900, - 5630, - 13420, - 15332, - 22180, - 26210, - 29820, - 33700, - 40430, - 41620, - 46490, - 48220, - 49340, - 51356, - 56980, - 60470, - 65045, - 68245, - 71970, - 76360, - 78970, - 82350, - 83930, - 84742, - 89520, - 93440, - 97280, - 99890, - 101520, - 104900, - 107890, - 109980, - 111990, - 115760, - 118600, - 121590, - 123930, - 127070, - 130220, - 132140, - 133905, - 135460, - 139350, - 140990, - 144760, - 148480, - 149760, - 153500, - 156260, - 158920, - 163150, - 165940, - 168990, - 174090, - 176080, - 186760, - 191610, - 194060, - 201090, - 202620, - 208240, - 210200, - 210995, - 213130, - 213940, - 214860, - 216990, - 219540, - 220710, - 224310, - 226120, - 229150, - 230900, - 232610, - 233830, - 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"lumped elements by the vi characteristics, OK?", - "You apply a voltage, measure the current, So what I can do", - "is I can plot i here and v here and see", - "what it looks like.", - "I can characterize elements by their vi relationship, and", - "there are a bunch of elements that I can create based on the", - "vi relationship.", - "So let me show you a few examples.", - "So for the resistor, since v is directly proportional to i,", - "and r is the constant, I get a straight line.", - "That's the i-axis, the v-axis, and this is a resistor.", - "What I actually have is a variable resistor, so I'm", - "going to change the resistance value r, and the curve will", - "also change slope.", - "I change the value r because it's a variable resistor, and", - "it changes slope because my r is different.", - "Next, let me go to--", - "LORENZO: Fixed.", - "ANANT AGARWAL: --a fixed resistor, and this guy here on", - "the screen to your left, I guess, is a fixed resistor.", - "And you see that its iv characteristic is a line of a", - "given slope, 1 by r, and that's it.", - "I can't change it.", - "Number three, I have another lumped element, called a Zener", - "diode, that you will see in the fourth week of this class.", - "And the characteristics for the Zener", - "diode look like this--", - "i, v. If my voltage goes across, that Zener diode goes", - "up slightly, the current shoots up.", - "But if the voltage becomes negative, I don't have any", - "current flowing through it until the voltage passes some", - "threshold, at which point my current begins to build up.", - "So you can increase voltage a little bit, and you can show", - "that the current starts building up again.", - "So that's another interesting lumped element", - "called a Zener diode.", - "Let's switch to the next one called a diode.", - "So a diode looks like this--", - "i, v. If the voltage across the diode becomes positive,", - "around 0.6 volts or thereabout, the current begins", - "to shoot up.", - "But if the voltage is below that threshold of 0.6, then my", - "current is almost zero.", - "It's another lumped element called a diode.", - "And you will begin using these elements in your 002 lives to", - "build interesting systems.", - "Next example is a thermistor.", - "A thermistor is a resistor whose resistance varies with", - "temperature, OK?", - "So this is a very expensive little drier, hair drier.", - "And what I'm going to do is blow some hot air at my", - "resistor, and you're going to see that its value is going to", - "change depending on how much I heat it.", - "As it cools down--", - "let me cool it down.", - "So you can see it's coming down.", - "I can zap it again.", - "[TURNS ON DRYER]", - "ANANT AGARWAL: I could do this all day.", - "This is so much fun.", - "[LAUGHTER]", - "ANANT AGARWAL: OK, so that's a another", - "interesting lumped element.", - "As the temperature rises, its resistance changes.", - "LORENZO: Photo.", - "ANANT AGARWAL: Next thing is called a photoresistor.", - "It's a resistor.", - "It used to be a resistor, Lorenzo?", - "LORENZO: Yeah.", - "OK, that's fine.", - "ANANT AGARWAL: So this is a photoresistor.", - "And notice that it almost behaves like an open circuit.", - "Well, what I'm going to do is shine some light on it.", - "When I shine light on it, it begins to conduct and becomes", - "a resistor of some value.", - "There you go, OK?", - "So that's a photoresistor.", - "LORENZO: Now, we go to the--", - "ANANT AGARWAL: So now I'm going to show you a battery.", - "Notice, we didn't talk about batteries before.", - "I'll show you a battery.", - "So before we show a battery, just think in your own minds,", - "what should the iv characteristic of a", - "battery look like?", - "i, v, a battery supplies a constant voltage.", - "You know, your little cell, your double A", - "battery, 1.5 volts?", - "So think about what the iv characteristic of a battery", - "should look like for three seconds before", - "I show it to you.", - "And so I show it, Lorenzo.", - "It's a straight line.", - "This is a good battery.", - "It's a straight vertical line, which says that the voltage is", - "1.5 volts or thereabouts no matter", - "what current it supplies.", - "As an ideal voltage source, it as a fixed voltage v no matter", - "what the current going through it is.", - "Now I'll show you a dud, a bad battery.", - "And this is what the bad battery looks like.", - "So many of you had a your car batteries die on you, and when", - "you go to the store, they check your batteries.", - "They use exactly this principle, that dead batteries", - "have resistance.", - "Whenever you see slopes here, you're thinking of resistance,", - "They can use this property to figure out that", - "your battery is dead.", - "So that's a dead battery.", - "And finally, let me show you a bulb.", - "We started with a bulb, and so I need to end--", - "OK.", - "We started with a bulb, so we need to end with a bulb.", - "And what you'll see is that a bulb is simply--", - "behaves like a resistor.", - "It's iv curve is going to look like this.", - "OK, notice, this is my bulb, and guess what?", - "It behaves like a resistor.", - "It's a very interesting kind of resistor.", - "So I won't go into details for now, but notice its iv", - "characteristic behaves like a resistor, OK?", - "So those are some pretty standard lumped elements.", - "You'll deal with a lot more set of lumped elements--", - "switches, MOFETs, capacitors, inductors, a bunch", - "of other fun stuff.", - "But before we do that, what I wanted to tell you is that", - "don't go berserk on this abstraction binge, OK?", - "Too much of anything is bad for you.", - "So what I'm going to show you is abstractions or models are", - "only valid provided you work within a set of constraints.", - "Notice, we've already had this tacit handshake, which said", - "that we'll follow the discipline, OK?", - "Even after we follow the discipline, there are ranges", - "to how well physical elements can behave like", - "ideal lumped elements.", - "For example, what I'm going to do is show you as a resistor.", - "And it's going to look like a resistor, and I'm going to", - "keep the voltage around it.", - "What's going to happen at some point?", - "I just keep doing that.", - "If it's an ideal element, if you're a theorist, you'll say,", - "oh yeah, the curve will keep extending", - "until I reach infinity.", - "But this is a practical resistor, so, you know.", - "The people out here, you're going to have to cover your", - "eyes or something.", - "So your abstraction can predict that.", - "It says the current is an amp.", - "It can predict the heat, light, or the smell.", - "Because in the laboratory, when you get the smell, you", - "know what somebody has just done.", - "They blown the resistor.", - "So that's one example of a lumped", - "abstraction breaking down.", - "So if I really believe in my own BS, anything's a lumped", - "element, so here's a pickle.", - "[LAUGHTER]", - "ANANT AGARWAL: A pickle's a lumped element.", - "I can treat it as a lumped resistor.", - "But this is a very interesting lumped resistor.", - "[LAUGHTER]", - "ANANT AGARWAL: Don't try this at home.", - "This is a standard pickle into which we are", - "pumping 110 volts AC.", - "[LAUGHTER]", - "ANANT AGARWAL: I promise you, this is a standard pickle.", - "So as you can tell, it has a fixed resistance, but your", - "lumped abstraction cannot predict the nice light and", - "sound effect.", - "[LAUGHTER]" - ] -} \ No newline at end of file diff --git a/subs/AfQxyVuLeCs.srt.sjson b/subs/AfQxyVuLeCs.srt.sjson deleted file mode 100644 index 229da9555d..0000000000 --- a/subs/AfQxyVuLeCs.srt.sjson +++ /dev/null @@ -1,1997 +0,0 @@ -{ - "start": [ - 0, - 4400, - 8922, - 15033, - 22366, - 28111, - 35195, - 38123, - 41620, - 44954, - 48858, - 52762, - 57397, - 62870, - 67407, - 71111, - 75277, - 80185, - 84259, - 90000, - 93539, - 97230, - 101447, - 104158, - 108150, - 111012, - 114025, - 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How do we define,", - "what is engineering? Well, the definition I like to", - "use is one put forth by Steve Senturia, one of our professors", - "who is now retired. He defined engineering to be", - "the purposeful use of science. All right, so what is 6.002", - "about? So, 6.002 is a first course in", - "engineering. And I like to view 6.002 as the", - "gainful employment of Maxwell's equations.", - "Many of you have seen Maxwell's equations before.", - "Most of you should have. And they are hard stuff.", - "6.002 is all about teaching you how to simplify our lives,", - "make things simple. So, if you can gainfully employ", - "Maxwell's equations, gainfully employ the facts of", - "nature to build very interesting systems.", - "So let me show you how the transition is made.", - "So, there's a world around us, nature, so we made some", - "observations in nature. We make measurements,", - "and we can write down large tables of measurements.", - "So, for example, we can take objects and measure", - "the voltage across them, and look at the resulting", - "current through the elements. So, we may end up getting a", - "bunch of values such as [CHALKBOARD].", - "So, we start out life with making measurements on what", - "exists. And we build a bunch of tables.", - "Now, we could directly take these tables,", - "and based on observations of these tables,", - "we could go ahead and build very interesting engineering", - "systems that help us out in day-to-day lives.", - "But that's incredibly hard. Imagine having to resort to a", - "set of tables to do any kind of useful work.", - "So what we do as engineers, we first layer a level of", - "abstraction. We look at all the data,", - "and somehow layer abstraction such that we can simplify or", - "much more succinctly put in a simple equation or a simple", - "statement what these numbers are telling us.", - "OK, so for example, our physics laws,", - "so laws of physics for example are simply abstractions,", - "the laws of abstractions. So, these sets of numbers can", - "be codified by Ohm's law, for example,", - "V is equal to RI, the voltage current,", - "relates to the resistance of the object.", - "So, V is equal to RI is a law that succinctly describes a set", - "of experiments, and replaces a large number of", - "tables with a very simple statement.", - "You could call this the law, or you could call it an", - "abstraction. OK so you see laws of physics,", - "call them abstractions of physics if you like.", - "Similarly, there are Maxwell's equations and so on and so", - "forth. So, this is what is.", - "This is what's out there. OK, and a law as an abstraction", - "describe the properties of nature, as we see it,", - "in some succinct form. Now, if you want to go and", - "build useful things, we could take these", - "abstractions, take Maxwell's equations,", - "and go and build things. But it's hard.", - "It's really, really hard.", - "And what you learn in, at MIT is this place is all", - "about simplifying things. Take complicated things,", - "build layers of abstraction, and simplify things so that we", - "can build useful systems. Even in 6.002 we start life by", - "making a huge leap from Maxwell's equations to a couple", - "of very, very simple laws. OK, I'm going to show you that", - "leap that we will make today. So, the first abstraction that", - "we layer is called the lump circuit abstraction.", - "OK, in the lump circuit abstraction, what we do is we", - "make a set of simplifications that allows us to view a set of", - "objects as discrete or lumped elements.", - "So, we may, I will define voltage sources.", - "We'll define resistors. We'll define capacitors,", - "and so on. OK, and I'm going to make the", - "jump, and show you how we make the jump in a few minutes.", - "So, on that sort of abstraction, we then layer yet", - "another abstract layer. And let me call that the", - "amplifier abstraction. OK, remember,", - "here we are absolutely down and dirty.", - "We are setting the probes, measuring objects,", - "and building huge tables. We abstracted things into", - "simple laws, and life got a little better.", - "OK, I'm going to show you can abstract things further out and", - "build discrete objects, and, you could build even more", - "interesting components called amplifiers and begin playing", - "around with amplifiers. OK, so when you are using", - "amplifiers, you don't really have to worry about the details", - "of Maxwell's equations. OK, I'll give you some very", - "simple abstract rules of behavior for an amplifier,", - "and you can go build very interesting systems without", - "really, really knowing how Maxwell's equations applies to", - "that because you will be working at this abstract layer.", - "However, since you're engineers, and you are good at", - "building such systems, it's very important for you to", - "understand how we make this leap from the laws of physics into", - "some of our very primitive engineering abstractions.", - "So, once we make the amplified abstraction in 6.002,", - "by the way, 6.002 starts here. We start from the laws of", - "physics and then proceed all the way out.", - "So, once we talk about amplifiers we will take two", - "pads. On the amplifier,", - "you will build the next abstraction called the digital", - "abstraction. OK, and with the digital", - "abstraction, we will build new elements such as inverters and", - "combinational gates, OK?", - "So, notice we are building bigger, and bigger things,", - "which have more and more complicated behavior inside", - "them, but which are very simple to describe, right?", - "So, following the digital abstraction, we will superimpose", - "the combinational logic abstraction on top of that,", - "and define functional blocks that look like this:", - "some inputs, some function,", - "some outputs. The next abstraction on top of", - "that will be the clock digital abstraction, where we will have", - "some notion of time introduced into the system.", - "There will be a clock, and this will be some function.", - "And there will be a clock that introduces time into the sort of", - "logic values that functions operate upon.", - "Following that, the next level of abstraction", - "that we build is called instruction set abstraction.", - "OK, now you begin to see things that consumers get to look at.", - "Can someone give me an example of, or name an instruction set,", - "or instruction set abstraction? Bingo.", - "So, x86 is one set of abstractions.", - "And in fact, in many universities,", - "education could well start just by saying, OK,", - "here's an abstraction. These are the x86 instructions,", - "OK? Some MIT gurus have designed", - "this awesome little microprocessor,", - "OK? So you just worry about,", - "you take this abstraction layer here, the assembly instructions,", - "and you go and build systems on top of that.", - "OK, so this is an abstraction layer called the x86 layer.", - "There are other abstraction layers.", - "In 6.004, you will learn about, I believe, the alpha or the", - "beta, OK, and various other abstractions at this point.", - "So, 6.002 kind of goes until here.", - "6.002 takes me from the world of physics all the way to the", - "world of interesting analog and digital systems.", - "OK, 004, the course on computation structures,", - "will show you how to build computers all the way from", - "simple digital objects all the way to big systems.", - "Following that, you learn about language", - "abstractions, Java, C, and other languages,", - "and that's in 6.002. And there are several other", - "courses that will cover that. Following this,", - "you learn about software system abstractions,", - "and software systems, you will learn about operating", - "systems. Any example of an operating", - "system abstraction that people know out there?", - "What's that? Linux.", - "What else? I'm just wondering how long", - "I'll have to go before I hear what I want to hear.", - "[LAUGHTER] OK, so we have a bunch of software", - "systems. So, if we have a bunch of", - "software systems, these are nothing but", - "abstractions. Linux simply implies a set of", - "system calls that the programs must adhere to.", - "Windows is another set of system calls.", - "That's it. And see how much money they", - "made out of it? OK, it's all about abstraction", - "layers, that all start from nature.", - "All right? Build abstraction upon", - "abstraction upon abstraction upon abstraction,", - "and someone out here are lots of dollars.", - "OK, so based on these abstractions,", - "we can then build useful things for human beings.", - "We can build very useful things, video games,", - "so we can send space shuttles up, and a whole bunch of other", - "systems. But it's based on these", - "abstraction layers. What's unique about education", - "at MIT? What's unique about 6.002 and", - "EECS? Is to my knowledge,", - "there are not many other places in the world where you will get", - "an education in everything going all the way from nature to how", - "to build very complicated analog and digital systems.", - "OK, we will show you layer upon layer upon layer upon layer,", - "peel away the onion until you are down to raw nature,", - "OK, through Maxwell's equations.", - "So, 6.002, 004, this is 033,", - "OK, 6.170, and so on. OK, the whole EECS is about", - "building abstraction layers, one on top of the other.", - "So that's one path. There's the analog path.", - "The analog path would take an amplifier, and build an", - "abstraction layer called the op-amp.", - "See how similar they all look? You know the amplifier,", - "the inverter of the digital world, and the operational", - "amplifier in the analog world, just different ways of looking", - "at the same devices. So, to build an analog system,", - "to build an operational amplifier, and then,", - "here we go end up building a whole bunch of different", - "interesting analog system components.", - "OK, and these components might look like oscillators.", - "They might look like filters. OK, they look like power", - "supplies, a whole bunch of very interesting abstract components,", - "which pulled together can then give you the next set of", - "systems. And these systems might be", - "toasters, or say for example other analog systems like the", - "various control systems for various power plants and so on", - "and so forth, and ultimately,", - "fun and dollars. OK, so 6.002 is about going", - "from physics all the way to this point.", - "We will build interesting analog systems,", - "and take you up to interesting digital system components,", - "from which 004 will take you all the way to building computer", - "architectures. So that, in a nutshell,", - "kind of gives you a feel for the space of EECS.", - "OK, this chart here is almost a vignette of what EECS at MIT is", - "all about. And this is the world according", - "to Agarwal, because he's teaching 002.", - "OK, so this is 6.002, and the rest of EECS is", - "somewhere out there. OK, so I'm going to do now is", - "throughout this course; I want you to think about which", - "part in this vignette we are in. So, right now,", - "I'm going to start here and take you here.", - "OK, and as you get closer and closer, things get simpler,", - "and simpler, and simpler.", - "Still, the final abstractions are pedal, brake,", - "steering wheel. I mean, that's the abstraction", - "to play a game, right, four or five very simple", - "interfaces, and that's all you need to know.", - "And everybody in the world can play stuff.", - "So remember, this stuff is complicated.", - "This stuff is very, very simple.", - "OK, and the more we build abstractions and come to this", - "side, things get simpler and simpler.", - "So, a large part of what I'll cover today is make the biggest", - "simplification. The biggest simplification we", - "will make his go from Maxwell's equation to some very,", - "very simple algebraic rules. OK, I did Maxwell's equations", - "myself. And I tell you,", - "they were very interesting stuff but complicated.", - "I can't imagine building efficient systems using", - "Maxwell's equations. So, let's take an example,", - "OK? So, let's say I have a battery.", - "Just switch to page three of your course notes.", - "And let's say I connect that to a bulb.", - "OK, and this is a wire. And, the battery supplies some", - "voltage, V, and I ask you a simple question.", - "What is the current through the bulb?", - "OK, so here is something that I can build using objects.", - "I can pick a round from stores and so on.", - "And I can collect them up in this way, and ask the question,", - "what is the current, I?", - "Now, if all you've done is learn about Maxwell's equations,", - "you can roll up your sleeves and say, ah-ha!", - "The first step is to write down all of Maxwell's equations,", - "and you can say, del cross E is minus del and go", - "on, and on, and on, OK, and write out all of", - "Maxwell's equations and say, now how do I get from there to", - "here? OK, it's very good.", - "You can do it. OK, you can do it,", - "but it's very complicated. OK, so instead,", - "what you're going to do is take the easy way.", - "So, what I want to remind you is that this course is actually", - "very easy. OK remember,", - "we're going to be building abstraction upon abstraction to", - "make your lives easier. If you think your lives are", - "getting more complicated, then you are not using", - "intuition enough. OK, just remember the big I", - "word. It's all about making things", - "simple. OK, so let me give you an", - "analogy. So, suppose you have an object.", - "OK, and I apply a force to the object.", - "It's an analogy, OK to get some insight into how", - "to do this. So, I say here's an object.", - "I apply a force, and I ask you the question.", - "What is the acceleration of the object when I apply a force,", - "F? So, how would you do it?", - "OK, and eighth, or ninth, or tenth grader can", - "do this. OK, they would ask me,", - "what's the mass of the object? OK, I ask you what is the", - "acceleration? You would turn around and ask", - "me, what is the mass of the object?", - "I tell you, the mass of the object is M.", - "And then you say, oh sure, A is F divided by M,", - "done. It's as simple as that.", - "OK, I could have gone into all kinds of differential equations", - "and so on to figure that out, but you asked me for the mass.", - "And you gave me the answer, A is F divided by M.", - "So, you ignored a bunch of things.", - "You ignored the shape of the object.", - "You ignored its color. You ignored its temperature.", - "OK, and you ignored the soft or hard or whatever.", - "OK, you ignored a whole bunch of things.", - "You were focused on one thing. OK, you're focused on its mass.", - "And, it turns out that the process really was developed", - "from a set of simplifications. That is called,", - "does anybody remember this? Point mass simplification.", - "OK, so, in physics, you've done this before.", - "OK, you've simplified your lives by viewing objects as", - "having a mass at a point, and force is acting at that", - "point. OK, M is that property of the", - "object that is of interest to you.", - "This process is called, in physics, point mass", - "discretization. OK, now using an analogy,", - "and I'm going to show you a similar simple process to do the", - "problem with the light bulb. OK, so take my light bulb", - "again,", - "And I focus on the filament of the light bulb.", - "OK, all I care about is the current flowing through the", - "light bulb. OK, I don't care about whether", - "the filament is twisted, whether it's hot.", - "I don't care about its shape. I don't care about its color.", - "All I care about is the current.", - "OK, so to do that, what we can do here at a very", - "high level is since we just need the current and don't care about", - "a bunch of other properties, we will simply replace the bulb", - "with a discrete object called a resistor.", - "So the discrete object is a resistor, much like the point", - "mass simplification that we did earlier that replaced the bulb", - "filament with a object called a resistor, a discrete object", - "called a resistor. Or a lump object called", - "resister, and put a value next to it just like the mass for the", - "object, a resistance value, R.", - "OK, now what I can do is in the same manner, replace the battery", - "with an object called a battery object, and connect that here,", - "the voltage, V, applied to it.", - "V falls across the resistor, and I get my I simply from", - "Ohm's law as we divide by R. So, notice here,", - "to replace this complicated bulb, this really twisty,", - "weird old thing with this discreet thing called a", - "resistor, and its only property of interest was its resistance", - "value, R, direct analogy to what we did there.", - "So, since R represents the only property of interest,", - "we can simply ignore all the other things.", - "So, notice here, we've done things the simple", - "way. And remember,", - "in EE, in the electrical engineering, we do things the", - "simple way. OK, we could go the hard route", - "and do Maxwell's equations, and get PhD's in physics,", - "and so on. But out here,", - "we are looking to do useful, interesting systems in the", - "simplest way that we can. OK, we do things a simple way.", - "All right, so we just did this, and boom, I found out what the", - "current was. Now, I cheated a little bit.", - "I've cheated a little bit. R is a lumped abstraction for", - "the bulb. So, you look at this resistor", - "here. That is simply a placeholder.", - "It's a stand-in for this complicated thing called a bulb.", - "It's a discreet object. It's a lumped object,", - "and represents the bulb. Now, so most of 6.002 will take", - "off from here, OK, and that's it.", - "To very simple stuff, like V is equal to IR,", - "it's a simple high school algebra to take off in that", - "direction. But before we go there,", - "it's important to understand, why was it that we were able to", - "make the simplification? OK, we did something else.", - "Something's going on under the covers here.", - "On the one hand, I say let's use Maxwell's,", - "and then I jump out and say, hey, we can just use this", - "simple thing. I did something that allowed me", - "to go from here to here. And you need to understand why", - "I did that and how I did that. Understand it once,", - "and then you won't have to need that information again.", - "You just need to understand it. So, let's take a closer look at", - "the bulb filament, and look at what we really did.", - "So, here's my filament, A, and let's say that the", - "surface area here, I label that SA,", - "and the one down here SB, my voltage, V,", - "applied there, and this is what I call my", - "black box that I've replaced with a resistor.", - "Notice that, in order for this to work,", - "V and I need to be defined. So I needs to be defined,", - "and V needs to be defined. OK, if I give you a random", - "object, and I don't tell you anything else about the object,", - "it's not clear I can do that. OK, if it's a much more general", - "situation, I have to write down Maxwell's equations,", - "and this is what I would write down.", - "Write down J dot dS as a function of the coordinate here", - "integrated over the area minus, OK, I would have to start from", - "there from one of Maxwell's equations.", - "All right, notice that this becomes IA, and this becomes IB", - "in our simplification. But, if I don't tell you", - "anything else, you have to start from here.", - "You will have some varying current here by point.", - "You might have some other current coming out here because", - "I may have some charge buildup happening inside.", - "If charge is building up inside the filament;", - "then I would have to put del q by del t out here,", - "right, the current in minus the current out must equal charge", - "buildup. Whoa, where is this and where", - "is that? So this is reality.", - "This is really, really what I have to do.", - "But how did I get there? How did I get there?", - "The key answer is, as engineers,", - "when in doubt we simplify. Remember, we are engineers.", - "Our goal in life is to build interesting systems.", - "OK and some are motivated by money.", - "OK, so our goal is to build interesting systems and do good", - "to humanity. So, as long as we can build a", - "good light bulb, we are happy.", - "So what we can do is we can say, look, all I care about is", - "building interesting systems. So I can say,", - "hey, this stuff is too hard. Let's make the assumption that", - "all the systems that we will consider will have this thing be", - "zero. OK, in other words,", - "if I take a complete object, if I take an element like a", - "resistor or a capacitor, the box around the entire", - "element, OK, and I want to just deal with those systems in which", - "this thing is zero. You can come and beat me up and", - "say, but why? Why not?", - "Why am I doing this? And I am saying the world is", - "arbitrary. I'm an engineer;", - "I want to build good systems. By making this simplification,", - "I eliminate this squiggle thing, and so on.", - "I don't want to deal with it. I want to make my life simple.", - "So this is gone to zero because, why?", - "Because I have said that in the future I will only deal with", - "those elements for which this is true.", - "I'm going to discipline myself. I'm going to discipline myself", - "to only deal with those systems. OK, Maxwell is turning around", - "and, you know, mad at me and all that stuff,", - "but tough. So this, what I've said about", - "making a simplification here, and this is one of the", - "simplifications I'm making. And I give a name to the", - "simplification. And that's called the lumped", - "matter discipline. OK, so I'm saying I will only", - "deal with elements for which if I put a black box around it,", - "this is going to be true. And if this is going to be", - "true, then notice, there is no charge buildup.", - "Current in must equal current out.", - "Ah-ha! So this becomes IA.", - "This becomes IB. Yes.", - "OK, I can now deal with IA's and IB's.", - "And IB and IA are equal because this is zero.", - "Notice that there is a whole bunch of depth here in the jump", - "from here to here. As MIT graduates,", - "you really, really need to understand why it is that we", - "made that jump, and then go and use that,", - "and do cool things. All right, this allows us to", - "define I. We have a unique I associated", - "with an element for the current through the element.", - "We still have to worry about B, and I won't go through that in", - "detail. The course notes have some", - "discussion of that and so does the textbook.", - "So V, AB is defined when del phi B, the rate of change of", - "magnetic flux is zero. So, if I take the element and I", - "take any region outside the element, this must be true.", - "And you say, why should that be true?", - "That's not true in general. Absolutely.", - "It's not true in general. But I, because I choose to,", - "I going to deal with only those elements.", - "I will discipline myself. But these are only those", - "elements for which this is true, and this is true.", - "I'm going to limit my world. I'm going to create a play", - "field for myself. You want to play;", - "follow my rules. OK, and that's called the", - "lumped matter discipline. So once you say that I'm going", - "to adhere to the lump matter discipline, and this is true", - "inside your elements. This is true outside the", - "elements. You can define VA and VB,", - "and good things happen to you. OK, let me show you a few", - "examples of lumped elements. But remember,", - "a large part of what we're doing is based on these two", - "assumptions. And to just go through the", - "background on that, I would encourage you to go to", - "chapter 1 of your course notes and read through just as how", - "this came about, that comes about.", - "So, by doing that by adhering to a lumped matter discipline,", - "we can now lump objects. We could lump a bulb into a", - "resistor. OK, so to be clear,", - "a certain number of lumped objects, and now,", - "the universe is going to be comprised into lumped objects.", - "OK, so before this, when he went home,", - "we talked about eggs, and omelets,", - "and light bulbs, and switches,", - "but once you come to MIT, and after you've taken 6.002,", - "you begin talking about lumped elements, you know,", - "resistors, voltage sources, capacitors, little inky-dinky", - "objects that follow the lumped matter discipline.", - "OK, they stick to very simple rules, and the math that you", - "have to do to analyze them is incredibly simple.", - "What could be simpler than V is equal to IR?", - "So, let me give you an example of interesting lumped elements,", - "and then show you a couple of really nasty lumped elements.", - "OK.", - "OK, so what you see out here, so we characterize lumped", - "elements by the VI characteristics.", - "OK, you apply voltage, measure the current.", - "OK, so what I can do is I can plot I here, and V here,", - "and see what it looks like. OK, I can characterize elements", - "by their VI relationship. And there are a bunch of", - "elements that I can create based on the VI relationship.", - "So let me show you a few examples.", - "So for the resistor, since V is directly", - "proportional to I, and R is a constant,", - "I get a straight line. That's the I axis,", - "the V axis, and this is the resistor.", - "What I actually have is a variable resistor,", - "so I'm going to change the resistance value,", - "R, and the curve will also change slope.", - "OK, I changed the value of R because it's a variable", - "resistor, and the changes slope because my R is different.", - "OK, next, let me go to a fixed resistor, and this guy here on", - "the screen to your left is a fixed resistor.", - "And you see that its IV characteristic is a line of a", - "given slope, 1 by R, and that's it.", - "I can't change it. Number three,", - "I have another lumped element called a Zener diode that you", - "will see in the fourth week of this class, and the", - "characteristics for the Zener diode look like this:", - "IV. If my voltage goes across the", - "Zener diode goes up slightly, the current shoots up.", - "But if the voltage becomes negative I don't have any", - "current flowing into it until the voltage passes on the", - "threshold, at which point my current begins to build up.", - "OK, so I can increase the voltage a little bit,", - "and it can show that the current starts building up", - "again. So that's another interesting", - "lumped element called a Zener diode.", - "Let's switch to the next one called a diode.", - "So a diode looks like this: IV.", - "As the voltage across the diode becomes positive,", - "around .6 volts, or thereabout,", - "the current begins to shoot up. But when the voltage is below", - "that threshold of .6, then my current is almost zero.", - "It's another lumped element called a diode.", - "And you will begin using these elements in your 002 lives to", - "build interesting systems. The next example is a", - "thermistor. A thermistor is a resistor", - "whose resistance varies with temperature.", - "OK, so this is a very expensive little hairdryer,", - "and what I'm going to do is blow some hot air at my", - "resistor, and you're going to see that its value is going to", - "change depending on how much I heat it.", - "So as it cools down, let me cool it down,", - "so you can see it's coming down.", - "I can zap it again. I could do this all day.", - "This is so much fun. OK, so that's another", - "interesting lumped element. As the temperature rises,", - "its resistance changes. The next thing is called a", - "photo resistor. It's a resistor.", - "It used to be a resistor; Lorenzo?", - "Oh OK, that's fine. So this is a photo resistor.", - "And notice that it almost behaves like an open circuit.", - "But what I'm going to do is shine some light on it.", - "When I shine light on it, it begins to conduct and", - "becomes a resistor of some value.", - "There you go. OK, so that's a photo resistor.", - "So now I'm going to show you a battery.", - "Notice we did talk about batteries before.", - "I'll show you a battery. So before you show a battery,", - "just thinking your own minds, what should the IV", - "characteristic of a battery look like?", - "IV. A battery supplies a constant", - "voltage. You know your little cell,", - "the AA battery, 1.5 volts?", - "So, think of what the IV characteristic of a battery", - "should look like for three seconds before it shows you.", - "This is the one I showed, Lorenzo?.", - "It's a straight line. This is a good battery.", - "It's a straight, vertical line,", - "but says that the voltage is 1.5 volts, or thereabouts.", - "No matter what current it supplies as an ideal voltage", - "source, it has a fixed voltage, V, and no matter what the", - "current going through is. Now, I'll show you a dud,", - "a bad battery, and this is what the bad", - "battery looks like. So, many of you have had your", - "car batteries die on you. When you go to the store,", - "they check your batteries. They use exactly this", - "principle, that dead batteries have resistance.", - "By the way, you see slopes here.", - "You're thinking of resistance. OK, they can use this property", - "to figure out that your battery is dead.", - "So that's a dead battery. And finally,", - "let me show you a bulb. We started with a bulb,", - "and so I need to end, OK, we started with a bulb,", - "so I need to end with a bulb. And what you will see is that a", - "bulb simply behaves like a resistor.", - "Its IV curve is going to look like this.", - "OK, notice this is my bulb. And guess what,", - "it behaves like a resistor. It's a very interesting kind of", - "resistor, so I won't go into details for now.", - "But notice its IV characteristic behaves like a", - "resistor. OK, so those are some pretty", - "standard lumped elements. You deal with a lot more sets", - "of lumped elements, switches, MOSFETs,", - "capacitors, inductors, a bunch of other fun stuff.", - "But before we do that, what I wanted to tell you,", - "don't go berserk on this abstraction binge.", - "Too much of anything is bad for you.", - "So what I'm going to show you is, abstractions or models are", - "only valid provided you work within a set of constraints.", - "Notice, we have already had this tacit handshake which said", - "that we follow the discipline. Even after we follow the", - "discipline, there are ranges to how well physical elements can", - "behave like ideal lumped elements.", - "OK, for example, what we will do is show you the", - "resistor. And it's going to look like a", - "resistor. And I'm going to keep", - "increasing the voltage around it.", - "OK, what's going to happen at some point?", - "I just keep doing that. If it's an ideal element,", - "if you're a theorist, you say, oh yeah,", - "the curve will keep extending until I reach infinity.", - "But this is a practical resistor, so people out here can", - "cover your eyes or something. OK, so you're abstraction can't", - "predict that. All it says is the current is", - "an amp. It can't predict the heat,", - "light, or the smell. In the laboratory,", - "even, you get the smell. You know what somebody has just", - "done. So that's one example of the", - "lumped abstraction breaking down.", - "So, if I really believe that my own BS, anything is a lumped", - "element. So here's a pickle.", - "A pickle is a lumped element. I can choose it as a lumped", - "resistor. But this is a very interesting", - "lumped resistor. Don't try this at home.", - "This is a standard pickle into which you are pumping 110 V AC.", - "I promise you, this is a standard pickle.", - "So, it has a fixed resistance, but your lumped abstraction", - "cannot predict the nice light and sound effect.", - "OK, so the last two or three minutes what I want to do,", - "so remember, don't get carried away by", - "abstractions. There are limits.", - "OK, you can't predict everything.", - "OK, that's the smell of a pickle.", - "OK, so let me give you a preview of some upcoming", - "attractions, and show you one more quick simplification in the", - "last few minutes. So what we can do,", - "once we build these lumped elements, we can connect them in", - "circuits. OK, so I can build a circuit,", - "of the sort. So here's a voltage source with", - "a bunch of resistors. I can connect them with wires", - "and build a circuit of the sort. One interesting question we can", - "ask ourselves is, under the lumped matter", - "discipline, what can we say about the voltages?", - "OK, if I go around the loop, provided my world adheres to", - "the lumped matter discipline, what can I say about the", - "voltages around this loop? Ah-ha, Maxwell again,", - "right? So, I can write Maxwell's", - "appropriate equation to solve that.", - "OK, voltages have something to do with E and your integral of E", - "dot dl and all of that stuff, right?", - "So this is the appropriate Maxwell's equations to use.", - "And I want to find out what happens here.", - "Now remember, under LMD, I made the", - "assumption. OK, my world,", - "my playground, has del phi B by del t being", - "zero. The rate of change of flux is", - "zero. So, under these circumstances,", - "I can write this. I can break up this line", - "integral into three parts across the voltage source and across", - "the two resistors and write that down.", - "OK, and then when I can do, is now that the right-hand side", - "is zero, I can simply take this. And I know that E dot dl across", - "this element is simply VCA. This is VAB,", - "and this is VBC equals zero. OK, so when I make the", - "assumption that del phi B by del t is zero, and I go around this", - "loop, apply Maxwell's equations, what do I find?", - "I find that the sum of the voltages, VCA plus VAB plus VBC,", - "is zero. That's fantastic.", - "So now, I could say hasta la vista to this baby here.", - "And I can focus on this guy and say, Maxwell's equations,", - "this thing with squiggles and dels and all that stuff,", - "can be simplified to the sum of the voltages across a set of", - "elements in a loop in a circuit is zero.", - "OK, and this is called Kirchhoff's first first law,", - "KVL. OK, similarly,", - "in recitation section, you'll see the application of", - "Kirchhoff's current law, which comes from this be equal", - "to zero, and all the currents coming into a node being zero.", - "So, KVL and KCl directly come out of the lumped matter", - "discipline. And you can use those to solve", - "circuits like this." - ] -} \ No newline at end of file diff --git a/subs/B-xRpQwZsYc.srt.sjson b/subs/B-xRpQwZsYc.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/B-xRpQwZsYc.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/BGU1poJDgOY.srt.sjson b/subs/BGU1poJDgOY.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/BGU1poJDgOY.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/BUsj70M8ikc.srt.sjson b/subs/BUsj70M8ikc.srt.sjson deleted file mode 100644 index 2c50e2fe77..0000000000 --- a/subs/BUsj70M8ikc.srt.sjson +++ /dev/null @@ -1,293 +0,0 @@ -{ - "start": [ - 0, - 2770, - 5930, - 8290, - 9100, - 13450, - 15570, - 18030, - 21130, - 22730, - 25740, - 28500, - 30270, - 31450, - 33700, - 34860, - 38490, - 42530, - 43650, - 47650, - 49550, - 51890, - 53520, - 56710, - 60300, - 64280, - 66200, - 67460, - 69160, - 70590, - 73900, - 75410, - 78800, - 81960, - 84220, - 86470, - 89960, - 92320, - 94760, - 96580, - 97580, - 100560, - 102230, - 105870, - 107190, - 110660, - 113800, - 115400, - 118670, - 120630, - 122320, - 123450, - 125820, - 126700, - 129440, - 132530, - 134120, - 136770, - 139390, - 143590, - 145640, - 147150, - 149650, - 152380, - 157400, - 159780, - 161350, - 163690, - 167750, - 171080, - 174430, - 176240, - 177680, - 181560, - 185390, - 187320, - 189050, - 190410, - 193040, - 196630, - 197370, - 198540, - 200630, - 202200, - 206620, - 210430, - 211480, - 215010, - 216520, - 221520, - 223950, - 227650, - 229890, - 230760, - 232670 - ], - "end": [ - 2770, - 5930, - 8290, - 9100, - 13450, - 15570, - 18030, - 21130, - 22730, - 25740, - 28500, - 30270, - 31450, - 33700, - 34860, - 38490, - 42530, - 43650, - 47650, - 49550, - 51890, - 53520, - 56710, - 60300, - 64280, - 66200, - 67460, - 69160, - 70590, - 73900, - 75410, - 78800, - 81960, - 84220, - 86470, - 89960, - 92320, - 94760, - 96580, - 97580, - 100560, - 102230, - 105870, - 107190, - 110660, - 113800, - 115400, - 118670, - 120630, - 122320, - 123450, - 125820, - 126700, - 129440, - 132530, - 134120, - 136770, - 139390, - 143590, - 145640, - 147150, - 149650, - 152380, - 157400, - 159780, - 161350, - 163690, - 167750, - 171080, - 174430, - 176240, - 177680, - 181560, - 185390, - 187320, - 189050, - 190410, - 193040, - 196630, - 197370, - 198540, - 200630, - 202200, - 206620, - 210430, - 211480, - 215010, - 216520, - 221520, - 223950, - 227650, - 229890, - 230760, - 232670, - 233920 - ], - "text": [ - "SPEAKER 1: Our third method is going to be the node method.", - "This method is going to be the most important method that we", - "learn, and you can apply it to all the circuits that you're", - "going to see.", - "This method is going to be a very specific application of", - "the KVL/KCL method.", - "This method has five steps.", - "The first step would be you go and select a reference node--", - "we call that a ground node--", - "represented by an inverted T symbol.", - "And you're going to measure all our voltages with", - "reference to this ground node.", - "The second step.", - "We label all the voltages of the remaining nodes with", - "respect to ground.", - "And these will be our primary unknowns.", - "As a third step, we will write KCL for all the nodes, leading", - "out the ground node.", - "And while writing KCL, we will apply a cool trick.", - "So KCL involves currents.", - "But notice that your primary variables", - "are your node voltages.", - "But KCL involves current, so what we will do is in step", - "three, we will derive the current, in terms of the node", - "voltages, and directly apply the element relationship", - "without actually having to write down", - "any specific current.", - "Then we go and solve for the node", - "voltages as our step four.", - "And finally, we go and back solve for the branch voltages", - "and branch currents.", - "Notice that for circuit analysis, our goal is to find", - "branch voltages and currents, and so to the extent that you", - "need to know all the branch voltages and currents, you can", - "go ahead and find them.", - "The node analysis method is the workhorse of our industry", - "and the workhorse of 6.002x.", - "And so you will be using it all over the place.", - "It's a very, very important method.", - "Let's get started.", - "And for this method, I'm going to use our", - "old faithful circuit.", - "For fun, I'm going to add a extra current source, I1, to", - "our circuit.", - "Notice that we now have seven elements in the circuit.", - "And with seven elements, the number of equations is going", - "to be completely unwieldy.", - "And so you will notice that with the node method, you will", - "be amazed that at the end, we will have to", - "solve only two equations.", - "Watch and see.", - "So as the first step of the node method, I have to select", - "the ground node.", - "Now, in general, you can select any node as the ground,", - "because voltages are always measured with", - "respect to a point.", - "There are differences in potentials between a pair of", - "points, so you can select any node as the ground.", - "But in general, to simplify our lives, I'd recommend using", - "a couple of rules to pick a ground node to", - "simplify the analysis.", - "The first thing to do is to find a node which has the", - "largest number of edges coming to it.", - "And in our circuit here, this node here, which connects R to", - "R5, and the current and voltage sources has the", - "largest number of edges.", - "So that seemed like a good candidate.", - "A second thing you can look at is look for a node that has", - "many of the sources connected to it.", - "And in this case, it does happen that the same node has", - "the voltage source also connected", - "to it with one terminal.", - "So let me go ahead and pick that as my ground node.", - "So let me go ahead and mark that as my ground node.", - "This will be my ground, and I mark it", - "with my ground terminal.", - "So this is step one.", - "Now, let's apply step two.", - "Step two will be label node voltages with respect to the", - "ground node.", - "So what are my nodes?", - "So I have a node here.", - "That's one node.", - "Let me label the node voltage with respect to ground as E1.", - "So if I take this as my ground voltage and", - "take that as a zero--", - "so the voltage at this node here is going to be E1 with", - "respect to the ground.", - "Let me pick this node here as E2 with respect to ground.", - "Finally, I have a third node here.", - "And what can you say about the voltage at that node?", - "Let me pause for a second while you think about it, and", - "then I will continue.", - "So what do you think the voltage is at that node?", - "Do I need a variable there?" - ] -} \ No newline at end of file diff --git a/subs/BX-ke_sOmJE.srt.sjson b/subs/BX-ke_sOmJE.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/BX-ke_sOmJE.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/CO1GaQ_aABk.srt.sjson b/subs/CO1GaQ_aABk.srt.sjson deleted file mode 100644 index 2f03bfd4ce..0000000000 --- a/subs/CO1GaQ_aABk.srt.sjson +++ /dev/null @@ -1,29 +0,0 @@ -{ - "start": [ - 250, - 3300, - 7990, - 13470, - 17840, - 18740, - 21970 - ], - "end": [ - 3300, - 7990, - 13470, - 17840, - 18740, - 21970, - 23220 - ], - "text": [ - "SPEAKER 1: OK, so this is case the V-I relationship is V", - "equals capital V. In this is it's a constant and so the", - "relationship is given by this where V is a constant at", - "capital V volts in respect to the current that is flowing", - "through the element.", - "So here are examples of a couple of elements and their", - "I-V relation." - ] -} \ No newline at end of file diff --git a/subs/COdQmA9g9S8.srt.sjson b/subs/COdQmA9g9S8.srt.sjson deleted file mode 100644 index 9fda17f3f1..0000000000 --- a/subs/COdQmA9g9S8.srt.sjson +++ /dev/null @@ -1,1916 +0,0 @@ -{ - "start": [ - 0, - 5154, - 12465, - 16900, - 24332, - 31643, - 36730, - 41169, - 43953, - 48242, - 49822, - 54186, - 57723, - 61410, - 66000, - 69656, - 71895, - 76447, - 80402, - 84805, - 89358, - 93087, - 96568, - 101440, - 106234, - 109946, - 112653, - 117061, - 122205, - 138000, - 143614, - 150000, - 157816, - 163287, - 167325, - 174490, - 179440, - 186332, - 189209, - 191619, - 195895, - 199238, - 203592, - 206469, - 210123, - 216666, - 226000, - 229047, - 233428, - 238952, - 251000, - 255538, - 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"Good morning. Today we move in the direction", - "that takes a big turn from the direction we have been going in", - "so far. All the devices we have had up", - "until now, resistors and voltage sources, and even your digital", - "devices like the AND gate or the inverter and so on had a very", - "specific property. We didn't dwell on that", - "property, but that property was that these were not what are", - "called memory devices. In other words,", - "the outputs at any given time are a function of the inputs", - "alone. In other words,", - "if you took your inverter or your NAND gate for that matter", - "and you build a circuit comprising 50 NAND gates", - "connected in structures that we have talked about,", - "you apply an input and boom you get an output.", - "And your output is a function of the inputs alone,", - "right? The same thing with your", - "resistors and voltage sources. At any given point in time your", - "output VO of T was some function of the input VI of T.", - "What we are going to do today is discuss a new element which", - "will introduce a whole new class of fun stuff for all of us to", - "deal with. And that is called storage.", - "In other words, the output of a circuit is now", - "going to depend not just on the inputs but it is going to depend", - "on the background or it is going to depend on where the circuit", - "has been in the past. So past is going to matter.", - "It is a very fundamental difference.", - "And what I would like to do is start by giving you folks a", - "little bit of a surprise. I am going to do a little demo", - "taking two of your inverter circuits.", - "I am going to start by taking a couple of inverters.", - "Remember, I am using this structure here as an inverter.", - "And I am going to couple this to another inverter and take an", - "output C, some VS, some load resistance RL,", - "my B terminal and my A terminal.", - "So I'm going to apply some input between ground and my A", - "terminal. And for fun I want to apply a", - "square wave at the input. A square wave between zero and", - "5 volts. And this is how my time goes.", - "Let's assume that VS is 5 volts.", - "So what I am going to do is plot for you the behavior of", - "this inverter. I am going to plot for you A,", - "which would look like this. I am going to plot for you B,", - "which would be the inverted wave form.", - "And then plot C, which would be a wave form that", - "looks like this again. Let me do a plot here.", - "So this is A.", - "-- and so on. Time goes this way.", - "And let's say this is between zero and 5 volts.", - "And B should be an inverted wave form that should look like", - "this.", - "If all that we believe of the world so far is true then this", - "is how things should behave, so C should look like this.", - "This is what the world should look like and if everything that", - "you learned about is true and correct and all of the good", - "stuff. Let me show you a little demo", - "and see if I can try to pull the rug out from under all that you", - "have learned so far and show you some surprising stuff.", - "Here are the three wave forms that I showed you up here.", - "This is my A. This is my A wave form.", - "This is the B wave form. Notice that B,", - "as you expect, is an inverted form of A.", - "And this is C. We all expect this,", - "correct? But what I am going to do is", - "let me expand the time scale on this so that I can look at these", - "transitions a little bit more carefully.", - "I am just going to expand the time scale.", - "There you go. All I have done is expanded the", - "time scale and spread that out a little bit.", - "And what you see there is quite different from what you expect.", - "A is a square wave as expected, but B is stunningly different.", - "It is a zero as expected because this is a one.", - "But here I get some really strange behavior,", - "behavior that is like nothing on earth.", - "Like nothing you have seen before.", - "And then, of course, it becomes a one eventually,", - "but there's some really, really shady stuff going on", - "here. And so far you are not prepared", - "to deal with this. We have not given you the", - "facility to deal with his issue. What is the problem with this?", - "We could say who cares? What is the problem with this?", - "Let's look at the result. I am looking at this,", - "I am focusing on this piece here.", - "And notice that instead of being a sharp rise it looks like", - "this. It is going up a little bit", - "more slowly. What kind of problem would that", - "create? The problem that it creates is", - "the following. Let me play around with this", - "graph a little bit more. What I am going to do is just", - "take this output here, the C output and line it up", - "against the A output. And so I am going to line up", - "the C wave form on top of the A wave form.", - "So you can see for yourself if something really,", - "really strange and nasty is happening, I am just going to", - "move up the C wave form and line it up.", - "What is happening out there? If you look carefully,", - "what you observe is that the C wave form transitions just ever", - "so slightly later than the A wave form.", - "Look here. And I claim that it is because", - "of this. Because of this,", - "the C wave form falls just a little bit later,", - "and that little thing we see out there is a delay.", - "So nothing you have learned so far prepares you for this.", - "Suddenly, instead of the output exactly following the input,", - "my output is following the input but a little bit later.", - "And it is this fact of life that things happen a little bit", - "later, is really the reason why each of you and all of us needs", - "to buy new computers every couple of years.", - "This simple basic fact. If this fact of life didn't", - "exist, you would buy one computer and be done with it for", - "life. Intel would make gobs of money", - "one year, and so would Dell and Gateway and so on,", - "and then no more. That's it.", - "This is it. But because of this a little", - "itty-bitty difference here the entire semiconductor technology", - "is charging along trying to do something about that.", - "You buy newer and newer computers each year.", - "It turns out this little itty-bitty thing here,", - "that is called the delay, the inverter delay.", - "And it happens because of a specific element that has been", - "introduced here that we have not shown you so far.", - "And a large part of the semiconductor industry and", - "follow-on courses and design and so on focuses on how could I", - "make my delay smaller, how can I get to be faster and", - "faster and faster? This relates to how fast we can", - "clock your Pentium IV. Remember it came all the way to", - "1.3 gigahertz? What's the fasted Pentium money", - "can buy today? What is the fastest P4?", - "Oh, 3.2 have come out? I don't know.", - "Ken claims 3.2. But, yeah, there you go,", - "3.2 gigahertz. It all has to do with this", - "little itty-bitty thing. You saw it for the first time", - "here. When some of you become CTOs at", - "Intel and so on, just remember that it all began", - "on October 16th with this little rinky-dink thing here.", - "What you are going to learn now is some really cool stuff that", - "has huge implications for life. So why does that happen?", - "Why did this transition happen just a little bit later?", - "The reason is that remember when this wave form reaches VT,", - "the threshold voltage of this MOSFET, this guy is going to", - "switch, right? So because of the slower rise", - "of the voltage, the VT is going to be reached a", - "small amount of time later. So I am going to hit VT", - "slightly later. And because of that this guy is", - "going to transition just a bit later because this intermediate", - "wave form B is slower. It hits VT just a little bit", - "later than if it would have made an instantaneous transition.", - "And therefore my output falls just a little bit later and this", - "gives rise to my delay in the inverter.", - "We can call that d if you would like, some delay.", - "In your course notes, this material is covered in", - "Chapters 9 and 10. That was to kind of motivate", - "why we are going to be doing all that you we will be doing.", - "Don't anybody come within a foot of this even by mistake.", - "I mean it. It is pretty deadly stuff.", - "Today we will talk about the capacitor.", - "And in the next couple of lectures I am going to tie it", - "all together and show you how this relates to that.", - "I will show you exactly how the delay happens.", - "You can compute it based on some simple principles that you", - "will learn about in the next couple of lectures.", - "What I am going to do is first of all show you,", - "I claim that that delay happens because of the presence of a", - "capacitor somewhere in there. What I will do now is take you", - "into a closer look, take a closer look at the", - "MOSFET and show you were the capacitor is.", - "This is the MOSFET that you have seen so far,", - "drain, gate and source. This is called an n-channel", - "MOSFET. And what I am going to do is", - "dissect this and show you what is actually happening,", - "what this looks like on silicon.", - "So here is my slab of silicon. It is very thin.", - "And let's say this is, I won't go into details here.", - "You will learn a lot more about this in future device classes", - "like 301 and so on, but suffice it to say I will", - "just introduce it here to give you a sense of where the", - "capacitor is. This is p-type silicon.", - "And the way you build a MOSFET is you create a couple of tubs", - "in which you dope to be n-type. The basic silicon is dope", - "p-type. And this guy here is n-type.", - "And what you do is a thin oxide layer is placed on top of that", - "and then on top of that a thin metal layer.", - "This is a metal layer. This is a thin piece of oxide,", - "silicon dioxide. And this is my P substrate.", - "Now this is a little metal layer that is really a wire on", - "top of the silicone. This metal layer could be some", - "sort of a wire that meanders around on the surface of", - "silicone. And this is a wire that", - "connects to the gate. This is the gate of my MOSFET.", - "And this guy here is the drain. And this guy here is the", - "source. And this is my gate.", - "So there is a little piece of metal here.", - "This is this piece of metal here.", - "And there is a piece of oxide and then my silicone substrate.", - "Notice that this is my oxide. When I apply a positive voltage", - "to the gate here with respect to the substrate,", - "what happens is that I draw up negative charges.", - "I draw up electrons here into this channel region and I have", - "corresponding plus type out here so that I get a view here that", - "looks like a couple of plates. And I end up with an oxide in", - "the middle. There is no connection.", - "Two plates separated by a small distance with plus q and minus q", - "on the plates. And, because of that,", - "what ends up happening here is that this piece behaves like a", - "capacitor. So a capacitor has two plates", - "with a thin insulating material in the middle with some", - "permittivity epsilon. And so I get a little piece of", - "a capacitor here. That is the capacitor that is", - "forming. I did not set out to build that", - "capacitor, but there is a capacitor nonetheless.", - "So when I apply a positive voltage at the gate,", - "negative electrons are pulled up here which forms a channel,", - "and then a current can then flow.", - "And that is how the MOSFET turns on.", - "So n-type electrons back to n-type, and I get electron flow", - "here and that gives me my channel.", - "This is just kind of devices in four minutes or less.", - "You will do an entire course on this, if you like,", - "if you take 301. What we do is to be able to", - "capture the behavior that we just saw, the funny delayed", - "behavior, we have to augment our model.", - "We have to introduce a new element.", - "So what we do is here is a MOSFET, gate,", - "drain and source. And notice here we model this", - "by putting a little capacitor, CGS between our gate and the", - "source. So this becomes a simple model", - "for our MOSFET device which is the good old gate drain source", - "device from the past with a little capacitor CGS having some", - "value for CGS in maybe ten to the minus 14 or thereabouts", - "farads. So that is a little capacitor", - "that has come about in this device that we fabricated here.", - "It is that capacitor that is at between node B and ground", - "because it is between the gate and the source of the second", - "inverter. And it is that capacitor that", - "is playing the games that we saw out there.", - "So let's look at some of the behavior of an ideal linear", - "capacitor. A capacitor,", - "as I said, has a couple of plates.", - "There are a couple of plates. Between the plates is some", - "dieletric, permittivity epsilon. Let's say the area of the", - "plates is A, and let's say the plates are separated by a", - "distance D. I get some charge here,", - "let's say q. So q and minus q on the", - "capacitor. And the capacitance C is given", - "by epsilon A divided by D. Epsilon, as I said,", - "is the productivity of the dielectric.", - "So if it is free space then it would be epsilon zero which is", - "the permittivity of free space. That is the capacitance in", - "farads. And the symbol looks like this.", - "Capacitor C. Voltage v.", - "Current i. So this, much like the", - "resistor, voltage source and so on, this now becomes a primitive", - "element in your tool chest of elements like the voltage source", - "and so onn. Capacitance with the voltage v", - "across it and a current i. And I have assigned the", - "associated variables here according to the associated", - "variable discipline. A question to ask ourselves is", - "remember we said we are all now in a playground from all of", - "nature, in this playground where the lumped matter discipline", - "holds? And also remember that we said", - "that for the lumped matter discipline to hold we have to", - "make a couple of assumptions. One of those assumptions was", - "that dq/dt, for all their elements should be zero for all", - "time. So right now what about the", - "capacitor? It has got some charge q.", - "So charge must have built up somehow.", - "Does that mean that I lied all along, that we are no longer in", - "this playground, that we have been ejected from", - "the playground because of the capacitor, or are we still in", - "the circuits playground in which the lumped matter discipline", - "holds and all good things happen and so on?", - "It seems like a contradiction, doesn't it?", - "I took you from Maxwell's playgrounds to the EECS", - "playground where I said the lumped matter discipline holds.", - "And one of the foundations of the LMD was that dq/dt should be", - "zero for all time inside the elements that we are going to", - "deal with. And right now boom,", - "it's not four weeks into the course and Agarwal introduces an", - "element and it has q in it. It turns out that the capacitor", - "also adheres to the lumped matter discipline.", - "Remember the discipline says that dq/dt is zero for all time", - "within elements. So I am going to be clever.", - "What I am going to do is I want to choose element boundaries in", - "a very cleaver way. Notice that if I have q here on", - "this plate then I get minus q on the other plate.", - "So if I take the whole element, the element as a whole,", - "if I am careful in terms of how I package my boundaries,", - "if I put both my plates inside my element boundary then I still", - "do get the net charge being zero.", - "So dq/dt is indeed zero for all time provided I make sure that", - "my element has both the plates. Therefore, if you come across", - "somebody else that gives you an element that says I have an", - "idea. Let's create a new branch of", - "electrical engineering in which we model the capacitor not as", - "one element for two plates, but let's build a capacitor by", - "combining two new elements, two garbage elements called G1", - "and G2. G1 is like the top plate.", - "G2 is the bottom plate. I put them together and I get a", - "capacitor. But notice if I just pick one", - "plate then the element G1 will not adhere to the LMD.", - "It adheres to the LMD because I choose my element boundaries in", - "a way that both plates come within it.", - "So it is very fundamental and key.", - "And you can read a lot more about it in the course notes.", - "I purposely dwelt on that simple point because I think it", - "is foundational and important. And you really need to", - "understand that the capacitor does satisfy LMD.", - "We are still in the good old playground.", - "A few simple facts here. These are in the notes.", - "And you have also seen this before, I am sure.", - "I can relate the charge to the capacitance and the voltage as q", - "is equal to Cv. And q is in coulombs,", - "this is in farads and this is in volts.", - "So there is some charge q stored on the capacitor and it", - "is in coulombs and q is equal to Cv.", - "So I can differentiate this with respect to time to get the", - "current, and that becomes i=dq/dt.", - "So the current at any given time is dq/dt.", - "And so I substitute for q in terms of Cv here.", - "That is what I get. So the current i=d(Cv)/dt.", - "A 6.002 assumption, capacitance in general can be", - "time-varying. I can get time-varying", - "capacitors. In fact, there are some sensors", - "which are capacitive. And, as I talk,", - "my sound waves can change the pressure on the top plate of the", - "capacitor. And move the top plate of the", - "capacitor, thereby changing the capacitance by moving the plate.", - "Remember d here, as the plate moves closer I get", - "a higher capacitance. So we won't be dealing,", - "unless explicitly said so, with time-varying capacitances.", - "So what we can do is 6.002 allows us to write Cdv/dt.", - "So my current source capacitor is Cdv/dt.", - "I can also write down the energy, capacitors store energy.", - "E=1/2Cv^2. I am sure you have seen all", - "this before in physics and so on.", - "That is the amount of energy stored in the capacitor if it is", - "holding a charge q. Let me do a little", - "demonstration for you. They don't make glasses like", - "they used to. Our friend Lorenzo has charged", - "up this capacitor. It is a huge capacitor.", - "It is a 250 volt capacitor so it is nasty.", - "He has charged it up and has kept it there.", - "And to show you that it does contain stored charges it has", - "been sitting there holding charge.", - "Maybe the first row should go backwards, just step back for a", - "second. I think you guys would be safe", - "but I just don't want to take any chances.", - "This is holding a bunch of charge.", - "It is kind of sitting there. If I short the terminals it", - "should try to say oh, I've got a path,", - "let me get my charge out. All right.", - "Let's do it. This is always a scary moment", - "for me. And I say a little prayer", - "before I do this.", - "Good? OK.", - "Gee, you guys would love to see me getting fried,", - "huh? All right.", - "Let's see.", - "So it did contain charge.", - "So there is a reason why Lorenzo puts one hand inside his", - "pocket when he shorts it, because there is a natural", - "tendency to hold the wire with both hands, and la,", - "la, la, la, la and put it across the capacitor.", - "By doing this you are guaranteed that you will just be", - "touching it with one hand. Hopefully you folks will", - "remember for life that a capacitor can sit around and", - "hold its charge for a while. All right.", - "That is enough of fun and games.", - "Let's get on with our business of building circuits.", - "What I am going to do is, as I promised you,", - "I am going to close the loop on that example by halfway through", - "the next lecture. I'm going take you on a bit of", - "a journey involving capacitors and resistors and involving some", - "analysis, and then we will close it all up for you at about the", - "middle of next lecture. What I would like to do next is", - "here is a new element. And let's do some fun stuff", - "with elements. Well, you know about voltage", - "sources, you know about resistors, let's put them", - "together and see how they behave.", - "Let's have a capacitor here, C, vc(t) and some current i.", - "What I am going to do, in general, whenever I have", - "something new or something strange, let's say like a", - "capacitor or some other device. It is interesting to model the", - "rest of the circuit behind it if it contains only resistors and", - "voltages and linear elements as a Thevenin equivalent.", - "So let me do that. This is R and this is vi.", - "This stuff in the back is my standard pattern,", - "voltage source in series with a resistor, and I connect that", - "across my capacitor. But remember,", - "although you saw those funny wave forms and so on,", - "the capacitor is a linear device.", - "Because you can see from here that the current relates to", - "dv/dt. That is a linear operation.", - "You don't see V squareds and Vis and things like that in", - "there. It's is a linear device.", - "Let's go back to our trusty old method, the node method.", - "If you just blindly apply the node method and simply grunge", - "through a bunch of math, you should be able to get to", - "the answer, that is for some voltage v or some form of", - "voltage vi, I should be able to figure out what vc looks like.", - "So let's do that. This is the node that is of", - "interest here with the unknown node voltage vc.", - "So let me apply the node method.", - "(vc-vi)/R is the current going this way.", - "That plus the current through the capacitor should equal zero.", - "And what is the current through the capacitor?", - "The node method tells me that, get the current in terms of the", - "element values. We know that the current is", - "given by CdvC/dt.=O. Just shuffling things around a", - "little bit, I can write RC dvc/dt+vc=vi.", - "We are writing the node equation and then getting the", - "equation that characterizes this little circuit.", - "Notice here that this has units of volts.", - "And since I have time here, this also must have units of", - "time.", - "Let's go about solving this little circuit and understanding", - "how it behaves. The specific example that we", - "will look at looks like this. Let's say the capacitor voltage", - "at time T=0 is V0. This is given.", - "So at time T=0, I am telling you that the", - "capacitor contains a charge. And because of that there is a", - "voltage V0 across it. That capacitor had a voltage of", - "250 volts across it and most of the devices we deal with in", - "laptops and so on today, like the Pentium IV,", - "voltages are on the order of 1.5 volts, very small voltages.", - "So that is the value in the capacitor, the voltage.", - "That is called a state. This is called the state,", - "capacitor state. It is the state of the", - "capacitor. And I also give you that", - "vi(t)=VI. So my voltage is VI.", - "And somehow, I am not telling you how,", - "but some how it arranged to have the capacitor voltage be V0", - "at time T=0. Now I want to look to the", - "solution to this for t greater than or equal to zero.", - "And in that time my voltage vi is at some capital VI,", - "some DC voltage VI. So I am going to solve the", - "differential equation RC dvc/dt+vc=vi given these two", - "values. Input is DC voltage VI and VC0", - "is V0, the initial charge in the capacitor.", - "So from now until almost to the end of the lecture,", - "it is just going to be math by solving this very simple first", - "order differential equation. And the key here will be that", - "throughout 6.002 we will be following one method to solve", - "these. There are many methods to", - "solving differential equations, and we will follow one method.", - "That method is called the method of homogenous and", - "particular solutions. In 1802, I believe,", - "you would have learned maybe this, and certainly other", - "methods. You can use any method to solve", - "it. We will just stick to one", - "method. And this is also used in the", - "course notes. In this method what we do is", - "take the solution VC by finding two other components.", - "One is called the homogenous solution.", - "And summing that up with the particular solution.", - "And that is the total solution. So total solution is the sum of", - "the homogenous and the particular solutions.", - "And the method has three steps. As I said before,", - "we will be using this method again and again with every", - "differential equation that we encounter in this course.", - "And you won't encounter a while lot.", - "The first step we find the particular solution.", - "The second step, find the homogenous solution.", - "The total solution is the sum of the two.", - "And then find ---", - "There will be some unknown constants depending on the", - "equation that you have. And in the end we simply find", - "the unknown constants by applying the initial conditions", - "that we have. Boom, boom, boom.", - "Particular. Homogenous.", - "Find constants. Three things.", - "So let's go about solving this equation and apply those three", - "conditions. Again, remember,", - "what I am doing now for the next 10 minutes or 15 minutes is", - "using math that you know about to simply solve this first order", - "of differential equations. There is nothing really new", - "that I am going to talk about here.", - "One is to find the particular solution vCP,", - "which will then be added into the vCH to get me the solution.", - "So the way you find the vCP is you find any solution that", - "satisfies this equation. This is the equation.", - "You find any solution that satisfies it.", - "And find the simplest possible solution that money can buy.", - "Find it. That's the particular solution.", - "Any solution is fine. In this case,", - "a really simple one would be vCP equals VI.", - "Let's see if a constant works. One thing you will realize in", - "differential equations is that they are actually much simpler", - "than they seem. And the reason is that almost", - "every time you have to assume you know the answer,", - "and then you are checking to see what you assumed was", - "correct. Assume the answer is this like", - "you are really smart, and then check it out and say", - "oh, yeah, that must have been the answer.", - "So here we assume that I think VI is going to work so let's try", - "it out. Substituting in here.", - "RC dvc/dt is 0. vi is a constant.", - "So I get vi equals vi, so therefore this is a", - "particular solution. Done.", - "I substitute vi here. So dvi/dt=0.", - "This vanishes and vi=VI. Bingo.", - "Therefore, VI is a solution to this equation.", - "So I am done with my vCP.", - "And in general what you have to do is use trial and error.", - "By trial and error try out a bunch of solutions until you get", - "lucky. In general, again,", - "in all of 6.002 for many of the excitations a simple constant", - "usually suffices. Our second step is to find the", - "homogenous solution. And we can also do that very", - "quickly. And to do that we have to find", - "a general solution to the homogenous equation.", - "The homogenous equation is the same differential equation but", - "with the drive set to zero.", - "We want to follow a set pattern to solve the differential", - "equations here, and the set pattern is find", - "vCP, vCH, find constants. And to find vCH we are also", - "going to follow a set pattern to find the homogenous solution.", - "So we set the drive to zero, so vi is set to be zero.", - "And I need to find a general solution to this.", - "As I promised earlier, diff equations are really,", - "really simple because the way we are going to solve them is we", - "are going to assume we know the answer and then go check it.", - "So let's try Ae^st. Let's try and see if this can", - "solve this particular equation for some values of A and S.", - "I am telling you that the solution is going to be of this", - "form. Assume it.", - "And then simply go ahead and find me A and S,", - "and do that by substituting it back into the equation and find", - "out the corresponding As and Ss. So let's go ahead and do that.", - "I get RC. I substitute this back up so I", - "get dAe^(st)/dt+Ae^st=0. And let me plug that in and see", - "what comes. I get RCAse^st+Ae^st=0.", - "I want to discard the trivial solution of A being 0.", - "That is a trivial solution so I will discard that.", - "And what I will do is cancel out the As from here,", - "assuming A is not zero, and cancel e^st here.", - "And what is left is RCs+1=0. What this is saying is that if", - "I can find an S such that this is true then Aest is a general", - "solution to my homogenous equation.", - "This is easy enough. And so S=-1/RC.", - "If I choose my S to be -1/RC then the simple math that I have", - "gone through shows me that this must be the solution to the", - "homogenous equation. Or in other words", - "vCH=Ae^(-t/RC). All this is saying is that", - "Ae^(-t/RC) is a solution to my homogenous equation.", - "A is an unknown constant. A is some constant.", - "I don't know what that is yet. Notice RC has popped up again.", - "And the cool thing about RC is that, this is time,", - "this also has units of time. We commonly represent RC as", - "some time constant tau, as units of time.", - "Associated with that circuit is the time constant tau,", - "which is simply RC. I commonly write this as", - "Ae^(-t/tau).", - "I am very the end here. I have the particular solution", - "here. I have got the homogenous", - "solution there. I need to tell you about", - "something else. The way I found the homogenous", - "solution was in four steps. I assumed a solution of the", - "form Ae^st. I created this equation here in", - "S. This is called the", - "characteristic equation for that circuit.", - "We will see this time and time again for RC and other forms of", - "circuits. Assume a solution of this form.", - "Construct the characteristic equation.", - "Find the roots of the characteristic equation.", - "In this case it is an equation in S.", - "So this is the root. And then form the solution", - "based on that root. Four steps.", - "Ae^st, characteristic equation, root and then write down the", - "general homogenous solution. Four steps there.", - "And finally I want to write down the total solution.", - "And the total solution is simply vCP+vCH.", - "And vCP was VI and vCH was Ae^(-t/tau).", - "tau was simply RC. That is my solution.", - "Now, remember the last step. The last step was form the", - "total solution and find out the remaining constants.", - "Find out the remaining constants by using my initial", - "conditions. At t=0, I know that vC=V0.", - "I know that. And so therefore I can", - "substitute t=0 to find the constant.", - "So I know that VO=VI+A. t=0, this thing becomes 1,", - "and so I get this equation from which I get A=V0-Vi.", - "In other words, my solution vC is simply", - "VI+(VO-VI) e^(-t/tau). So the last 15 minutes have", - "just been math. No electrical engineering here,", - "but electrical engineering stopped at the point where you", - "wrote this differential equation down, went through a bunch of", - "math and came up with a solution.", - "Purely mathematically. So here I simply used math to", - "get you the solution. And, as I have been promising", - "you throughout this course, in the next lecture I will give", - "you an intuitive EE method of doing it.", - "Real electrical engineers, real EECS folks don't do it", - "this way. Real EECS folks do it", - "intuitively. And I will show you how to do", - "it in four easy seconds in the next lecture.", - "But you need to understand the foundations of how this comes", - "about, and so this is the answer.", - "You can also get the current iC is simply Cdvc/dt.", - "I won't do that for you, but you can simply", - "differentiate it and get the current.", - "So I can plot for you vC, time t, vC.", - "The intuitive way of looking at this is I have VI which is the", - "final value of the voltage. When t is infinity this part", - "goes to zero so the vC is simply VI.", - "And then there is a component V0-VI which decays according to", - "this starting out at an initial value of V0.", - "Notice when t is zero vC is V0, you can see that in the", - "equation, and so it starts out at V0 and ends up at VI.", - "I start here, I end up here.", - "And this portion V0-VI decays out over time like this.", - "And this decay is governed by the RC time constant or tau.", - "I am going to show you very quickly a couple of examples of", - "wave forms, one that goes like this and one that looks like", - "this. This is when I start with some", - "value V0 and I don't apply any input, it should decay down to", - "zero, t, t, vC, vC.", - "If I apply zero for VI then this should simply decay down to", - "nothing over time. And if I apply some VI but", - "there is no state in the capacitor then that same", - "equation is going to look like this.", - "You can go and confirm for yourselves that when I apply", - "some input but the capacitor has zero state, I start at zero,", - "I finish up at VI and my wave form looks like this.", - "There you go. That's the first one.", - "The second one where I have 5 volts on the capacitor and no", - "input. Assume that at time equals zero", - "I take away an input, short the input voltage to", - "ground for example, apply zero volts.", - "You will see the decay from 5 volts to 0 volts.", - "And in the first case I start with zero volts in my capacitor,", - "I apply input of 5 volts, and notice that at t=0 the", - "capacitor rises up to that level.", - "So notice that these circuits with capacitor and resistors are", - "typified by wave forms that are exponential rises and", - "exponential decays. We will see more of that next", - "time." - ] -} \ No newline at end of file diff --git a/subs/CcgAYu0n0bg.srt.sjson b/subs/CcgAYu0n0bg.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/CcgAYu0n0bg.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/CdS_Zi6hCeI.srt.sjson b/subs/CdS_Zi6hCeI.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/CdS_Zi6hCeI.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/Duh1RHZGMQ0.srt.sjson b/subs/Duh1RHZGMQ0.srt.sjson deleted file mode 100644 index d74a1aafbc..0000000000 --- a/subs/Duh1RHZGMQ0.srt.sjson +++ /dev/null @@ -1,287 +0,0 @@ -{ - "start": [ - 140, - 1920, - 4050, - 7780, - 11670, - 13790, - 16775, - 21040, - 22530, - 24520, - 27320, - 30430, - 33450, - 36090, - 37460, - 41160, - 43730, - 48030, - 48790, - 52080, - 55050, - 56430, - 59550, - 63590, - 67390, - 69850, - 73910, - 76660, - 77410, - 80030, - 82200, - 84780, - 88950, - 93500, - 96400, - 98060, - 102300, - 104110, - 107260, - 110820, - 113980, - 118695, - 119250, - 121980, - 126220, - 130270, - 135080, - 138750, - 141600, - 144020, - 147160, - 149750, - 150030, - 153060, - 156260, - 160060, - 162770, - 164880, - 168590, - 168870, - 170560, - 174770, - 177460, - 180290, - 182210, - 183570, - 186930, - 189690, - 193210, - 195810, - 198050, - 202650, - 204340, - 209000, - 211830, - 214500, - 215630, - 220430, - 221500, - 224790, - 227200, - 229290, - 232150, - 235160, - 238490, - 240740, - 245210, - 248470, - 251420, - 252660, - 255480, - 256890, - 260010 - ], - "end": [ - 1920, - 4050, - 7780, - 11670, - 13790, - 16775, - 21040, - 22530, - 24520, - 27320, - 30430, - 33450, - 36090, - 37460, - 41160, - 43730, - 48030, - 48790, - 52080, - 55050, - 56430, - 59550, - 63590, - 67390, - 69850, - 73910, - 76660, - 77410, - 80030, - 82200, - 84780, - 88950, - 93500, - 96400, - 98060, - 102300, - 104110, - 107260, - 110820, - 113980, - 118695, - 119250, - 121980, - 126220, - 130270, - 135080, - 138750, - 141600, - 144020, - 147160, - 149750, - 150030, - 153060, - 156260, - 160060, - 162770, - 164880, - 168590, - 168870, - 170560, - 174770, - 177460, - 180290, - 182210, - 183570, - 186930, - 189690, - 193210, - 195810, - 198050, - 202650, - 204340, - 209000, - 211830, - 214500, - 215630, - 220430, - 221500, - 224790, - 227200, - 229290, - 232150, - 235160, - 238490, - 240740, - 245210, - 248470, - 251420, - 252660, - 255480, - 256890, - 260010, - 261260 - ], - "text": [ - "PROFESSOR: In the previous segment, we looked at the", - "Thevenin method, which applied to linear circuits.", - "And in that method, I could take an arbitrary network, n,", - "containing a whole bunch of sources and resistors where", - "the current sources are voltage sources.", - "And I could replace that with its Thevenin equivalent, where", - "the Thevenin equivalent pattern was given by a voltage", - "source VTH.", - "in series with the resistance RTH.", - "Now one of the things that I want you to think about in", - "circuits is that whenever you have circuits containing", - "voltages and properties involving voltages, you can", - "immediately think of complimentary properties", - "involving current sources.", - "So much as I was able to replace an arbitrary network n", - "with its Thevenin equivalent, you can think about replacing", - "the arbitrary network n with some pattern involving a", - "current source.", - "And indeed, that method where you replace an arbitrary", - "network with a pattern involving a current source is", - "called the Norton method.", - "So in the Norton method, what we do is we are able to", - "replace an arbitrary network n with its Norton equivalent,", - "where the Norton equivalent contains the current source IN", - "in parallel with the resistance RTH.", - "The current source in parallel with RTH is a Norton pattern,", - "and you should contrast it with the corresponding", - "Thevenin pattern.", - "So a voltage source in series with a resistor is a Thevenin", - "pattern, and a current source in parallel with the", - "resistance is the Norton pattern.", - "So in the case of the Norton pattern, which contains the", - "current source IN and the Norton resistance RN, in the", - "same manner that you defined the Thevenin equivalent, we", - "can derive the Norton equivalent.", - "So to obtain the current IN, what you do is you obtain the", - "short circuit current seen at the port.", - "So recall for the Thevenin method, I open-circuited the", - "port here, and measured the voltage, and that was my VTH.", - "So the Norton method, what I do is I short circuit this", - "port and measure the current I. That current is IN, or the", - "Norton current.", - "And then I can get a Norton resistance RN--", - "oh, I should say RN here-- the Norton resistance RN, which,", - "incidentally, is identical to the Thevenin resistance RTH.", - "I can get that in the same manner as I got RTH, which is", - "I shut off all the independent voltage sources and current", - "sources and simply take the resistance measure at the", - "port, of course, without the short.", - "I go ahead and measure the resistance seen at the port", - "with all the voltages and currents turned off.", - "OK?", - "That would be my Norton resistance, RN.", - "So again, we stated this pattern, a current source IN", - "parallel to a Norton resistance RN, where this", - "corresponds to the Thevenin equivalent, where I have VTH", - "and RTH in series.", - "So the Norton is the dual of the Thevenin.", - "OK?", - "Where the Thevenin is the voltage in series with the", - "resistance, and its dual is the Norton equivalent, which", - "is the current source in parallel with resistance.", - "An immediate question that comes to mind is how are the", - "Thevenin and Norton equivalents", - "related to each other?", - "After all, they are the duals of one another.", - "And so notice the Thevenin equivalent on the left-hand", - "side and the Norton equivalent on the right-hand side.", - "The resistances RTH and the Norton", - "resistance RN are equal.", - "And then we can also relate the Norton current IN and the", - "Thevenin voltage as follows.", - "IN is VTH divided by RTH.", - "And so if you take the Thevenin voltage and divide", - "that by the Thevenin resistance, you get the Norton", - "current, IN.", - "So this very quickly shows you how you can go from the Norton", - "to the Thevenin.", - "One question I am often asked is when do I use the Thevenin", - "method and when do I use the Norton method?", - "Well, you know, that comes from experience.", - "Like you look at circuits in one of our earlier examples", - "where the external network contained a voltage source in", - "series with a resistance, it made sense to take the rest of", - "the network and turn that into Thevenin equivalent.", - "However, if I have a basic circuit containing a current", - "source and a resistance in parallel, then it might be", - "easier to take my external network and convert that into", - "a Norton equivalent.", - "So, really, when you want to get things in", - "parallel, think Norton.", - "When you want to get things in series to simplify analysis,", - "think Thevenin." - ] -} \ No newline at end of file diff --git a/subs/EG-fRTJln_E.srt.sjson b/subs/EG-fRTJln_E.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/EG-fRTJln_E.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/EWD-sNLs2Xw.srt.sjson b/subs/EWD-sNLs2Xw.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/EWD-sNLs2Xw.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/FGx1I9LAIGs.srt.sjson b/subs/FGx1I9LAIGs.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/FGx1I9LAIGs.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/FpSJg9HQvhA.srt.sjson b/subs/FpSJg9HQvhA.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/FpSJg9HQvhA.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/G_2F9wivspM.srt.sjson b/subs/G_2F9wivspM.srt.sjson deleted file mode 100644 index 34fc42d535..0000000000 --- a/subs/G_2F9wivspM.srt.sjson +++ /dev/null @@ -1,191 +0,0 @@ -{ - "start": [ - 0, - 1800, - 2440, - 7270, - 11690, - 13030, - 17060, - 21240, - 24980, - 29930, - 33740, - 37930, - 40340, - 46830, - 50200, - 52890, - 59450, - 60430, - 66640, - 69640, - 72148, - 77730, - 83080, - 99630, - 110800, - 118220, - 121940, - 131580, - 134300, - 137730, - 140540, - 143860, - 146050, - 149850, - 157140, - 161820, - 164460, - 165600, - 169520, - 174040, - 176290, - 178310, - 181070, - 182920, - 184160, - 189960, - 192630, - 193480, - 199020, - 201540, - 204520, - 208180, - 211470, - 217120, - 220790, - 224490, - 227200, - 229150, - 232940, - 236320, - 239070 - ], - "end": [ - 1800, - 2440, - 7270, - 11690, - 13030, - 17060, - 21240, - 24980, - 29930, - 33740, - 37930, - 40340, - 46830, - 50200, - 52890, - 56355, - 60430, - 66640, - 69640, - 72148, - 73398, - 83080, - 84330, - 103660, - 114250, - 121940, - 131580, - 134300, - 137730, - 140540, - 143860, - 146050, - 147300, - 157140, - 161820, - 164460, - 165600, - 169520, - 174040, - 176290, - 178310, - 181070, - 182920, - 184160, - 189960, - 192630, - 193480, - 199020, - 201540, - 204520, - 208180, - 211470, - 217120, - 220790, - 224490, - 227200, - 229150, - 232940, - 236320, - 239070, - 242480 - ], - "text": [ - "SPEAKER 1: So I want to show you a simple circuit that", - "looks like this.", - "And let's go ahead and measure some voltages and currents.", - "In terms of terminology, remember", - "this is called a loop.", - "So if I start from the point C, and I travel through the", - "voltage source, come to the node A, down through R1 and", - "all the way down through R2 back to C, that's a loop.", - "Similarly, this point A is a node where the register R1,", - "the voltage source V0 and R4 are connected.", - "Just make sure your terminology is correct.", - "So what I'll do is let me make some quick measurements for", - "you, and show you that these KVL and KCL are indeed true.", - "So the circuit's up there.", - "So let me take some measurements.", - "And why don't you write down what I measure on the board.", - "Let me borrow another piece of chalk here.", - "What I'll do is focus on this loop here and focus on this", - "node and make some measurements.", - "So you see the circuit up there.", - "[INAUDIBLE]", - "So I get three volts for the voltage from C to A. So why", - "don't you write down three volts.", - "OK, so the next one is minus 1.6.", - "And so that will be I'm doing AB, VAB.", - "And then let me do the last one.", - "And it is minus 1.37.", - "Within the bonds of experimental error, notice", - "that if I add up these three voltages, they", - "nicely sum up to zero.", - "OK, next let me focus on this node here.", - "And at this node, let me go ahead and", - "measure some currents.", - "What I'll do now is change to an AC voltage so that I can go", - "ahead and measure the current without breaking my circuit.", - "This time around, you'll get to see the measurements that", - "I'm taking as well.", - "What I have here is three wires that I have pulled out", - "from D. And this is the node D. So three wires coming into", - "the node D just to make it a little bit easier for me to", - "measure stuff.", - "So everybody keep your fingers crossed so I don't", - "look like a fool here.", - "Hope this works out.", - "So it's about 10 millivolts peak to peak out there.", - "Let's say that if the wave form rises on the left hand", - "side, it's positive.", - "So it's positive 10 millivolts.", - "And another positive 10 millivolts.", - "So that's 20 millivolts.", - "And this time it's a negative, roughly 20, I", - "guess, negative 20.", - "So I'm getting, in terms of currents, I have a positive", - "10, a positive 10 and a negative 20 that adds up to 0.", - "But more interestingly, I can show you the same thing by", - "holding this current measuring probe", - "directly across that node.", - "And notice that the net current that is entering into", - "this node here is zero.", - "So that should just show you that KCL does indeed hold in", - "practice, and it is not just a figment of our imaginations." - ] -} \ No newline at end of file diff --git a/subs/HeMlMvI0SvY.srt.sjson b/subs/HeMlMvI0SvY.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/HeMlMvI0SvY.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/IzULGSWdcGk.srt.sjson b/subs/IzULGSWdcGk.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/IzULGSWdcGk.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/JB2HgohNHYQ.srt.sjson b/subs/JB2HgohNHYQ.srt.sjson deleted file mode 100644 index 64f63eb681..0000000000 --- a/subs/JB2HgohNHYQ.srt.sjson +++ /dev/null @@ -1,1580 +0,0 @@ -{ - "start": [ - 0, - 5970, - 13106, - 17766, - 24757, - 30000, - 35076, - 40246, - 44953, - 48553, - 54184, - 59630, - 63784, - 70724, - 74400, - 84900, - 94000, - 97527, - 101201, - 104507, - 108916, - 112738, - 117000, - 122135, - 127081, - 131361, - 135070, - 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Good morning.", - "Let me take a quick poll. So, how many of you have", - "completed Lab 4. Completed Lab 4?", - "Wow, that's great. So, how many people have begun", - "Lab 4? OK, well that's good.", - "I won't ask the last question. OK so, well I hope you're", - "having fun with this lab. Lab 4 was designed to be almost", - "like a mini-project. And, it sort of ties together a", - "lot of the content of the entire course.", - "And, it's not unlike the kind of systems that people design in", - "industry, in systems that go into a variety of devices like,", - "say, for example, digital CD players and stuff", - "like that. A lot of mixed signal stuff", - "goes in. OK, so today,", - "I'm going to continue with our discussion of energy and CMOS.", - "CMOS will be a new topic that I will introduce.", - "So, the last lecture, we spent a fair bit of time", - "talking about energy, and how to compute the energy", - "of our inverter. So, let me start from where I", - "left off, and I've given you a couple of extra pages of notes", - "today just to sort of tie it to the previous lecture.", - "Right now, I'm going to start off on page three.", - "So, what we saw last time was an inverter of this sort,", - "Vs, VIN, and we said, let's study the situation where", - "this inverter was driving a load capacitor, C.", - "Where did this load capacitor come from?", - "Well, this inverter could be driving one, or two,", - "or three, or four other larger gates, OK?", - "So, this C is lumped value of the gate capacitances of all of", - "those inverters. This may also include some", - "component due to wiring capacitance and stuff like that.", - "So, for an inverter like this, we showed in the last lecture", - "that the formula for the average power was,", - "so this was a static power independent of frequency,", - "and this was called dynamic power, and it had some bearing,", - "it's related to the frequency at which you clocked your", - "circuit. So, this was related to standby", - "power, and this to dynamic. So, what I also said is that I", - "gave you a bunch of numbers so you could compute the power", - "consumption of a chip that included 10^8 gates,", - "100 million gates, and at a frequency of 1 GHz,", - "and a bunch of other numbers. C was given to be 0.1", - "femtofarads. Femto is 10^-15.", - "So, F was 10^9. VS was 5V, and for these", - "numbers, if you plonk them down in something like this,", - "for 10^8 gates on a chip, the average power would be 10^8", - "times these two. So, this would be five squared,", - "which is 25, divided by twice.", - "RL was given to be 10 kilo-ohms, so,", - "twice, 10^4. And here we had CVS^2.", - "So, C was 10^-16, 0.1 femtofarads.", - "Vs^2 was 25, and F was 10^9.", - "So, if you commence through the numbers here,", - "what you end up getting is something that looks like this,", - "10^8 times this guy here. This is 1.25mW plus this guy", - "ends up being 2.5 microwatts. So, this should come as a bit", - "of a shocker. If I take 1.25mW,", - "and multiply that out by 10^8, this says that each gate", - "suffers a standby power loss of 1.25mW.", - "So times 10^8, I get 125kW,", - "and this guy yields 250W. OK, the 250W is manageable.", - "It's still high, and just so you don't think", - "that this is unreasonable, when the Pentium 4 first came", - "out, it was consuming 170W of power.", - "OK, you should see the heat sinks on there.", - "There's actually a huge heat sink with a fan built into the", - "top of the heat sink. OK, today it's down to more", - "reasonable numbers like 100W and so on, but when it came out it", - "was in this range. So it's high but not", - "unreasonable. But this, of course,", - "is totally wacko. OK, imagine carrying a laptop", - "around, and the sucker is blowing 125kW.", - "That'll be fun. So, clearly there's something", - "wrong here. What this is saying is that", - "this gate here consumes 125kW, there are 10^8 of these on a", - "single chip. OK, so we clearly have to do", - "something about this, otherwise the semiconductor", - "industry would fail. So, anybody have any ideas?", - "What do you think you might do here?", - "What do you think you might do to this inverter to make this", - "look better, to bring it down? What can I do?", - "Anybody? Any ideas?", - "What do you think? Well, the problem is that if I", - "look at this 125kW, well, there's a VS term here", - "and an RL term here. So, I can increase RL.", - "OK, I can make RL four times or eight times as large.", - "That'll bring the power down somewhat.", - "Can anybody think of any problem with increasing RL?", - "If I make RL really, really large,", - "will I run into other problems? Yes?", - "Exactly, the slowdown of the inverter.", - "Remember, the rise time of the inverter depends on how quickly", - "I can charge this capacitor through RL.", - "So, if I make my RL really large, I will consume less", - "standby power from hundreds of kilowatts to merely tens of", - "kilowatts. But my gates will run as slow", - "as molasses. So, clearly that's not a", - "tradeoff I would like to make. So, I can reduce my voltage to", - "maybe a volt. But that just reduces it by a", - "factor of 25, VS squared.", - "So clearly, this is not going to work.", - "I have to somehow do something else, and that will be the topic", - "of today's lecture. Also, I will dwell for a moment", - "on this term. So, if you look at the spec", - "sheet for the IBM's ASIC processor that we handed out,", - "if you recall, we talked about power", - "dissipation of 0.006 microwatts per MHz per gate.", - "OK, now you see where this is coming from.", - "Per MHz, that's because it's a multiple of f,", - "the power. Second is that it's per gate,", - "so this is the power per gate. So, as I have more gates,", - "I just have that much more power dissipation.", - "It also says power supply voltage in the range of 0.7 to", - "1.3 right next to the power expression.", - "So, you can see why they tell you all of that,", - "because both voltage, and the frequency,", - "and the number of gates come into the power of equation.", - "OK, this really simple expression here,", - "it's amazing how close this is to what people use for the", - "dynamic power in chips. OK, so as the next step,", - "what I'd like to do is, this guy, what do we do about", - "that? OK, so we've taught you to", - "build gates in a particular matter, but it's a non-starter.", - "So, how do we get rid of static power?", - "How do we get rid of static power?", - "OK, to do so, let's build up a little bit of", - "intuition. OK, so the intuition goes as", - "follows. So let's say I take my", - "inverter. Let me draw the circuit both on", - "the on state and in the off state.", - "So, when VIN is high, when VIN is high,", - "I get the MOSFET turning on and has a resistance,", - "RON, and Vo is the output voltage.", - "Similarly, when VIN is low, so when VIN was high,", - "Vo was low because RON is much less than RL.", - "So, this voltage was low, while here, when VIN is low,", - "the MOSFET is off, and so I have an open circuit", - "out here. And because of that open", - "circuit, the voltage here was going to be high because VS", - "would simply appear there. So let's tailor this and see if", - "we can build up some intuition as to what to do.", - "So, when VIN is low, I don't have any static power", - "being dissipated because I don't have a connection from VS to", - "ground. OK, the current,", - "i, is zero. And, VS simply appears at the", - "output. The reason this is so is have a", - "switch here. So when this is low,", - "the switch opens up and cuts the path from power to ground.", - "This is a nice situation. Here, when VIN was high,", - "there was no switch that turns off.", - "Rather, I get a connection from VS to ground.", - "OK, so think about this situation here.", - "The insight here is, just imagine if I could do the", - "following. Imagine if I could somehow", - "magically elevate RL to be a very, very, very large number,", - "if I could make this so high as to make the power really low", - "only in the situation when the input was high,", - "OK? So, imagine if I could do", - "something like this. Imagine I could open circuit", - "this guy, RON, so when VIN was high,", - "if I could, instead of having an RL here, what if somehow I", - "could make this RL become infinity?", - "OK, so in this case, output VO would be low.", - "OK, I get many benefits by doing this.", - "One benefit is that, look, I have opened this switch", - "here so I don't have any standby current.", - "OK, the standby current is zero.", - "The second benefit is that my output gets dragged down to", - "ground, OK? Out here, my output was VS", - "multiplied by RON divided by the sum of these two.", - "Out here, I have a direct connection to ground,", - "and nothing to the power supply, VS, and so therefore I", - "have a nice, solid low. So the question is that,", - "can I get this situation? OK, that is a key insight.", - "So, imagine that somehow, when this was high,", - "I could get this to open up, much like when this was low,", - "I got this to open up. OK, so think about it.", - "So, the intuition is that what I need instead of a resistor", - "here, what if I have something like the MOSFET that I have", - "here? So, I have a MOSFET here that", - "turned off when VIN was low. OK, what if I did the", - "complementary thing? What if I put in some kind of", - "MOSFET here that would turn off when VIN was high?", - "OK, so, much like the MOSFET turned off when VIN was low down", - "here, imagine if I could find a device that could turn off when", - "VIN was high? OK, this would be on,", - "but this would be off. So the behavior of this device", - "would have to be complementary to this device.", - "So, we need some sort of a switch to introduce this new,", - "little MOSFET device with slightly different properties,", - "let me quickly review for you the properties of the MOSFET", - "that we know about, so our N channel MOSFET,", - "also called the NFET, this is what we've been seeing", - "all this while, is drawn like this.", - "I have a gate; I have a drain;", - "I have a source. And this guy is on when VGS is", - "greater than or equal to VT, OK, and off when VGS is less", - "than VT. You saw this before,", - "OK, nothing new here. So, what I need is a device", - "that behaves in a complementary manner.", - "OK, so the device is a P channel MOSFET.", - "By the way, I must point out, till about 1983-84 until the", - "early '80s, that's exactly pretty much how chips were", - "designed, OK, using an NFET for the switch", - "looking down here, and a variety of different", - "kinds of devices to be used as resistors.", - "OK, that's when technology began moving towards this new", - "kind of technology I'm going to talk about, and that", - "dramatically reducing the power consumed.", - "And, the P channel MOSFET was created, and this guy's called", - "the PFET. It's a complementary device", - "that looks as follows. OK, the difference here is", - "that, to show this is complementary,", - "I'll put a little circle here. It has a gate.", - "Just to make things a little clearer, flip the drain and", - "source terminals, and this guy is on at a", - "distinguished threshold voltage of this with the NFET device,", - "let me put an N here to say that this is the VT for the N", - "channel device. And for this guy,", - "this guy came on when VGS was greater than some voltage.", - "So, VTN could be, for example,", - "one volt. So, VGS was more than one.", - "This turned on. In this case,", - "I wanted this to turn on when VGS is some value which is lower", - "than, or much lower than, the source voltage.", - "OK, so this guy turns on when the gate voltage is higher.", - "This guy should turn on when the gate voltage is", - "significantly lower than the source voltage,", - "just the complementary behavior.", - "OK, so when VGS is less than or equal to VTP.", - "And in this case, the threshold voltage for the", - "PMOS device, say, just as an example,", - "maybe -1V. So this means that if the", - "source is at, say, 5V, OK,", - "then this device would turn on if the gate, for example,", - "using that example was less than 4V.", - "So, this is five. If the gate fell below 4V,", - "this guy would turn on. In this situation,", - "remember, if this was at zero, the gate would have to be", - "greater than 1V to turn on. In this situation,", - "the gate has to be less than 4V if the source was at five to", - "turn on. And, it's off.", - "OK, so this is a complementary device that I postulate that", - "behaves in a complementary manner.", - "So, the gate voltage rises, this guy turns on,", - "and in this situation, when the gate voltage drops", - "below the source voltage, this guy turns on.", - "OK, so when there's a rising guy that turns on in this", - "particular situation when it falls, the gate turns on and", - "shows some resistance. In this case,", - "the resistance would be RON. And to show that it's N", - "channel, let me say N. And in this case,", - "the resistance, when it turns on,", - "would be RONp to represent P channel.", - "OK, so now consider the following circuit for the", - "inverter. So, instead of my resistor,", - "I put a complementary device, OK, and that's it.", - "So all I've done here is replace my resistor with a", - "MOSFET that behaves complementary to the N channel", - "MOSFET. So this is my gate,", - "my drain. This is my source,", - "my gate, my source, and my drain.", - "OK, and this guy is called a pull up, and this guy is called", - "a pull down. OK, and the reason is that this", - "guy pulls the output to ground when it's turned on,", - "while this guy, when switched on,", - "will pull this node up to VS. So, I pull it down or pull it", - "up based on when the VIN is high or low.", - "So, let's look at the two situations.", - "So, let's say, as an example,", - "my VS is 5V, and let's say VIN in one", - "situation being 5V, and another situation being", - "equal to 0V. Let's draw the equivalent", - "circuit in both these cases. So, when VIN is high,", - "I have my usual circuit. When VIN is high,", - "this MOSFET, as before, when VIN is 5V,", - "the N channel MOSFET below is turned on, and so I have an RON", - "resistance here. But remember,", - "VIN is 5, and VS is 5V, then the voltage across the", - "source and the gate of this P channel FET is now equal,", - "five and five. OK, so this one would turn off.", - "And that's the circuit that I get.", - "The output is suitably low. In this situation,", - "if VIN is zero, what happens in this situation?", - "Here's my output. If VIN is 0V,", - "the lower device turns off. This is zero.", - "This is zero. This guy turns off,", - "and that's the situation for the N channel MOSFET.", - "How about this guy here? What happens here?", - "This is at 5. So let me just,", - "this is at 5V. OK, and VIN is at 0V.", - "OK, so therefore, the GS of this is -5V.", - "If this is zero and this is five, G, source,", - "and drain, GS is -5V, and -5V is significantly less", - "than the threshold -1V in our example.", - "So, this one will switch on. And if this one switches on,", - "what I end up getting is RONp out there.", - "So, when this one kicks in, it pulls the output high and VO", - "goes high. So, all I've done is replaced", - "my resistor with a complementary device, which switches off when", - "the input is high, and switches on when the input", - "is low. And the beauty of this is that", - "at no point, assuming all the devices are ideal here,", - "at no point do I have a short circuit between the output,", - "do I have a current path from the output to the ground from", - "the supply to ground, OK, I have this turned off or", - "this turned off. So, this type of logic", - "involving a PMOS transistor here, and the N channel", - "transistor here is called CMOS logic for, OK,", - "it's called complementary MOS logic.", - "That's what CMOS comes from. OK, so I'm sure you've read in", - "a number of places that most digital chips today use CMOS", - "technology. It comes from complementary", - "MOS, and complementary comes from the use of complementary", - "transistors: N channel, P channel, turns on when high,", - "turns off when high, turns off when low,", - "turns on when low. OK, that's exactly", - "complementary to each other. OK, so what you've seen here", - "has been the workhorse of the digital industry for the past", - "two decades, 20 years, CMOS logic.", - "OK, and even the most advanced chip from Intel has an inverter", - "that looks exactly like that. OK, if you count all the", - "inverters in the universe today, I would say a significant", - "fraction of those look exactly like that, no difference,", - "just so simple. So, the key with something like", - "that is there is no path from the power supply to the ground,", - "and so by that model, I did not consume any standby", - "power. OK, my standby power in that", - "idealized model is zero. So, let's compute P.", - "So, what is P dynamic? Let's use the method that we", - "adopted in the last lecture, and draw the equivalent", - "circuit, and compute the power. OK, so I'm going to model the", - "following situation, and assume that I drive a", - "capacitive load, C.", - "OK, and as an input, as I did the last time,", - "I'm going to assume I have some input voltage,", - "VIN, that looks like this. The cycle time,", - "T, and the frequency is 1/t, and let me assume that this is", - "T1, and this is T2. OK, and I'm assuming that T1", - "and T2 are both much larger than the respective time constants.", - "OK, the time constants when, for discharging here,", - "is C RONn, and here the relevant resistance is RONp.", - "The charging time constant is RONp times C.", - "OK, so T1 and T2 are assumed to be much greater than these two.", - "So when you look at this, there's one other benefit", - "besides the power benefit, OK, of using CMOS logic", - "compared to using NMOS. OK, it not only cuts out my", - "standby power, but there is another", - "significant advantage which is almost equal to the power", - "advantage of this kind of CMOS technology.", - "Anybody have any ideas? What's the advantage?", - "What does intuition tell you? Is CMOS going to be faster or", - "slower than NMOS? Why?", - "That's right. The key here is that the NMOS", - "design I showed you earlier was relatively slow because it took", - "me a while to charge up the load capacitor from RL.", - "In this situation, RL will become really,", - "really small; it's RONp.", - "It's roughly the same magnitude as RONm.", - "OK, if so both of these on resistances are more or less", - "equal and small, then the rise time will be of", - "the same order of magnitude as the fall time,", - "which makes this much faster than the NMOS.", - "In NMOS, my time constant was RLC, and RL was pretty large.", - "In this case it's RONp C, and RONp can be made to be very", - "small because when it's switched off, the resistance here is", - "infinity. So, in this situation,", - "if I assume T1 and T2 are much larger than the respective time", - "constants, I can go ahead and draw my equivalent circuit.", - "So, here's VS. So, for charging up,", - "let's say this one is going to a one, or to a high.", - "So, I have VS going through a resistor, RONp,", - "to a capacitor, and this thing is a switch.", - "So I have RONp, an ideal switch,", - "going to a capacitor, C, this is my V out node,", - "OK, so it's VS going through a resistance, RONp,", - "an ideal switch, to a capacitor,", - "C. That's a charging circuit.", - "For discharging, I have C, discharging through", - "an ideal switch with RONn. So, this situation,", - "I have an ideal switch, RONn.", - "OK, so that's the equivalent circuit for something like this.", - "So, in this circuit, during T1, this guy's off,", - "and this guy's on, on during T1,", - "and off otherwise. This guy is on during T2,", - "and off otherwise. OK, so just imagine,", - "this guy switches on, this guy switches off,", - "this guy switches on, this guy switches off,", - "OK? And remember,", - "this is exactly the circuit I had analyzed last time in the", - "last lecture, and the result given by v", - "double asterisk. And that result was simply", - "average power being CVS^2f. That's the exact circuit we", - "used to compute the dynamic power, CVS^2f.", - "OK, so we're done. And how did this come about?", - "This came about because the intuition here is that I'm", - "charging up the capacitor fully, and then I'm discharging the", - "capacitor through this other side, OK, and I'm consuming", - "power, dissipating power, in these two resistances during", - "charge up and during the discharge.", - "Half the power gets consumed during charge up,", - "and half during the discharge. So, I'd like to go back to", - "doing a few numbers here, and taking a look at how,", - "even with this expression, life can get pretty thorny as", - "we go ahead into the next decade.", - "OK, so for our previous example, we assumed that 10^8", - "gates, F=1 GHz, C=0.1 femtofarads,", - "VS was 5V, and I don't need RL anymore.", - "OK, why is it that I don't have any resistance component here?", - "I don't have it here because the power consumed by this", - "circuit is independent of those resistances, provided T1 and T2", - "are long enough, are much longer than the two", - "time constants, RONp C, and RONn C.", - "OK, so I don't have RL in my equation anymore.", - "I don't have any standby power. So, based on this calculation,", - "the calculation I did up there showed that I had 2.5 microwatts", - "per gate, and for 10^8 gates I had 250W for a chip with 10^8", - "gates. So, I'd like to dwell on this,", - "if you can move over to page eight in your notes,", - "here. Let me dwell on this for some", - "time, and pontificate on a few things.", - "First of all, this number,", - "as I said before, is high, but not a disaster.", - "OK, so you can't use this in laptops, but it's quite OK for a", - "desktop or a server, and so on.", - "If you just go and put your ear to a pedestal computer,", - "you'll always hear it making a sound, and that sound is because", - "of a big fan that's inside it. And, if you have a big enough", - "fan, 250W is not such a big deal.", - "But, this is certainly a real problem for mobile devices.", - "For a laptop, this is unthinkable.", - "OK, so we have to deal with this.", - "The second issue is the following, that it's 250W for", - "1GHz. Now, the fastest Pentium 4s", - "that money can by today are, what, how many GHz?", - "What's the fastest Pentium 4 you can buy today?", - "What's that? Does anybody have a 4GHz", - "Pentium 4 here? Oh, darn, you beat me.", - "Anybody have a 3? 3GHz?", - "A couple. So, I have a couple of 3GHz", - "machines, and our lab has a whole ton of them.", - "So, if Intel comes out with 4GHz machines today,", - "they've been going up by about 1GHz roughly every year for the", - "past couple of years. And, within three or four", - "years, you're going to see chips, microprocessors that are", - "in the 5-10GHz range, OK, assuming that all other", - "things stay equal, which of course they're not,", - "but just to give you some insight here,", - "if I clock these guys and build circuits that are ten times", - "faster, I very soon go up to 2.5kW, again as I said,", - "all things being equal which they're not.", - "But just to give you a sense, as I increase my frequency,", - "so does the power consumed by the chip, OK?", - "So, I really have to do something here.", - "So, if I stare at this equation, CVS^2f,", - "I want to increase f because people will buy computers if I", - "have higher frequencies. And, Intel has managed to use", - "its marketing campaigns to pretty much convince consumers", - "that high frequencies are a good thing.", - "OK, and whether they really mean anything or not,", - "that's a different issue. So, we've got this huge power", - "for assuming 5V, OK, so it turns out that", - "microprocessors, as they come out,", - "newer and newer versions run at lower and lower voltages.", - "OK, they invent technologies that use lower and lower", - "voltages, and go from VS 5V to, today, VS on the order of 1.5", - "to 1V, somewhere in that range. So the moment you do that,", - "you get a 25x reduction in power.", - "OK, so in going from 2.5kW, you would now come down to", - "something on the order of 100W, which is, again,", - "much more reasonable, again, all other things being", - "equal. It turns out that the", - "capacitance of devices also changes as you go to smaller and", - "smaller devices. And, 100W is also pretty high,", - "and still not good enough for mobile computers.", - "So, there are many, many other tricks that people", - "use to get even lower powers. One trick is to play games with", - "the clock. OK, what you do is,", - "let's say for example in some computation you are not going to", - "be using your floating point unit.", - "Or let's say I'm going to be using your integer adder unit.", - "OK, so what you can do is you can turn off the clock to those", - "devices so that those devices do not even switch when they're not", - "working. OK, if I turn off the clock to", - "a device, the device isn't even going to switch,", - "it's just going to sit there in limbo without consuming any", - "power. It's equivalent to turning off", - "both transistors. If you turn off both the PMOS", - "and NMOS somehow, OK, it's not consuming any", - "power. And by doing that,", - "you can further cut down the power.", - "So, if you can idle some of your function units,", - "it's called idling a function unit, idle a function unit for,", - "let's say, half the time. OK, you would cut down power by", - "another factor of two. We can idle,", - "then, 75% of the time, come down to 25W.", - "So, those are the classes of tricks that people play.", - "I'm going to stop here and allow the underground guide", - "folks to do the survey. But, suffice it to say that the", - "power discussion that I've gone through with you is a very high", - "level discussion as to the real thing.", - "In real life, what actually happens is that", - "there is a fair amount of standby power even for CMOS", - "logic. It turns out that although I", - "don't have a path from VS to ground for my two transistors,", - "it turns out that there are many leakage currents.", - "OK, currents leak through all kinds of places through the", - "drain of the inverter, and so on and so forth.", - "And so, there is some standby power.", - "So, let me show you a quick demo while, I guess,", - "the review handouts are going around.", - "And this shows the temperature of my CMOS inverter,", - "and as I increase the frequency, you can just watch", - "the temperature go up, and hopefully we'll blow this", - "transistor. So, I'm increasing the", - "frequency as you can see on the side here, and higher frequency", - "implies more power consumption, more temperature,", - "OK, and hopefully you will see some smoke coming out of,", - "OK, I think I blew the inverter.", - "So, the output is gone. So, it's at 110 degrees there,", - "and that blew it. Sometimes we see smoke come", - "out, but I guess today is not one of our lucky days.", - "OK, so let me stop here and have the underground guide folks", - "go through the reviews." - ] -} \ No newline at end of file diff --git a/subs/Je6sMyc4TRU.srt.sjson b/subs/Je6sMyc4TRU.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/Je6sMyc4TRU.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/JqvKtMNz3RQ.srt.sjson b/subs/JqvKtMNz3RQ.srt.sjson deleted file mode 100644 index a702fd649a..0000000000 --- a/subs/JqvKtMNz3RQ.srt.sjson +++ /dev/null @@ -1,1958 +0,0 @@ -{ - "start": [ - 0, - 6936, - 17514, - 27919, - 32500, - 36293, - 40689, - 46206, - 51551, - 56206, - 60000, - 63976, - 67530, - 71507, - 76500, - 80646, - 85638, - 88599, - 93000, - 97186, - 100255, - 104302, - 108488, - 112534, - 116162, - 118813, - 123068, - 126532, - 132670, - 137520, - 143162, - 147121, - 152467, - 156921, - 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So before we begin,", - "I just thought I'd show you a little news item that I happened", - "to read that was very relevant to what we covered recently in", - "6.002. So you recall when we did the", - "digital section a few days ago last Thursday,", - "we talked about a switch. We talked about the MOSFET", - "switch, which when turned on and off, by input signals could help", - "build gates which would then be combined in tens of millions of", - "quantities and go into chips like the Pentium 4 and AMD", - "Athlon 64, and so on it so forth.", - "So I just saw this news item that I came across,", - "and this says they are rethinking the basic", - "construction of the products. It talks about the", - "semiconductor manufacturers like AMD, Intel, and others that", - "build digital chips. They are rethinking the basic", - "construction of the products down to the architecture of the", - "transistor. That's a MOS transistor,", - "and the on/off switch inside the chip.", - "OK, now this might imply that there is a single switch inside", - "the chip, but no, there's tens of millions of", - "transistors, or tens of millions of switches inside a chip.", - "And pretty much any advancement that can be made to the basic", - "transistor can have a 10 million to 20 million times effect", - "because there are that many of them on a single chip.", - "So I thought that was very appropriate.", - "OK. Let's dive into a quick review.", - "So this week, we had begun nonlinear", - "analysis, and I just thought I'd blast through a few animations", - "that I've created, trying to give you more insight", - "into the behavior of some of the things that we have done.", - "Now first of all, as I did the last time,", - "let me try to put it in perspective most of what you've", - "learned thus far, and what we will be learning", - "today. So the past week,", - "we have been focusing on nonlinear analysis.", - "And as I pointed out, here is how this fits into the", - "big picture. So, we had our 6.002 world,", - "at what we said is that we are engineers.", - "We are going to devise our own playground in which to play with", - "our own rules. And that's our playground.", - "That's what we're going to learn about in 002,", - "and for that matter, the rest of EECS at MIT.", - "It's all within this playground here.", - "And this is the playground with lumped circuit abstraction,", - "and good old KVL, KCl, node method,", - "your basic composition rules apply within this playground", - "that directly come from Maxwell's equations because you", - "have made the lumped matter discipline assumptions.", - "OK, so then we said a large part of the playground is", - "linear, and some other much more intuitive techniques apply", - "within the linear portion of that playground,", - "techniques like the superposition,", - "Thevenin and Norton. In most exercises,", - "and quizzes, and experiments,", - "and so on that you do in real life, you can pretty much apply", - "these simple techniques. Very rarely do you have to go", - "into the node method for circuits that are more", - "complicated than single source and a couple of elements.", - "And then, there's the nonlinear part.", - "Remember, the reason I showed this is that this is the same", - "playground. OK, linear and nonlinear are", - "part of the same playground. OK, even nonlinear elements are", - "lumped circuit elements, and they follow KVL,", - "KCl, the node equation, and so on.", - "And then, last week we spent some time talking about the", - "digital abstraction. So we focused on a smaller", - "region of the playground. And the assumptions we made in", - "there were even tighter. We said that it is part of the", - "playground we shall only deal with binary values.", - "We'll digitize or lump values into highs and lows,", - "and that's where our circuits are going to be.", - "And these circuits, when looked at as a whole,", - "were nonlinear. So, this is a simple NAND gate", - "circuit. And this is the input/output", - "characteristic. So, for example,", - "if I hold B at zero, and I apply a zero to one", - "transition at A, then this is the output that I", - "will see at C. So notice, this is decidedly", - "nonlinear. Then I said that,", - "look, suppose we had to fix the input values at a given set.", - "OK, so let's say, for example,", - "I fix A at one, and B at one.", - "OK, and then look at the circuit in this situation.", - "What do I find? What I find is that the entire", - "digital set of circuits that we were looking at move over into", - "the linear space for a given set of switch settings,", - "OK? So, when I set A 1 and B 1,", - "A equal to one and B equal to one, my NAND gate becomes like", - "this. OK, it's a simple resistive", - "network with a voltage source, VS.", - "So, for a fixed set of inputs, for a given set of inputs,", - "if I don't change my inputs, then my circuit looks like a", - "linear circuit, and my good old linear analysis", - "techniques apply. So that was last week.", - "And this week, we are looking at the nonlinear", - "space. And we looked at a couple of", - "techniques in the nonlinear space, analytical techniques and", - "graphical techniques. And then, I showed you an", - "example. OK, I showed you an example", - "circuit that was something that I would like to build involving", - "the light emitting expo dweeb, my little garage door opener", - "thingamajig, and I wanted to transmit music over that light", - "beam. I also showed you that it was", - "highly distorted because it was in the nonlinear space.", - "So, today what I'm going to do is introduce a new part of the", - "playground. There's a new part of the", - "playground, and I'll show you a technique whereby by focusing on", - "this part of the playground and disciplining ourselves in the", - "kind of inputs we apply to circuits, I'm going to show you", - "that certain kinds of nonlinear circuits also move over,", - "when used in a particular way, also move into the linear", - "analysis domain. OK, so let me leave that for", - "now and go back into quickly reviewing the motivating example", - "of music that I had taken last time.", - "OK, so here was a little example.", - "So I have a music source, VI, and I apply that.", - "This device that I call the, lightheartedly,", - "the Light Emitting Expo Dweeb has a current,", - "VD, across it, or a voltage,", - "VD, across it, and a current ID through it.", - "And the light intensity, I said, was proportional to the", - "current. And because of that,", - "I was able to get the light to impinge on a receiving device,", - "which produced a current that was proportional to the", - "intensity of light falling on it.", - "And that signal would then be amplified somehow.", - "We haven't talked about all of this stuff yet.", - "This will happen next week. But let's say we somehow", - "amplify the signal and then played out through a set of", - "speakers. All right, so if I had some", - "sort of a music signal here, then I could then transmit the", - "music signal over to the side on top of this light beam.", - "But the problem, as I said the last time,", - "was that our device, the Light Emitting Expo Dweeb", - "had an exponential characteristic,", - "so that I had some trouble in getting undistorted music.", - "So, the characteristic of the VI characteristics of my device", - "looked like so. The ID versus VD curve looked", - "as follows. OK, it was decidedly nonlinear.", - "And because of that, I was getting a lot of", - "distortions in my signal, and I showed you a little trick", - "to plot, given an input waveform at a transfer function such as", - "here to plot the output function.", - "OK, let me show you another little animation that I have", - "created here for you that should give you even more intuition in", - "terms of how it happens. So, this is a characteristic I", - "showed you up here. It's on both sides,", - "but I guess it points to only one unless I shuttle back and", - "forth really fast. So on average,", - "I'll be in both places. But anyway, so here's my ID", - "versus VD characteristic. And as I said,", - "there's an exponential ID versus VD curve.", - "And I want to see what the output looks like,", - "for example, a sinusoidal input.", - "So I said, let's place the input along a little graph,", - "rotate it so, and take a sinusoid,", - "and apply a sinusoid to the input, VI, which would also", - "appear across the Light Emitting Expo Dweeb.", - "And then, what I wanted to see was how the output looked.", - "OK, so let me tell you that the output is going to look like", - "this. OK, the output is going to look", - "like so. And, a little artifice to", - "discover curves like this is to think about a point here", - "corresponding to the point on the transfer curve here,", - "because this is VD, looking at the Y intercept.", - "That's a value of ID, and that's a value of ID here.", - "And, time moves along here, and time moves along here.", - "So, I did this little animation.", - "You'd better be impressed. It took me six hours to do it.", - "So, here it goes. So, let's say I start by", - "focusing on this little point that corresponds to this point", - "on the transfer function, which then, in turn,", - "points to a time, zero, this point on my ID", - "curve. OK, I hope this works.", - "So, as my point moves down [LAUGHTER], this was fun to do,", - "I promise you. So notice that as this point", - "has the following excursion, this had the following", - "excursions here. OK, all right.", - "So let me pause that little animation there.", - "At the end of the lecture, I'll put that up again if you", - "like, and you all can come and play with it.", - "So, you can actually do this in PowerPoint.", - "It took me quite a bit of time to figure out how to do it,", - "though, but it's fun. OK, so let me show you a little", - "demo, and show you a sinusoid, and show you what the output", - "looks like if I apply a sinusoid for VI.", - "So, I'll show you ID as a function of VI when VI is a", - "sinusoid. There you go.", - "So, I applied my sinusoid VI, and this is the current that I", - "get. And notice, this is the", - "transfer function that I talked about, the ID versus VD curve of", - "my Light Emitting Expo Dweeb. And I get this highly nonlinear", - "transformation of the input as I get to the output.", - "OK, so that is a problem. And then, I also played some", - "music for you. Let's do that,", - "too. I played some music for you.", - "I applied the music as an input to the circuit,", - "and that's the output. OK, that's the output that I'm", - "observing at the amplifier. It's highly distorted.", - "OK, we can stop that. There you go.", - "OK, so that was my problem. OK, so we had covered,", - "we had gone this far last Tuesday.", - "I set the problem up for you, motivated what we had to do,", - "and showed you that I was able to transmit music over my garage", - "door opener, but I did not think I could listen to that music for", - "very long. So, I challenged all of us to", - "think about how a trick that I could use to be able to transmit", - "music and have a linear response.", - "So, did you people get time to think about it?", - "So how many people here think they know the answer?", - "It's OK, don't be modest. Go ahead.", - "Could you speak louder? Yeah, you find another", - "something, kind of element, that's got the opposite graph", - "so that when you add them together.", - "Oh, this guy wants to cheat. No.", - "He wants a new element. So, no, no new elements.", - "Pardon? Build an MP3 encoder.", - "Ah-ha, so that will happen much later.", - "Yes? Digitize the signal before you", - "send it to the LED? Digitize the signal before you", - "send it to the LED. But in some sense,", - "each of these solutions is a huge sledgehammer approach to", - "look at solving it. There's a much simpler", - "technique I can apply here. Yeah?", - "Add a voltage offset. Ah, ah-ha, that might work.", - "What else? So let's say,", - "here's my signal, right?", - "If I add a voltage offset, that will just bump the signal", - "up here. Then the curve is still", - "nonlinear. But you're getting there.", - "Well, I'll tell you what. Let's pause here.", - "Let me quit while I'm ahead. OK, so the answer here,", - "folks, is Zen. OK, what I want you to do is,", - "so, in Zen, what you have to do is you have to sit down in a", - "courtyard, and look at a rock, like a small rock on the", - "ground. And you got a focus on it till", - "the rest of Earth kind of vanishes.", - "Just focus on the rock. OK, now make like you're in a", - "courtyard, and you're looking at this little area here.", - "Just look at this. OK, and I'll give you ten", - "seconds. Sit down quietly,", - "and no sounds. Just stare at the spot here.", - "OK, make believe this is your little rock, and just stand", - "there and think about it. OK, I'll give you five seconds", - "to do that. Just stare at it.", - "And very soon, the answer should pop into your", - "heads. OK, what do you see?", - "This guy, if I focus on this really small region of the", - "graph, this small little piece looks more or less linear.", - "OK, hmm, so that should give me some insight.", - "This whole thing, the macrograph is nonlinear.", - "But I focus on a little rinky dinky piece of that graph like", - "so, that appears more or less linear.", - "If it's small enough, that appears linear.", - "So, I'm staring at this, and that appears linear.", - "The question is, how do I exploit this little", - "small, little, linear region to get a linear", - "response from my device. OK, so here's the trick that", - "I'm going to use. The little trick that I'm going", - "to use is the following. Notice that,", - "let me call this voltage at the center of this region capital", - "VD. What I can do,", - "if I take my input signal, and I just pointed out earlier,", - "I bump it up. I boost it.", - "OK, so I apply a DC offset to my input signal,", - "like so. So I apply some input signal,", - "VI, which is also equal to the VD if I look at a variable", - "across the nonlinear element. If I apply a DC offset,", - "VI, and I superimpose the music on top of that,", - "let me call my music, just to distinguish between the", - "two, capital VI, and the small vi.", - "OK, that's my music. So here's my capital VD,", - "my DC offset. And I want to superimpose my", - "music on top of that. OK, so I've gotten halfway", - "there. By superimposing my music here", - "instead of having excursions out here, I now have excursions out", - "here. OK, and so I'm using some", - "portion of the graph here. But that's still way beyond the", - "small little element there. So a second think that I do in", - "addition to boosting up the signal is shrink it.", - "Think of boost and shrink, BS.", - "So what I want to do is boost up the signal using a DC offset,", - "and shrink the sucker. OK, so I'm going to go with a", - "small signal and bump it up. OK, so now what happens is that", - "small signal in its excursions, only uses that little portion", - "of the graph. OK, again, remember:", - "bump and shrink, bump and shrink,", - "two things, boost and shrink. So what do you think of that", - "trick? So, by doing that,", - "what happens is that signal that has excursions here will", - "produce a corresponding response in this region,", - "OK? And I argue that since this is", - "more or less like a straight line, I invoke Zen here,", - "and argue that this little signal now gets transformed,", - "and I get a linear response. OK: boost and shrink.", - "So in terms of my circuit, let me draw it out for you.", - "My Light Emitting Expo Dweeb, and this whole signal was what", - "I used to call V capital I, and that's made up of two", - "components now, a bump offset,", - "and a shrunk voltage VI. It shrunk, so therefore I've", - "used the small v and small i, like, really,", - "really small. In the same manner,", - "I get a VD ID across the LED, and the corresponding values", - "here will also have a DC offset and a small response.", - "Let me call that ID plus I small d.", - "I'll do all this mathematically in a second as well,", - "but first let me do it completely intuitively so you", - "get some insight into what's going on.", - "And, VD is simply capital VD plus small vd.", - "OK, and this is the same as VI, I, and VI.", - "OK, so what have I done? I've done two things.", - "I have said, as an engineer,", - "OK, I care about getting music across my garage door opener.", - "And I'll do what it takes to do that.", - "OK, so as an engineer, I'll do two things.", - "I'm going to bump my signal up and shrink it.", - "And the bumping and shrinking, and I do it like this.", - "I shrink my signal, the music signal here,", - "and add a DC offset. OK, and I claim that the music", - "I listened on the other side now, provided I have enough", - "amplification there, is going to be undistorted.", - "OK, so far I've showing this to you completely intuitively using", - "little sketches, no math.", - "I promise you, I'll give you a bunch of math", - "in a few seconds, but just get the basic idea,", - "and get the intuition behind it.", - "So let's go back to our demo and take a look.", - "So remember, BS, right, bump and shrink.", - "So what I'm going to do is first of all,", - "let me bump up the signal. So, what I'll do is I want to", - "add an offset to my input, and let me bump it up.", - "Let me shrink it first. It'll make the point a little", - "clearer. So, the big input,", - "green, is a big input. Let me shrink it.", - "OK, so I've made my input small, and in the middle of that", - "picture out there, you see the region of the", - "transfer curve that's being articulated.", - "OK, this region of the curve is being articulated by the small", - "signal. It's a much smaller signal.", - "And the output is still distorted because I have to do", - "two things: bump and shrink. I've only shrunk.", - "OK, let me bump it up now. What's the yellow curve?", - "It's going to get linear. It's going to get proportional", - "to the input. Then I'm bumping it up now.", - "I can make it smaller, make it even smaller,", - "there you go. Isn't that fantastic?", - "So, I'm making nature do my bidding here,", - "OK? So, this is one of those,", - "when I learned electronics and so on many, many years ago,", - "this was one of those really big ah-ha moments for me,", - "saying, wow, that stuff is cool.", - "It's something that I couldn't think about myself,", - "and it's not obvious, and by being disciplined and", - "creative in how I use circuits, I can do really,", - "really cool things. OK, remember this as a big", - "ah-ha moment for you. So, here's my little signal", - "that I've shrunk and bumped up, and my output is a sinusoid,", - "and not this funny, distorted waveform.", - "And notice that this is the region of the curve that is", - "being articulated. So, I can make the signal even", - "smaller if I like. OK, and what I'd like to do", - "next is play music for you, and if you don't believe your", - "eyes, you can at least believe your ears.", - "Let me go to the distorted signal again,", - "switch to music, and raise it up.", - "OK, now what we'll do is shrink the music signal and then bump", - "it up. Can I turn the volume down a", - "little bit? That's good.", - "OK, so if I shrunk the volume a little bit, and let me bump it", - "up, now. [MUSIC PLAYS] Just remember", - "this as a big ah-ha moment. OK, the signal is really,", - "really small. I like that.", - "I like the enthusiasm. OK, so the signal's very small,", - "and I get a more or less linear response.", - "OK. All right, so that's intuition,", - "and the approach that I've taken is called,", - "it's variously called small signal analysis,", - "incremental analysis, small signal method,", - "small signal discipline, whatever you want.", - "OK, this simply says that by boosting and shrinking my", - "signal, I get a response that's more or less linear even when I", - "have a nonlinear device. And this technique is called", - "the small signal approach. So, just to focus on that a", - "little bit longer, switch to page five of your", - "notes and let me draw something out for you.", - "OK, so what I have here, this is my offset VD,", - "and from the VD offset I have my little signal V small d,", - "and the total signal is called V capital D.", - "Offset, small signal, and that's my total signal.", - "OK, notice the offset is all capital.", - "The total signal is small v capital D, and the music or the", - "small signal is small v small d. Similarly, the output is going", - "to look like this, and here I get an offset in the", - "output ID. I get a corresponding signal,", - "I small d, and I get a total signal, I capital D,", - "OK? The cool thing to notice is", - "that the signal here, the output signal here", - "corresponding to the input signal, the music signal,", - "VD, is small I small D, and that is more or less", - "linear. OK, and I can even plot the", - "signal like so. This is my input,", - "v capital D. That's T.", - "This is VD, V small d. That is my total input.", - "And similarly, I have an output.", - "And this is my output ID. And, that looks like this,", - "I capital D, small i small d,", - "total signal I capital D. OK, so that's the small signal", - "method. So, let me summarize that for", - "you.", - "There are three steps to the method.", - "So, first of all, operate at some DC offset.", - "This is also called DC bias, and in that example it's VDID.", - "OK, so I choose an operating point that bumps up the", - "operation in some region of interest.", - "The second step is to superimpose small signal on top", - "of VD, capital V capital D, to superimpose a small signal,", - "and the third step is observe the response --", - "-- and the response, small i small d,", - "that's the music part of the response, ID,", - "is approximately linear. OK, three steps to the method", - "here, and just remember this notation.", - "And, my notation in the small signal model is as follows.", - "My total signal ID is the sum of two signals,", - "I capital D plus small i small d.", - "This is called the total signal.", - "That's called the DC offset. And this is the superimposed", - "small signal. OK, total signal,", - "DC offset, plus the small signal.", - "And sometimes, especially when doing math,", - "and so on, we may oftentimes represent ID as a delta,", - "I capital D, OK, to show that ID is", - "incremental change in the value of I capital D.", - "And because of that, this method is also often", - "called the incremental method, incremental analysis.", - "OK, so far what I've done is given you some intuition.", - "I've developed a small, simple method,", - "given you some insight into why we use this method,", - "and also shown you some demonstrations that show that", - "when I bump and shrink, and observe the response,", - "I do get a more or less linear response.", - "So let me now do this mathematically and show you that", - "mathematically, you can also derive your", - "response to be a linear response.", - "This is page seven. So, I know that ID is some", - "function of the diode voltage. F was my nonlinear function.", - "OK, so my function F was a nonlinear function.", - "So therefore, ID was nonlinearly related to", - "VD. So, let's do the math.", - "So as a first step, what we did was replace VD by a", - "DC offset, the small signal method, a DC offset,", - "plus a small incremental change.", - "OK, by doing the math, let me simply use the delta VD", - "notation to show you that I'm dealing with small increments,", - "and also because in the mathematics community,", - "when you learn about some of these techniques,", - "they will use the incremental change notation,", - "which is the delta VD notation. In electrical engineering,", - "we use a small v, small d notation.", - "So, this is a large DC offset, and this is a small change", - "about that offset. So, you folks have taken math", - "courses before, and been looking at finding out", - "the value of a function, which is a small change for an", - "input value, which is a small change about a big input value", - "or a big DC point is Taylor's expansion.", - "OK, so let's use Taylor's series expansion,", - "OK, and substitute VD plus delta VD into this,", - "and see what ID looks like. Again, let me tell you where", - "I'm going with this. ID equals F of VD.", - "This is a nonlinear function, OK?", - "I claim that by replacing VD, the input, with the DC offset", - "plus a small value, the resulting response to the", - "small value will be linear, OK?", - "So what I'm going to do next is replace VD with this sum here,", - "and then do the math, and show you that the response", - "corresponding, or the change in ID", - "corresponding to the change in VD is going to be linear.", - "All right, so let's expand this function using Taylor's series", - "near the DC offset point, capital V capital D.", - "OK, so ID is simply, by Taylor's series,", - "I want to find out a value of the function close to V capital", - "D. OK, so I take the value of the", - "function at that point, and then I add a few terms in", - "my Taylor's series expansion. The first term is simply the", - "good old Taylor's series stuff. OK, the first term is the first", - "derivative of the function times the change.", - "And then, the second one is second derivative.", - "OK, and then I get higher order terms.", - "So this is nothing new here. This is good old Taylor series", - "expansion, and again, let me tell you where I'm", - "going. I want to look at the response", - "for an input that looks like this, and I want to show you at", - "the end of the day that the response in ID,", - "the effect on ID of using an input like this is as if that", - "effect, the incremental change is linearly related to the small", - "input, delta VD. So here's my Taylor's series", - "expansion for delta V. Now remember,", - "I told you that delta VD is much, much smaller than V", - "capital D. OK, it's a very,", - "very small quantity. But that quantity is really", - "very small. Then what I'm going to get is", - "that my output is, I can begin to ignore my second", - "order terms. OK, delta VD is very,", - "very, very small. Then, what I'm going to do is", - "that ignore higher order terms. So I'll go and ignore higher", - "order terms. They'll all go to zero.", - "Remember, I can do this because by design I've chosen delta VD", - "to be very, very, very small.", - "OK, remember, we are engineers.", - "I've chosen it in a way that this is very small.", - "OK, so I'm telling you that's the case, and under those", - "conditions, I can ignore second higher order terms,", - "in which case I am left with this expression here.", - "So let me rewrite this. Let me rewrite this down here.", - "OK, I've just copied this turnout, I've ignored all these", - "terms here, and so I have a more or less equal to sign that", - "remains. So what I'm going to do is when", - "I apply a small input of this form to a large DC offset,", - "my output is also going to look like some output offset with a", - "change in the output offset. And let me call the output", - "offset I capital D, and some small change in the", - "output delta ID. OK, we'll make sure we can", - "convince ourselves that this is indeed the case.", - "Notice that this guy here, F of capital V capital D is a", - "constant. That's a constant with respect", - "to the incremental change, delta VD.", - "Similarly, this part here is a constant.", - "Notice that this term here is the first derivative of the", - "function evaluated at the DC bias point, capital V capital D.", - "OK, so this term is also a constant with respect to delta", - "VD. So notice, then,", - "I have a constant term plus a constant term multiplying a", - "small change, delta VD.", - "So what I can do next is, in this case,", - "given that I have a constant term on both sides,", - "and on this side it's a time varying term,", - "what I can do is equate the two constant terms.", - "I can go ahead and equate these two terms.", - "Remember, I have a constant plus a time varying term,", - "OK, if I'm assuming here that delta VD, my little music signal", - "is a time varying term. So, this constant will equal", - "this, so ID must equal F of VD. And I know that's the case", - "because the function evaluated at the DC offset gives me the DC", - "current ID. And similarly,", - "ID is equal to that component. Delta ID is equal to D,", - "F of --", - "OK, so my incremental change in the output is the first", - "derivative multiplied by the small change in the current.", - "OK, so I'm pretty much done. So, therefore,", - "notice that delta ID is proportional to delta VD.", - "OK, and that's what I had set out to show.", - "Remember, I had set out to show that provided my input is a", - "small excursion around a large DC offset,", - "then my output could also be a large DC offset with a small", - "excursion on top of it where the two excursions,", - "the input excursion and the output excursion would be", - "linearly related like so. OK, and the method is very", - "simple. I simply expanded the function", - "about that point, that DC point,", - "neglected higher order terms, and notice that my incremental", - "term was simply the derivative plus the incremental change,", - "a derivative times the incremental change in the input.", - "Move onto page nine, and I'd like to give you a", - "quick graphical interpretation of this.", - "So I gave an intuitive explanation earlier.", - "This is a mathematical explanation that shows you that", - "the input could be linearly related to the output,", - "provided, the outputs would be linearly related to the input,", - "provided the input has a DC offset, and small excursions", - "about that DC offset. So, let me give you some", - "intuition in what you've really done here, using a little graph", - "here. So, I'm going to plot ID versus", - "VD, and notice that I have some point here, V capital D,", - "I capital D. That's my DC bias.", - "So, I have some DC bias point here.", - "OK, what is this? That is simply the slope of the", - "curve at that point. OK, it's the slope of this", - "curve evaluated at this point. So this guy here is simply the", - "slope of this curve evaluated at ID VD.", - "OK, now, what I care about is this point here,", - "and this point here. So let's say that this is delta", - "VD, all right, and that corresponds to this", - "point here. So what I've done is taken the", - "slope and multiplied that by delta VD.", - "So I've taken the slope, and multiplied it by delta VD,", - "OK, and that gives me this component here.", - "OK, and so, this is the point that I'm going to get.", - "So in other words, what I've done is approximated", - "point A using the Taylor trick by the point B.", - "OK, so this is a point, A, which is what I really want,", - "and I've approximated that by taking the slope of the function", - "at V capital D, and multiplying that by the", - "change in the input to get the corresponding Y offset,", - "and that's the point that I get.", - "And notice that if I make this delta VD small enough,", - "then the error between these two points becomes smaller and", - "smaller. So back to our example,", - "so ID was a e to the BVD. This was the relation for our", - "Expo Dweeb, and let me just plug in the values.", - "So, ID plus small id. Notice, I'm just shuttling back", - "and forth between the notation delta VD, and small v small d.", - "OK, and so that is given by a e to the BVD, oops,", - "plus, I'm just writing that equation up there.", - "Let me call this equation X. And so, I get the second term", - "is the derivative, ab times e to the BVD times", - "delta VD, small VD, and equating this term that the", - "DC offset. Notice that this is the DC", - "offset in the output, and the small signal,", - "ID is, further notice that in this particular example,", - "what's that? a e to the BVD.", - "That's simply ID again. It just happens to be that way", - "in this example. So, I get ID times BVD.", - "So, for my input, small id, my incremental change", - "in the output is some ID times B times VD.", - "And notice that this is a constant.", - "And because that is a constant, my small signal behavior ID is", - "going to be linearly related to the signal, VD,", - "the input signal VD. OK, in the last three minutes,", - "I'd like to give you one additional insight.", - "So what we've shown so far is if I have an offset and a small", - "change above it, then my output ID will be", - "linearly related to my input. Now let's stare at this thing", - "again. Let me rewrite it.", - "It's some constant IDB times VD.", - "So, where have we seen such an expression before?", - "OK, where ID was some constant times VD.", - "OK, remember, I equals V divided by R:", - "Ohm's law. What I want to show you now is", - "how we constantly keep simplifying our lives.", - "The moment we hit some complication and things get too", - "painful to analyze, as engineers,", - "we come up with some clever tricks to make an analysis and", - "use of circuits simple again. And so, notice that this is", - "similar to some, one by RD VD,", - "where RD is simply one over IDB.", - "I'm just defining this to be RD.", - "And what that means is that I can take a nonlinear circuit", - "that looks like this. OK, and what I can do is", - "replace this by its incremental equivalent, and build what is", - "called a small signal circuit. And I'll just introduce it", - "here. And we will revisit the circuit", - "in much more gory detail a couple of weeks from now.", - "So, what I can do is build a small signal circuit where I", - "have all the small signal variables, and replace a", - "nonlinear device by a simple little resistor whose value is", - "given by IDB. OK, so therefore,", - "what I can do is take my nonlinear circuit,", - "and for small, incremental changes,", - "replace that circuit with this equivalent small signal circuit,", - "and go back to doing simple stuff again.", - "Thank you." - ] -} \ No newline at end of file diff --git a/subs/KLim9Xkp7IY.srt.sjson b/subs/KLim9Xkp7IY.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/KLim9Xkp7IY.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/KawScqSYew0.srt.sjson b/subs/KawScqSYew0.srt.sjson deleted file mode 100644 index fe8b0e2a73..0000000000 --- a/subs/KawScqSYew0.srt.sjson +++ /dev/null @@ -1,515 +0,0 @@ -{ - "start": [ - 0, - 3390, - 6630, - 8860, - 10230, - 12240, - 13650, - 17510, - 20900, - 23500, - 26410, - 29420, - 32790, - 34430, - 37960, - 40480, - 43120, - 45440, - 47790, - 50481, - 54750, - 55970, - 59050, - 61500, - 66830, - 68220, - 72570, - 75820, - 77090, - 80440, - 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518520, - 520780, - 524169, - 528000 - ], - "text": [ - "PROFESSOR: So far in 6.002, you've seen how by making some", - "simplifications of Maxwell's equations, we've ended up with", - "very simple algebraic laws that can be", - "used to analyze circuits.", - "And in this little playground of ours,", - "really good things happen.", - "This is our EECS playground, where by making some", - "simplifications, we've been able to really come up with", - "very simple techniques for analyzing circuits.", - "So today, as we build up our arsenal of techniques for", - "analyzing circuits, we'll look at a further simplification.", - "We're going to look at a part of this playground in which", - "linear circuits reside.", - "These kinds of circuits allow us to use some even more", - "powerful techniques to analyze them.", - "These new techniques that you will learn today include", - "superposition, Thevenin and Norton.", - "It's pretty amazing to think of these techniques as the", - "bazookas of EECS.", - "OK, let me start with a quick review as is my usual practice", - "of what we've seen so far.", - "So the circuit analysis method you've seen so far include,", - "first of all, the KVL, KCL method.", - "In this method, the KVL, KCL, and the element rules are used", - "to analyze circuits.", - "The KVL method, as you've seen before, is one where you take", - "the various voltages in a loop in a circuit and they should", - "all sum to zero.", - "Similarly, the currents at any given node,", - "must also sum to zero.", - "That's KCL.", - "And so you apply these KVL, KCL and element rules to", - "circuits, and then go solve them.", - "But we did see that they ended up with a very large number of", - "equations that were quite messy to resolve.", - "The second technique that we looked at last week included", - "circuit decomposition rules, where you applied some of", - "these rules to compose resistors and other elements,", - "and solved circuits that way.", - "And then, we looked at the node method, where you chose a", - "ground in a circuit.", - "And then you applied KCL at each of the nodes, the", - "reference to the ground node.", - "And what was interesting is that the KVL was implicit in", - "the pattern that you used in the node method, where the", - "pattern was the ei minus ej, divided by the resistance of a", - "given [UNINTELLIGIBLE].", - "And this was a pattern that you really borrowed from KVL,", - "and this was implicitly used in the node method.", - "The node method, of course, is the workhorse of 6.002 and can", - "be applied to all kinds of circuits.", - "It really applies in the entire playground of ours.", - "So when in doubt, simply go ahead and", - "apply the node method.", - "OK, as I promised, we'll now look at the smaller region of", - "the playground, and see if some interesting things happen", - "in that playground.", - "So to give you a quick review, let me start by looking at", - "some basic properties of linear circuits.", - "Following that, I will look at the superposition tool kit for", - "your arsenal of techniques to analyze circuits.", - "And then I will talk about the Thevenin method.", - "And finally, I'll talk about the Norton method.", - "OK, so let's get started with linear circuits and see what", - "linearity means.", - "So I want to do an example using the following little", - "circuit, in which I have a voltage source", - "and a current source.", - "And my goal here is to find the voltage at this node e.", - "And I'm going to pick a ground node here and find the voltage", - "e referenced to this ground node that I've just", - "marked out for you.", - "So to analyze a circuit, you're supposed to write down", - "the node equations.", - "And write down the mode equations for the node.", - "That's the only node for which we have an unknown.", - "Recall that I have another node here, but because that is", - "connected by a voltage source to ground, its voltage is", - "simply V.", - "OK, let's start by writing the node equations for the node", - "with unknown voltage e.", - "So let's start by looking at the current that goes from the", - "node with voltage e to the left.", - "And so I take e minus V divided by R1.", - "That is the current headed in the direction from e to v.", - "And then I add the current that is going down this edge.", - "That is just simply e divided by R2.", - "And then I take the current that is", - "headed in this direction.", - "And that is simply minus I. According to the KCL rule,", - "they all sum up to 0.", - "So the first thing you will notice as you write the node", - "equation right away is that this equation here shows you", - "that it is linear in the various voltages and currents", - "e, V, and I. In other words, you don't have terms, no terms", - "that are eV, or V squared, or VI, and so on.", - "So this circuit here is", - "characterized by the node equation.", - "And notice that it is linear in the e, V, and I terms.", - "OK, let's go ahead and look at this in some more detail.", - "And I'm going to simplify the equation a little bit more to", - "really get a much clearer sense of the linearity here.", - "So I've written down the node equation.", - "And I'm going to simplify by rearranging some of the terms", - "in the equation.", - "So let me collect the various coefficients.", - "So let me write down e on this side, and look at and collect", - "all the terms that multiply e.", - "So I see a 1 by R1 term here.", - "Let me write that down.", - "I see a 1 by R2 term.", - "And so e is my unknown.", - "Let we collect the knowns on the right-hand side.", - "So one of the knowns is I. So let me move it to the", - "right-hand side and put that there.", - "The other known is this one here, V divided by R1.", - "I'm going to take it to the right-hand side.", - "It becomes plus V divided by R1.", - "So let me introduce a little bit of nomenclature here.", - "So notice I've rearranged the terms. And I get some", - "coefficients multiplying e, and that is a sum of the", - "sources, V and I, where V has been scaled by", - "1 divided by R1.", - "So when you look at these terms, let's understand a", - "couple of things.", - "Let's understand a couple of things right away.", - "So if you look at the coefficient of the unknown e,", - "in general when you have a much larger circuit, it is not", - "a single value, but rather it is a matrix of values.", - "And it's just good to know these terms. It's called a", - "conductance matrix.", - "Similarly, it's usually given the symbol G.", - "Similarly, the node voltages becomes a column vector of", - "node voltages, and it's given the label e.", - "And then, on the right-hand side, you have the linear sum", - "of sources, and that is given the term S. And so you get the", - "form G times e equals S, where G is a matrix usually, e is a", - "column vector.", - "And similarly, the sum of sources ends up being a column", - "vector as well.", - "So with that bit of cultural background in terms of what", - "these things are called in general, let me", - "simplify them further.", - "And what I get now is--", - "let's try to have e on the left-hand side all by itself,", - "and divide both sides by the coefficient of e.", - "And this guy here, if I simplify it, becomes R1 R2", - "divided by R2 plus R1.", - "So when I multiply out both sides by that, what I end up", - "getting is I have a V here, and I have the I here.", - "So what is the coefficient of V?", - "So I multiply both sides by R1 R2.", - "And so R1 and R1 cancel out.", - "So I end up with R2 at the top.", - "And I get R1 plus R2 down here.", - "Similarly, so what do you think we get for I here?", - "For I, I end up with R1 R2 divided by R1", - "plus R2 down here.", - "So notice that the linearity becomes much more obvious at", - "this point where my unknown e is some constant coefficient", - "times the voltage v and some constant coefficient times the", - "current I.", - "In other words, e is of the following form. e is some", - "constant coefficient times my first source, some constant", - "coefficient times V2, and so on.", - "Plus some other coefficient times I1, some other", - "coefficient times I2, and so on.", - "So if you look at this form here, notice that this is", - "linear in the sources VIs and IIs." - ] -} \ No newline at end of file diff --git a/subs/Km9YIdkc2Oo.srt.sjson b/subs/Km9YIdkc2Oo.srt.sjson deleted file mode 100644 index 6c55eb710c..0000000000 --- a/subs/Km9YIdkc2Oo.srt.sjson +++ /dev/null @@ -1,1766 +0,0 @@ -{ - "start": [ - 10000, - 19000, - 22870, - 28675, - 32207, - 37193, - 38910, - 42833, - 47738, - 52724, - 57956, - 62466, - 67228, - 70205, - 75392, - 80070, - 83387, - 89000, - 93295, - 96517, - 98879, - 102244, - 105896, - 110263, - 114057, - 117852, - 122636, - 124896, - 129886, - 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Today we are going to take a", - "fresh look at some of the stuff we covered in the last two", - "lectures. And the graph I want you to", - "keep in mind as we go through this lecture in terms of what to", - "expect. This was time.", - "And last Tuesday's lecture we covered some stuff.", - "I talked about a method for the sinusoidal response which was", - "agony, I warned you it will be agony, and then towards the end", - "I showed you another method that was quite a bit easier but still", - "pretty hard. And I promised you that today", - "there will be a new method which is going to be so easy ,", - "actually almost trite. Just imagine.", - "I am going to make a statement right now that I think you will", - "all find hard to believe. What I am going to say is just", - "imagine your RLC circuit, your resistor,", - "inductor and capacitor, a parallel form or series form.", - "Imagine that you could write down the characteristic equation", - "for that by observation in 30 seconds or less.", - "Just imagine that. By observation,", - "boom, write down the characteristic equation for", - "virtually any RLC circuit or RC circuit or whatever.", - "And we all know that once you have the characteristic equation", - "you could very easily go from there to the time domain", - "response intuitively or to the sinusoidal steady-state", - "response, too. So just keep that thought in", - "mind. Imagine 30 seconds.", - "And that is what you should expect in today's lecture.", - "Students often ask me, if this stuff is actually so", - "easy why do you take us through this tortuous path?", - "Are we just mean? Do we just want you show you", - "how hard things are and then show the easy way?", - "I have argued with myself every year as to whether to just go", - "ahead and give the easy path and that's it.", - "But I think the reason we cover the basic foundations is that it", - "gives you a level of insight that you would not have", - "otherwise gotten if I directly jumped into the easy method.", - "So you need to understand the foundations and you need to have", - "seen that at least once. And second, once you do", - "something the hard way, you appreciate all the more the", - "easy method. All right.", - "Today we cover what is called \"The Impedance Model\".", - "First let me do a review just because of the large amount of", - "content in the last two lectures.", - "I did them using view graphs. I usually don't like to do", - "that, but even then it was quite rushed.", - "So let me quickly summarize for you kind of the main points.", - "We have been looking at, on Tuesday, the sinusoidal --", - "--looking at the sinusoidal steady state response.", - "Also fondly denoted as SSS. And the readings for this were", - "Chapters 14.1 and 14.2. what we said was if you took", - "this example circuit and we fed as input cosine of omega t,", - "we have an R and a C, and let's say we cared about", - "the output response and we cared about the capacitor voltage.", - "What we talked about was focused on the sinusoidal", - "steady-state response. And what that meant was first", - "of all focus on steady-state. In other words,", - "just to capture the steady-state behavior when t", - "goes to infinity after a long period of time.", - "And for most of the circuits that we consider,", - "because of the R or presence of any resistance,", - "the homogenous response usually would die out because the", - "homogenous response is usually of the form minus t by tau.", - "And as t goes to infinity this term tends to go to zero.", - "We are just looking at the steady-state.", - "And therefore, because of the circuits we", - "looked at, we can ignore the homogenous response.", - "All we are left to do is to find the particular response to", - "sinusoids of this form. And second was focus on", - "sinusoids. We said the reason for this was", - "that, let's say we did not care particularly", - "What happened when I just turned on my amplifier.", - "I just turned on my amplifier, often times you see some", - "distorted sound coming out for a few seconds and then hear a much", - "clearer sound. And that initial part is due to", - "the transient response. And let's say we don't care", - "about that. We care about the steady state.", - "Second we focus on sinusoids because based on the Fourier", - "series experience that you had previously, we can represent", - "repeated signals as a sum of sines.", - "And therefore it is important to understand the behavior of", - "these circuits when the input is a sinusoid.", - "And what was important was this introduced a new way of looking", - "at circuits, and that was the frequency viewpoint.", - "When we looked at transient responses, we plotted response", - "as a function of time. And when we look at sinusoidal", - "steady-state, it becomes interesting to plot", - "the response as a function of the frequency,", - "a function of omega.", - "What I will do is draw a little chart for you to sort of", - "visualize the various processes we have been going through.", - "We can liken obtaining the sinusoidal steady-state response", - "to following these steps. Here is my input.", - "What I did as a first step was fed my input to a usual circuit", - "model. My elements were lumped", - "elements, built the circuit and wrote down the VI relationship", - "for the element. As a second step I set up the", - "differential equation.", - "This was the first of four steps, set up a differential", - "equation. And then the path that I took", - "first was fraught with real nightmarish trig.", - "By the end of the day it would still yield an answer.", - "It could be a nightmare. But I would get something", - "cosine omega t plus something, some phase.", - "I could grunge through the trig.", - "And I gave up halfway in class here, but you could grunge", - "through it if you would like. And you would get the answer to", - "be some sinusoid with some amplitude and some phase.", - "So Vi cosine omega t would produce the response that was", - "something cosine omega t plus some phase.", - "We said this was too painful so let's punt this.", - "Instead, what we said we would do is take a detour,", - "take an easier path. And the easier path looked like", - "this. I said let's sneak in --", - "-- Vie^(j omega t) drive. That is just imagine,", - "do the math as if you had fed in not a Vi cosine omega t but a", - "Vie^(j omega t). And from Euler's relation you", - "know that the real part is Vi cosine omega t.", - "So we said that I am going to sneak in this thing,", - "find the response and just take the real part of that because", - "the real part of the input gives me this.", - "So this is my \"sneaky path\". And what I did there,", - "as soon as we fed in the e^(j omega t), because of the", - "property of exponentials, the e^(j omega t) cancelled out", - "in my equation. And what was left was some", - "fairly simple complex algebra. And at the end of the day,", - "after I grunged through some fairly simple complex algebra,", - "I ended up with some response that looked like this.", - "Vpe^(j omega t). What I would find is that for", - "the input Vie^(j omega t), I would get a response Vpe^(j", - "omega t). And then what I said we would", - "do is take the real part. Why take the real part?", - "Because this is a fake, a sneaky input.", - "The input I really care about is the real part of the sneaky", - "input. So this is my sneaky output.", - "And what I care about is the real part of the sneaky output.", - "That is sort of the inverse superposition argument that I", - "made on Tuesday that if what I care about is the real part of", - "this input, then I just take the real part and get the output", - "that I care about. So I take the real part.", - "Notice that Vp here, in the examples we did,", - "we did an RC example. The Vp here was a complex", - "number. So I could represent that", - "complex number as, in many ways.", - "This is e^(j omega t). I could represent Vp in an", - "amplitude, as a phasor, actually polar coordinates.", - "I can say that the equivalent to Vpe to the j angle Vp.", - "Vp is a complex number. If you look at the complex", - "appendix in your course notes, I can represent a complex", - "number as an amplitude multiplied by e raised to j", - "times some phase. It's simple complex algebra.", - "And then what I could do here is take the real part of that.", - "And when I took the real part of that what came about was that", - "this was simply Vp. Notice that the angle Vp goes", - "in here so it becomes j times omega t plus angle Vp.", - "It is Vp amplitude times e raised to j omega t plus j angle", - "Vp. And the real part of that is", - "simply Vp cosine of that stuff. What I end up getting here is", - "Vp cosine omega t plus Vp. The cool thing to notice was", - "that once I found out this response here,", - "I could immediately write down the output based on Vp.", - "In other words, once I had Vp,", - "I could stop right there in my math.", - "I got Vp very quickly here. This step produced Vp very", - "quickly, after two algebraic steps.", - "And then from here I could directly write down the answer", - "as homogenous of Vp cosine omega t plus angle Vp.", - "Boom, right there. So this was a much shorter", - "path. And here I just described to", - "you how this yields an expression for Vp and angle Vp.", - "And for our example Vp was 1/(1+j omega RC).", - "And we often times write a shorthand notation 1+sRC,", - "where S is simply j omega. We commonly jump back and forth", - "between the shorthand notation S and j omega.", - "S has some other fundamental, has another fundamental", - "significance you will learn about in future courses,", - "but for now S is simply a short form for j omega.", - "This was the path that we took. There is a hard path and an", - "easier path. Today I am going to claim that", - "even this was too hard. There is an even easier path.", - "And today what I am going to show you is that from here we", - "are going to take one step and get here.", - "I am going to show you today that we won't do this,", - "we won't do this, not this, not this,", - "none of this. One step and then we are going", - "to get the answer. So let's do that.", - "Before we jump into the impedance method and get into", - "doing that, I just would like to plot for you this function here", - "just so we can understand a little bit better exactly what", - "is going on. As I mentioned to you,", - "the output vO for our circuit there was simply Vp cosine of", - "omega T plus angle Vp. Oh, that's Vp so this one", - "should be Vi here. I am showing you Vp so there is", - "a Vi in there. Vp/Vi=1/(1+j omega RC).", - "This is a complex number, and it is simply a number that", - "when multiplied with Vi gives me the output.", - "This is also called a transfer function and represented as H(j", - "omega). This guy is a transfer", - "function, much like the gain of my amplifier.", - "Which when multiplied by the input to get me the output.", - "This guy is a complex multiplier which when multiplied", - "by Vi gives me Vp. And as such we call it a", - "transfer function H(j omega). And we can plot this function.", - "Notice that this a function of omega.", - "Remember we are taking the frequency domain view,", - "so where has time vanished? Remember that we are taking the", - "steady state view. So we are saying in the steady", - "state, if I wait long enough this is how my circuit is going", - "to behave, this is how a circuit is going to behave.", - "And the transient responses have died away and I have time", - "in my output here so my output is a cosine.", - "But that in itself is not very interesting.", - "It is a cosine of some amplitude and has some phase.", - "What we will plot is we are going to plot this property", - "here, Vp as a function of the frequency.", - "Vp is frequency dependent. As an example,", - "I could plot the absolute value of Vp/Vi, the modulus of that", - "versus omega. And notice that when omega is", - "zero again intuitive ways of plotting this is to look at the", - "value at zero and look at the value at large omega.", - "For small omega, omega goes to zero this is one,", - "so it starts off here. And when omega is very large", - "then it is much bigger than one here, so this goes down.", - "Far away this one looks like 1/omega RC.", - "And this function, assuming I have linear scales", - "on my X and Y axes looks like this.", - "We also commonly plot this using log-log scales.", - "And when you do log-log scales you get a straight line here,", - "and then you actually get a straight line of slope minus one", - "because the log of this gives you a line with a constant", - "slope, it's a slope of negative one so it becomes a straight", - "line going down. The other interesting thing to", - "realize is that this magnitude is simply one by one plus omega", - "squared R squared C squared, the square root of this.", - "That's the magnitude here. And notice when omega equals", - "1/RC, this thing, the denominator becomes one by", - "square root of 2. Somewhere here when omega", - "equals 1/RC The output is one by square", - "root 2 times the input. It's an interesting point.", - "And this is called the \"break frequency\".", - "You can view it as a frequency where I am getting this", - "transition from one to a lower value, and it is where the", - "output is one by square root two times the value of the input.", - "Now you can think back on the demo we showed you earlier.", - "And in the demo remember that as I increased the frequency of", - "my input sinusoid my output kept becoming smaller and smaller and", - "smaller. And you notice that you can see", - "this dying out or decaying of the amplitude as I increase my", - "omega. Let me go back.", - "What you have done is that, we're going to apply a bunch of", - "sinusoids to the same circuit and plot the frequency response,", - "the ratio of the output versus input as a function of", - "frequency. And kept applying a variety of", - "frequencies. So you can listen to the", - "frequencies as they go by, and we will plot the amplitude", - "up on the screen for you. Just for fun we are going to", - "play frequencies between, say, 10 hertz and 20 kilohertz.", - "It will be fun for you to figure out at what point you", - "stop hearing the frequencies. We are going to play from 10", - "hertz to 20 kilohertz. And figure out where your ears", - "cut out. That will tell you what the", - "break frequency of your ear is.", - "You can see the amplitude being articulated.", - "The bottom figure is the phase. This is the frequency axis.", - "This is the amplitude, log-log scales.", - "I am not sure about you but I cannot hear anymore.", - "If you bring your canine friends to class it is quite", - "possible that they would go berserk somewhere here.", - "As I promised you, when I plot this on a log-log", - "scale I get a straight line here and a straight line out there as", - "well and the bottom line gives you the phase.", - "Now, what you can also do is you can also go to Websim.", - "Websim is now linked on your course homepage.", - "You can go to Websim and you can play with various L and C", - "and R values. And if you plot frequency", - "response, if you click on the frequency response button,", - "boom, it will give you frequency responses for your", - "circuit that look exactly like that.", - "You can go and play around with that.", - "Thank you. All right.", - "As the next step I promised to show you an easier path.", - "And let's build some insight.", - "Is there a simpler way to get where we would like to get?", - "In particular, is there a simpler way to get", - "Vp? Let's focus on Vp.", - "Why Vp? Because remember Vp was the", - "complex amplitude of e to the j omega t.", - "And once I know Vp then I know this expression here.", - "Also notice that this here, the denominator is simply the", - "characteristic equation for, I wonder how many of you", - "noticed it, is simply the characteristic equation for the", - "RC circuit. If I can write down Vp,", - "I can write down the characteristic equation,", - "it will be in the denominator. I can also write down the", - "frequency response very easily by taking the magnitude and", - "phase of Vp. So Vp has all the information", - "humankind needs for those circuits.", - "Is there a simpler way to get Vp?", - "To bring some insight, let's go ahead and write down", - "--", - "Let's stare at this for a while longer and see if light bulbs go", - "off in our minds. Of course, I could write this", - "as Vi/(1+sRC). I just replaced the shorthand", - "notation for a j omega. And I simply divide by SC", - "throughout. So I get Vi times,", - "I simply divide by SC throughout.", - "Here is Vi. I have one by SC,", - "one by SC plus R. Light bulbs beginning to go", - "off?", - "The form we have here is 1/SC, some function of my capacitance", - "divided by something connected to my capacitance plus R.", - "This is Vi multiplied by something connected to", - "capacitance divided by something connected to capacitance plus R.", - "And remember your circuit.", - "What is that reminiscent of? What does that remind you of?", - "Voltage divider? Hmm.", - "There is some voltage divider thing going on here.", - "I just cannot quite pin it. It is something about the", - "capacitor, capacitor plus booster, some voltage divider", - "thingamajig happening here. We will try to figure that out.", - "What I will do is replace those terms with something called Zc.", - "Zc plus Zr. If I can find out the Zr and Zc", - "somehow, I can write down the Vp by inspection by the voltage", - "divider action, by some generalization of the", - "good old Ohm's law that I know about.", - "Let's proceed further and see if we can make some kind of a", - "connection between this and this.", - "If I can make the connection then boom, I'm done.", - "I will just use voltage dividers and I am home.", - "OK, so let's play around and see.", - "There is something in there. By now you should know that we", - "are very close. There is something going on in", - "there. I just need to get that spark.", - "I just need to make that spark so I can bridge the gap between", - "something that is really easy versus where I am.", - "Let's take a look at the resistor.", - "I have my resistor with the voltage vR across it and a", - "current iR. Remember to get to any sort of", - "steady state you are going to be dealing with the drives of the", - "form vI e to the j omega t, exponential drives.", - "And by taking the real part, I know I get the input,", - "and the real part of the output gives me the actual output.", - "Let's say my iR is simply Ire^st and my vR is Vre^st.", - "The S is, again, a shorthand notation for j", - "omega. If my current Ire^st of the", - "exponential form shown there and here is Vr, I need to find out", - "what relates Vr and Ir for the element relationship for the", - "resistor to hold. In general, Ir and Vr are", - "complex numbers. For the resistor,", - "I know that Vr=RIr. And I substitute using my", - "complex drives here. So it is Vre^st=RIre^st.", - "I am just substituting for these drives,", - "Ohm's law should apply, and I cancel off e^st.", - "And so I get Vr=RIr. Interesting.", - "For the resistor I find that, based on the fundamental", - "principles of resistor action, the complex amplitude of the", - "voltage simply relates to the complex amplitude of the input", - "by the proportionality factor R. In other words,", - "for the resistor -- Just as the time domain V and I", - "were related by the proportionality constant R,", - "the complex amplitudes Vr and Ir are also related in the same", - "way. That's interesting.", - "Now let's look at the capacitor.", - "Some current ic flowing through it and a voltage vc.", - "Let's say the current is Ice^st and the voltage is Vce^st.", - "Let's plug these into the element law for the capacitor", - "and see if we can find out a way of relating vc and ic.", - "I know that ic is simply Cdvc/dt.", - "So I replace this with Ice^st=Cd/dt(vce^st),", - "which is simply Ice^st=CsVce^st.", - "So I can cancel this out again. Interesting.", - "Ic=CsVc. Very interesting.", - "What is interesting here? Notice that in the time domain", - "Ic=Cdvc/dt, the element law for the capacitor.", - "So I said let's use exponential drives, Ice^st,", - "Vce^st, that's an exponential drive, and try to find out what", - "the relationship between the complex amplitudes are.", - "I plug them and what do I find? I find that if my input is", - "Vce^st, and Vc is the amplitude of the input,", - "then the current is simply given by something multiplied", - "Vc. It's very similar in form to", - "what I saw here. The resistor,", - "Vr=RIr. For the capacitor,", - "Vc=Ic/sc. 1/sc kind of plays the role of", - "R. In other words,", - "the complex amplitudes around the capacitor are related by Vc", - "equals some constant times Ic. Almost like a funny Ohm's law", - "kind of relationship where Vc and IC are complex amplitudes.", - "For the inductor it is the same way, iL, vL and L.", - "Let's say iL=Ile^st and vL=Vle^st.", - "Substitute the values for the inductor into its element", - "relationship as well. I know that vL=LdiL/dt.", - "Therefore, substituting the complex amplitudes is L.", - "And diL/dt will simply be Ilse^st.", - "So I cancel out the exponentials.", - "The reason we're able to do all of this is simply the remarkable", - "beauty of exponentials. Exponentials are absolutely", - "stunningly beautiful. The reason is that when I", - "differentiate them what I get back is the exponential times", - "some constant, and the constant was in its", - "numerator multiplying t. And that's the beauty of", - "exponentials. If this was a sine then I would", - "get cosine and a sine. With exponentials these cancel", - "out and what I am left with is something that is LsIl.", - "Again, for the inductor, the voltage across the inductor", - "relates to some constant Ls here times Il.", - "This is absolutely stunning and almost looks like a form of", - "Ohm's law here. What I am going to do is let's", - "give this the name Zr. Let's give this 1/sC the name", - "Zc. And let's give this the name", - "ZL. It kind of behaves like a", - "resistor, so the resistor simply becomes Zr.", - "And 1/sC behaved like a resistor so I called it Zc.", - "And this is a ZL. These are called \"impedances\".", - "In other words, for a capacitor,", - "as far as complex inputs and outputs are concerned,", - "if Vc and Ic is fed to it, the capacitor can be replaced", - "by an impedance Zc where I can write the relationship between", - "Vc and Ic as Vc=ZcIc. Where Zc is simply one by sc.", - "Similarly, for an inductor --", - "-- I can write its impedance ZL as sL and I get Vl=ZLIl.", - "And finally for a resistor it is pretty simple.", - "What I am saying is that if I am in the region of the", - "playground, if I constrain myself in the region of the", - "playground where my inputs are something Vi e to the j omega t", - "or exponentials, in that little region of the", - "playground now, I am focusing more and more on", - "small parts of the playground so I am kind of boxed in right now.", - "In that region of the playground this applies.", - "In that region of the playground, I can replace", - "resistors by impedances, capacitors with impedances of", - "value 1/sC. And within that playground the", - "beauty of analysis there is that in that region of the playground", - "where the inputs are of the form Vie^st, it turns out that the", - "element laws are simply generalizations of Ohm's law.", - "That is absolutely stunning. It is one of the biggest", - "hallelujah moments in learning circuits.", - "This is really big. And I think this is almost as", - "big as the realization that you can take a nonlinear circuit,", - "operate it at a given operating point, and you can sit around", - "doing Zen things, looking at small perturbations", - "in there, those are going to be linearly related.", - "This is one of the big hallelujah moments in 6.002.", - "And this is of the same magnitude as the small signal", - "response being linear. It is something that is", - "completely non-intuitive. It is something that you just", - "would not have known until you had seen it happen.", - "The same way here. This is very important so I", - "will repeat it again. I have boxed myself into this", - "small region of the playground where all I care about are", - "sinusoidal inputs and steady-state responses.", - "So there I focus on complex inputs, Vi e to the j omega t.", - "And I have just shown you that I can replace inductors,", - "capacitors, resistors with their impedances.", - "And the amplitudes of the corresponding signals around", - "them are related by just a simple Ohm's law like", - "relationship using impedances. I am sort of boxed into this", - "playground, right? In my playground it is all", - "about e to the ij omega t. e to the ij omega t is implicit", - "everywhere. I just don't show it.", - "If I want to talk to somebody else outside but within MIT in", - "this small region, it's all e to the ij omega t in", - "there. If I want to talk to somebody", - "outside, get out of MIT, get out of this playground,", - "what else do I have to do? I have to take the real part.", - "Don't forget that. Remember that,", - "take for example Vc here, so Vc is this,", - "so implicit in all of this is that if I measure Vc at some", - "place it is really going to be Vce to the j omega t.", - "And if we the cosine, the real part,", - "then I have to take a real part of this.", - "And the real part of that would Vc cosine of omega t angle Vc.", - "This piece here kind of goes unsaid.", - "We will agree that we have to do it, but we just skip that", - "step because it is obvious. We just deal with Vcs and Vls", - "now. So a new notation certainly", - "sneaked by you, and that notation looks like a", - "big letter and a small letter. Remember you have seen vL,", - "this is the total behavior, you have seen vl,", - "that's a small signal behavior, and now you see this,", - "Vl, capital V small l. And we also have DC,", - "we have labeled operating point values as VL,", - "capital V, capital L. We have one thing left so", - "nobody go out there inventing something new because we would", - "be in trouble. This is capital V,", - "small l, and this is simply \"complex amplitude\" in the small", - "boxed region of my playground where good things happen and", - "exponentials fly. Whenever someone gives you a", - "variable, capital V, small l, remember it's a", - "complex amplitude, a complex number,", - "and you know how to get to the time domain from there.", - "You take that number, take the real part,", - "multiple the number by e to the j omega t and take the real", - "part, which is tantamount to magnitude cosine omega t plus", - "angle of that number. Actually, you know what?", - "Let's send this up.", - "Back to an example.", - "Oh, I'm sorry. I'm sorry.", - "This is not good. This is my time domain circuit.", - "Remember this was my time domain circuit.", - "A vI input. A vC output.", - "I wanted to analyze this. What I am telling you now is", - "let's box ourselves in this impedance playground.", - "And in the impedance playground the input becomes the complex", - "amplitude of the input, my resistance gets replaced by", - "a box Zr, my capacitor gets replaced by a box Zc.", - "And the voltage I care about here is Vc.", - "Zr = R and Zc=1/sC. Now, there we go.", - "I can write down Vc using a voltage divider action as Vc is", - "simply Zc/(Zc+Zr), done, times Vi of course.", - "And that gives me 1/sC divided by 1/sC+R and multiplying", - "throughout by sC I get 1/1+sCR where S is j omega.", - "Just cannot get any simpler. How long did I take to do this?", - "30 seconds. Where I spent a whole lecture", - "on Tuesday grinding through first trig, giving up halfway", - "and collapsing, and then showing you the sneaky", - "path which was still pretty painful, but 30 seconds,", - "boom. This stuff is spectacularly", - "beautiful. The really cool thing here is", - "that in this impedance domain for linear circuits all your", - "good old tricks apply. Your Thevenin,", - "your Norton, your superposition,", - "name it and it applies for this linear circuit.", - "If you close your eyes and make believe that Zr is like an R and", - "simply apply all the techniques you have learned so far in this", - "linear playground. Just a little hack at the end", - "where this is the complex amplitude.", - "And if you want to go to the time domain part then you do the", - "usual thing. Modulus Vc cosine omega t plus", - "angle Vc. Just remember that.", - "That's the jump to get back to the time domain.", - "Just to show you that this not just works for one little", - "rinky-dink circuit here, let me take a more complicated", - "circuit. If I believe in my own BS,", - "I should be able to apply this theory to my series RLC,", - "the big painful circuit that we did differential equations for", - "about a week ago. Let's do it.", - "I have an inductor, a capacitor and a resistor.", - "What I am going to do is replace this with the impedance", - "model. Input Vi.", - "Let's say this was vI. Let's say I cared about vR.", - "L, C and R. The impedance model would", - "simply be Vi. What's the impedance of an", - "inductor? SL.", - "And for the capacitor it is 1/sC.", - "And for a resistor it is simply R.", - "And just remember, if I can find out VR then for", - "an input cosine of the form Vi cosine omega t the output will", - "given by |Vr| cosine of omega t plus angle Vr.", - "Just remember this last step. But Vr itself is trivially", - "determined. It is the voltage divider", - "action again times Vi. And the voltage divider action", - "is in the denominator I sum these thingamajigs,", - "so ZL+ZC+ZR, ZR in the numerator.", - "And Zr is simply R. ZL is sL.", - "Zc is 1/sC. And R is R.", - "Vi. And I multiply through by,", - "in this particular situation, by s/L.", - "I want to get it into the same form as you've seen before.", - "Multiply throughout, the numerator and denominator", - "by s/L, what do I get? I get RS/L and out here I end", - "up getting S squared plus 1/LC, and I get plus R/L S.", - "I am done. Look at that.", - "Well, a little more than 30 seconds.", - "Maybe a minute. What is this?", - "Where have you seen this before?", - "The denominator of this expression here?", - "Ah, characteristic equation for the RLC.", - "Remember I promised you in the beginning that when we come to", - "the end of the day using a simple one-minute expression I", - "am going to write down the characteristic equation?", - "Boom, here is what I get. Did somebody hear an echo in", - "there? Notice that just by doing a", - "simple voltage divider thingamajig, I got this", - "expression. And now I can write down the", - "frequency response by replacing s is equal to j omega.", - "Even more beautiful and what is even more stunningly pretty here", - "is that remember the intuitive method I taught you about?", - "The characteristic equation gives you alpha,", - "omega nought, omega d and Q.", - "And based on those we can sketch even the time domain", - "response. Guess what?", - "RLC circuits are pass\u00e9 now. You can just write this thing", - "down and you're done, 30 seconds or less.", - "No DEs, no trig, no nothing.", - "OK." - ] -} \ No newline at end of file diff --git a/subs/KsDpWC2M-i0.srt.sjson b/subs/KsDpWC2M-i0.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/KsDpWC2M-i0.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/NAlQWlfiB_Y.srt.sjson b/subs/NAlQWlfiB_Y.srt.sjson deleted file mode 100644 index fe174cbd90..0000000000 --- a/subs/NAlQWlfiB_Y.srt.sjson +++ /dev/null @@ -1,527 +0,0 @@ -{ - "start": [ - 480, - 3370, - 5480, - 9000, - 12620, - 16290, - 18680, - 22130, - 23780, - 29080, - 33400, - 34820, - 37230, - 41160, - 43480, - 48850, - 49960, - 53760, - 56670, - 57790, - 61270, - 66320, - 67390, - 71110, - 71930, - 73370, - 74830, - 78565, - 81020, - 84290, - 87060, - 90080, - 91750, - 95050, - 98260, - 100960, - 104130, - 107780, - 108600, - 111870, - 113100, - 116580, - 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493610 - ], - "text": [ - "SPEAKER 1: All right, let's begin by building a tool chest", - "of our analysis techniques.", - "But before we begin, it would worth while asking the", - "question, what does it mean to analyze a circuit?", - "Well analyzing a circuit simply means find all the", - "element v's and i's.", - "In other words, find all the branch variables.", - "And so what are these branch variables?", - "Well if you look at element R1, I can write its branch", - "variables as plus minus v1 here, so the", - "voltage across R1.", - "And I can assign a current i.", - "And for R4, as an example, I can say there's", - "v4 and there's i4.", - "And in general I'm pretty free to assign voltage and currents", - "in any direction.", - "But you will notice that I'm going to follow a discipline", - "where I'm going to draw the current entering into the", - "positive terminal.", - "And I will show you why in a quick second.", - "So as another example, I can define the element value for v", - "for the voltage source.", - "The branch variables here would be v0 and a current i0", - "going here.", - "And so on and so forth and I can do the", - "same for all the elements.", - "So analyzing a circuit really means go find all the element", - "v's and i's for the circuit.", - "Now we're ready to start with our analysis techniques that", - "will go into our tool chest. The first method that we will", - "look at is called a very basic KVL, KCL", - "method of circuit analysis.", - "And as I mentioned earlier, our goal with circuit analysis", - "is to find all the element v's and i's.", - "The KVL, KCL method is extremely simple.", - "In the first step in this method, you take your circuit", - "and you write down for each element their v-i", - "relationships.", - "Then, the second step, you pick all the nodes and for", - "each node you write KCL.", - "Then as a third step, you go through the loops one by one", - "and you write KVL for each of the nodes.", - "Notice that each of these equations is a very simple", - "equation containing simple algebraic expressions of the", - "currents and the voltages.", - "Now you'll end up with lots and lots of equations and you", - "will have lots of fun solving them.", - "Let's take a look at an example.", - "So our goal, as I said earlier, was to find all", - "elements v's and i's.", - "Now before we go in and do an example of using the KVL, KCL", - "method, I want to spend 30 seconds telling you about a", - "couple of ideas on how to label element v's and i's.", - "So for example, here's an element, the", - "Element e in some circuit.", - "And notice it has a v and an i.", - "In general, what we're going to do is we are going to", - "follow a little discipline or a little convention in how we", - "assign the voltage and currents.", - "Specifically, we are going to take the current to be", - "positive going into the positive voltage terminal", - "So in this case, here is the positive voltage terminal of", - "the Element e.", - "And so we're going to be assigning currents to be going", - "into the positive voltage terminal.", - "Now you can do whatever you want, it", - "really doesn't matter.", - "You can go and assign currents and voltages any which way and", - "reverse them and KVL, KCL will simply work.", - "It just turns out that in a lot of what we do in circuits", - "and electronics, it is useful to follow conventions so that", - "you don't make silly algebraic mistakes.", - "So whenever you have a choice of being able to do something", - "10 different ways, it is just good to be disciplined and use", - "one technique all the time so that you", - "just don't make mistakes.", - "Now one benefit of taking the current to be going into the", - "positive terminal of the element is that the power", - "consumed by the element, which is given by vi, is positive.", - "So if you choose your convention of the current", - "going into the positive terminal, then the power", - "consumed by the element, vi, is going to be positive.", - "So this way, or this convention, of assigning", - "voltage and currents as the branch variables is called the", - "associated variables discipline.", - "And again, as with all disciplines, it's something we", - "impose on ourselves, it's a convention.", - "We just follow this convention to simplify our lives and to", - "reduce the chance that we're going to make mistakes.", - "And if you don't like this, don't worry, go ahead, make my", - "day, pick different convention for v and i, just be careful.", - "If you follow this convention, it is less likely you will", - "make mistakes.", - "Now before we actually begin the KVL method, there is one", - "more thing that I need to quickly cover which is a few", - "elements relationships.", - "So you have seen resistors before.", - "So for a resistor with the resistance value R, the v-i", - "relationship is simply given by v equals iR.", - "Where if this is my voltage v, and the", - "current i, v equals iR.", - "Next, for our voltage source, let me draw out a voltage", - "source with voltage V0 in this case.", - "And let me assign branch variable, v plus v and v, and", - "the current i.", - "Then the element relationship, v is given by V0.", - "One of the places where I find students getting confused is", - "the difference between element values and the", - "component value itself.", - "So if you look at a voltage source of this sort, V0 is a", - "property or this voltage source.", - "So if it's a battery, it might supply a", - "voltage V0 of 1.5 volts.", - "However, when I take this voltage source and I put that", - "into a circuit, with the circuit it's going to draw", - "some current i and there will be some voltage across it.", - "If there's a resistor, it will be some of the voltage.", - "But if I put an ideal voltage source with internal voltage", - "V0 and I stick that into a circuit, then the branch", - "variable v associated with that will also be equal to V0.", - "But in general, that doesn't have to be true.", - "Next, let me go to a current source.", - "In this case, I would define my current source like so.", - "I can also apply branch variables v and i.", - "And the equation, if the current source supplies a", - "current I0, then the element relationship for this is given", - "by i equals I0.", - "So these are three examples of element relationships for", - "resistors, voltage sources, and current sources.", - "OK, we are done with the preamble.", - "We are now all set to dive into method one of circuit", - "analysis, the KVL, KCL method.", - "So let's apply this method to the demo circuit", - "that we used earlier.", - "And let's see how we can find out all the", - "element v's and i's.", - "Now recall, the KVL, KCL method said, in fact circuit", - "analysis said, that solving a circuit involves finding all", - "the element v's and i's.", - "So why don't we start this example with labeling all the", - "v's and i's for our demo circuit.", - "OK, so let's get started and very quickly label all the", - "branch variables.", - "And I'm going to to follow the associated variable discipline", - "in doing that.", - "So let me start by labelling all the branch variables.", - "Let me call this v0, current is i0 coming in here.", - "Let me call this v1 and let me say this is current i1.", - "Let me say this is v4, current i4.", - "Let me say this is v3 and current i3.", - "Let me then say that this guy here is v5 and current is i5.", - "In this case, it's v2 and the current is i2.", - "So I have a bunch of branch variables assigned.", - "And I also have these branch variables involved with the", - "currents and voltages.", - "And notice here that in this example I have used the", - "associated variable discipline, that I have", - "assigned all my currents flowing into the positive", - "terminal of each of the assigned branch voltages.", - "So here I get 12 unknowns in all.", - "If we count v0, v1, v2, v3, v4, and v5, that's 6.", - "And i0 through i5, that's another 6, so I have a total", - "of 12 unknowns.", - "Also notice that is a is a node, b is a node, c is a", - "node, and d is a node.", - "And so those are my nodes.", - "I will be writing KCL for those nodes.", - "And then I have a bunch of loops.", - "So what are my loops here?", - "So I have a loop L1, I have a loop L2, I have a loop L3.", - "Now I claim there is one more loop.", - "Like let me pause here for a second and have you think", - "about where that fourth loop is." - ] -} \ No newline at end of file diff --git a/subs/NEXQhlQhg7s.srt.sjson b/subs/NEXQhlQhg7s.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/NEXQhlQhg7s.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - 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Let's get started.", - "I guess this watch is a couple minutes fast.", - "First a quick announcement. In case you have forgotten,", - "your lab notebooks are due tomorrow with the post-lab", - "exercises for the first lab. OK, so I am going to continue", - "with amplifiers today. And to just give you a sense of", - "where we headed, we have this five lecture", - "sequence covering different aspects of amplifiers with", - "dependent sources and showed how we could build an amplifier with", - "it on Tuesday. Today I am going to show you a", - "real device that implements a dependent source.", - "And then next Tuesday we will talk about analysis of an", - "amplifier. Wednesday is our quiz.", - "Thursday and the Tuesday after that we then talk about small", - "signal analysis and small signal use of the amplifier.", - "Today we will talk about the MOSFET amplifier.", - "So let's start with a quick review.", - "And in the last lecture, I showed you that I could build", - "a amplifier using a dependent source.", - "And a dependent source worked as follows.", - "Let's say I had a circuit and I connected a dependent source", - "into the circuit. Let's say in this example I", - "have a current source. So this is some circuit.", - "And the current i is a function of some parameter in the", - "circuit. That's why this is a dependent", - "source. This is a dependent current", - "source. So it could be that I have some", - "element inside. And I measure,", - "I sample the voltage across the element or between any two", - "points in the circuit. And, in this little example", - "here, this current could be dependent on that voltage.", - "So notice that although I showed you the two terminals of", - "the dependent source that carried a current,", - "there is another implicit port, another implicit terminal", - "there. And that terminal there is", - "called the \"control port\" of the dependent source at which I", - "apply a voltage or current that will control the value of the", - "current source. As a quick aside.", - "There is a small glitch with the tools in your tool chest.", - "We talked about the superposition technique where", - "you were taught to turn on one source at a time,", - "for a linear circuit one source at a time, and then sum up the", - "responses to all the sources acting one at a time.", - "Well, what do you do about dependent sources?", - "A dependent source is a source. And we have to modify the", - "superposition statement just a little bit.", - "And for details you can look at Section 3.5.1 of your course", - "notes on the details and some examples on how to do this.", - "So the approach is very simple, actually.", - "The approach is, for the purpose of", - "superposition, to not treat your dependent", - "source as sources that you turn on and turn off.", - "So what you do is when you do superposition with dependent", - "sources simply leave all your dependent sources in the", - "circuit. Just leave them in there and", - "turn on and off only your independent sources.", - "So look at the response of the circuit by turning on your", - "independent sources one at a time and summing up the", - "responses. And your dependent sources stay", - "within the circuit and simply analyze them as you do anything", - "else. So essentially what it says is", - "that just be a little cautious when you have dependent sources,", - "but the basic method applies almost without any change.", - "The readings for today's lecture are Section 7.3 to 7.6.", - "So since we are going to build up on the dependent source", - "amplifier, let me start with a quick review of that amplifier.", - "We built our amplifier as follows.", - "We connected our dependent source in the following manner.", - "And the current through the dependent source in the example", - "we took was related to an input voltage vI.", - "So some voltage vI. And so these two were the", - "control port of the dependent source and a vI was applied", - "there. And I showed you a simple", - "amplifier built with a dependent source that behaved in this", - "manner. And again I will keep reminding", - "you, just remember that the dependent source is actually", - "this box here, the control port and the output", - "port. And commonly we don't", - "explicitly show the control port for those dependent sources for", - "which the control port does not have any other affect on the", - "circuit, like it doesn't draw any current or things like that.", - "So in this particular example we said that this behaved in the", - "following manner for vI greater than or equal to 1 volt and iD", - "was zero otherwise.", - "So we can analyze the circuit to figure out what vO is going", - "to look like. And a simple application of KVL", - "at this loop here, again, you know,", - "when I say this loop here, I am pointing at something", - "here. That is the VS source that is", - "implicitly across these two nodes.", - "Again, this is a shorthand notation where this little up", - "arrow here implies that I have a voltage source connected between", - "these two terminals here. And so there is a loop here", - "that involves VS. So Vo is simply VS minus the", - "drop across this resistor. So it's VS minus the drop", - "across this resistor gives me vO.", - "And the drop across the resistor is simply iD RL.", - "iD is the current here and that's the drop across the", - "resistor. And I could get the explicit", - "relationship of vO versus vI by substituting for iD as vI minus", - "one all squared. So vO relates to vI in the", - "following manner. Nothing new so far.", - "I have pretty much reviewed what we did the last time.", - "Here is where we take our next step forward with some new", - "material. Up to now I have talked as a", - "theoretician would where I said just imagine that you had", - "spherical cow or something like that.", - "Here I just asked you to imagine this ideal dependent", - "source, control port and an output port, and it behaved in", - "this manner. So as a next step what I would", - "like to do is show you a practical dependent source which", - "turns out to be a little bit more complicated than this", - "idealized dependent source that I showed you in many dimensions.", - "Real life tends to impose a bunch of practical constraints", - "on you, and we will look at those in a second.", - "If I could find a dependent source that looked like this --", - "We had a control port A prime and output port B prime.", - "And I looked at some examples where the current through the", - "dependent current source was some function of the input", - "voltage. This is a \"voltage controlled", - "current source\". What I am going to do is talk", - "about a device that can give me this behavior or some close", - "approximation to it. It turns out that under certain", - "conditions the MOSFET that you have already looked at behaves", - "in this manner. The MOSFET that you've seen", - "sort of behaves like this. And let me show you under what", - "conditions the MOSFET behaves in that manner.", - "Let me create some room for myself.", - "Notice that I need a control port, needed an output port.", - "And I am going to view my MOSFET in a slightly different", - "manner than you have seen before.", - "I draw these two terminals here.", - "And this was a three terminal MOSFET.", - "This was my drain, my gate and my source terminal.", - "It was a three terminal device, but what I do is I view the", - "MOSFET slightly differently. I will just use this terminal", - "to be common across both the gate and the drain.", - "And so this voltage here is vGS.", - "I am just using the source port, the source terminal along", - "with the gate as a terminal pair.", - "I am using the same source along with the drain as another", - "terminal pair. So I have a vDS out there and I", - "have some current iDS that flows out here.", - "Notice that when I view the MOSFET in this manner I have", - "accomplished my first step, which is I seem to have a box", - "which has a port here and a port here.", - "And I also explained to you that a MOSFET behaves in a", - "particular manner. For one, the output port", - "behaved as an open circuit under certain conditions when --", - "This was vGS, G, drain and source.", - "When vGS was less than a threshold voltage VT this MOSFET", - "had an equivalent circuit that looked like this.", - "So when vGS was less than some threshold voltage VT then there", - "was an open circuit between the drain and the source.", - "And you saw this before. So far nothing new here.", - "However, when vGS is greater than or equal to VT --", - "vGS was greater than VT. The MOSFET behavior we looked", - "at earlier showed that this behaved either like a short", - "circuit in the simplest form or in a slightly more detailed form", - "it behaved like a resistor. We call that the SR model of", - "the MOSFET. So when vGS was greater than VT", - "we said that a simple way to approximate MOSFET behavior was", - "to view this as a resistor connected between the drain and", - "the source. That was our SR model use of", - "the MOSFET. It turns out that we kind of", - "lied. We were sort of looking at the", - "MOSFET in a really funny way. And I shone the light on the", - "MOSFET in a really, really clever way.", - "Well, I shouldn't say clever. A really, really tricky way.", - "And tricked you into believing that it was just a resistor.", - "And we constrained how you use the MOSFET.", - "So that behavior was indeed a resistive behavior.", - "But it turns out that in real life the behavior of the MOSFET", - "between the drain and the source terminals is much more", - "complicated than the limited form in which you saw it.", - "So today what I am going to do is take the wraps off the", - "complete MOSFET and show you its full behavior in all its gory", - "glory. And I will spend a bit of time", - "on that to clearly emphasize under what conditions the MOSFET", - "behaves like a resistor, as you saw when you did digital", - "circuits, or behaves differently in other domains of use.", - "Let me pause for a second and leave this space blank here.", - "And let's do some investigations.", - "Let me leave this here. I won't draw in anything yet.", - "You will figure out what it looks like yourselves under", - "certain conditions. What I will do next is apply", - "some voltages on a MOSFET and observe the current versus vDS", - "behavior and plot that on a scope and take a look at it.", - "What I am going to do --", - "-- is figure out what iDS looks like for --", - "Remember iG into the gate for 6.002 is always going to be", - "zero. In much more detailed analyses", - "of the MOSFET, in future courses you may see", - "slightly more complex behavior. But as far as we are concerned", - "it is an open circuit looking into the gate.", - "So I am going to apply a vGS across the MOSFET,", - "apply a vDS across the MOSFET and plot iDS versus vDS.", - "First let me show you what you already know.", - "What you already know --", - "This is vDS. I will just keep doing as much", - "as I can of what you already know.", - "And then when I do some new stuff I will tell you", - "explicitly. You've seen this before.", - "The MOSFET behaves like an open circuit when vGS less than VT.", - "That is when vG is less than a threshold voltage VT,", - "I have zero current flowing through the MOSFET.", - "And when vGS was greater than VT then the S model of the", - "MOSFET the switch model simply said that look,", - "we can model the D2S as a short circuit.", - "You saw this in your labs and you saw that it was a very,", - "very small resistance between the drain and the source and it", - "kind of looked like a short circuit.", - "But then we said well, that's not quite it.", - "There is some resistance. And so we said a slightly more", - "accurate model would have this line droop a little bit to imply", - "that there was some resistance R_on between the drain and the", - "source, so vDS iDS. So this was when vGS less than", - "VT and vGS greater than or equal to VT.", - "I have some resistance. And that showed me a straight", - "line kind of like behavior. And I showed you that behavior.", - "So far absolutely nothing new. Now what I have plotted there", - "for you is that behavior. Up here notice that this is the", - "vDS axis, this is the iDS axis. I am plotting iDS versus vDS.", - "And when vGS -- The gate voltage is more than a", - "threshold, notice that I see what looks like something more", - "or less like a straight line. And this is a straight line", - "with some slope, more or less a straight line", - "implying resistive behavior. And we also had some fun and", - "games here. We said hey,", - "what if I turn vGS off? Boom.", - "That would be my iDS of zero implying that the MOSFET behaved", - "like an open circuit between the drain and the source.", - "I applied a positive vGS more than VT and it began to look", - "like a resistor. Open circuit,", - "resistor, open circuit, resistor, OK?", - "Up until now nothing new. So you shouldn't have learned", - "anything at all that is new until now in today's lecture.", - "Now watch. What I am going to do is,", - "as I said, I kind of lied all this time and I just showed you", - "this behavior. And what I have been doing all", - "along is very carefully using a very small value of vDS.", - "Notice it's a small values of vDS.", - "I haven't told you what it looks like as vDS increases.", - "Well, let's go try it out. We have a scope here.", - "We have the MOSFET here. Now, I am not sure what is", - "going to happen now. You may see smoke or have an", - "explosion, who knows what? But look up there for a second.", - "I am just going to increase vDS and you can figure out what", - "happens for yourselves. I increase vDS.", - "Whoa, what a liar. Agarwal is a liar.", - "I have been kind of tricking you.", - "I have been putting -- Covering up all this part here", - "and showing you just this region of the curve for small values of", - "vDS. But as I increase vDS this is", - "nothing that looks even close to that of resistive behavior.", - "So what's happening here? What's happening is that as I", - "increase my vDS the iDS curve tails off and saturates at some", - "value of current. Notice it saturates at some", - "value of current. And so I am going to look at", - "this region of behavior. Notice that what we have looked", - "at so far was the behavior for small vDS.", - "It kind of looks resistive. But when I pump up the vDS,", - "really whack this node really hard with a much larger vDS the", - "guy says, oh, I give up.", - "And the current saturates out and flattens out and holds the", - "value steady at some value. So what's that behavior look", - "like? What is my horizontal line", - "above the X axis in terms of V I elements?", - "What is that behavior like? Current source,", - "exactly. So this is current source like", - "behavior. And so let me start by drawing", - "you a little model and explaining it in more detail.", - "What happens is that under certain conditions,", - "and the conditions are the following, when vDS,", - "that is my drain to source voltage is greater than or equal", - "to vGS minus VT. When my drain voltage goes", - "above vGS minus VT, so if vGS is 3 volts and if VT", - "is 1 volt, then if vDS goes above 2 volts,", - "if I am hammering the drain of the MOSFET with a higher voltage", - "then this guy says I give up, can't show you nice restive", - "behavior, and the current saturates out and it doesn't", - "allow you draw any more current than a maximum value.", - "And that's the current source behavior.", - "This one behaves like a current source.", - "And the current iDS is given by the following expression.", - "The current is given by iDS is equal to a constant K divide by", - "two times (vGS-VT) all squared. Kind of reminiscent of the", - "carefully chosen dependent source example,", - "just that this one here is VT. This model, which applies when", - "vGS is greater than VT, the MOSFET has to be on and the", - "drain to source voltage in the MOSFET must be larger than some", - "value, and that value is vGS minus VT then this guy begins to", - "behave like a current source. This model of the MOSFET is", - "called the \"switch current source model\".", - "So in the region of the MOSFET characteristics where vGS is", - "greater than VT and the drain to source voltage is larger than", - "vGS minus VT, the MOSFET behaved like a", - "current source between its drain and source terminals.", - "And in that part we model the MOSFET as a current source.", - "And so not surprisingly that part of the model is called the", - "SCS model in contrast with the SR model where we had a", - "resistor. Again, remember,", - "this is not meant to be conflicting.", - "It is not like gee, how can the MOSFET look like a", - "resistor, and then suddenly what happens it becomes a current", - "source. Well, the two regions are", - "different. It is not that it is behaving", - "as a current source for the same parameters, no.", - "When vDS is less than this right-hand side it does behave", - "resistive. The SR model applies.", - "But increase vDS beyond a point, the current saturates and", - "the SCS applies like so. So let's draw.", - "The SCS behavior can be drawn here vDS and iDS.", - "As I mentioned to you, for small values of vDS,", - "let's say I pick some value of vGS, let's say vGS3,", - "some value vGS, it is going to look like a", - "resistor until vDS becomes equal to vGS3 minus VT.", - "And after that it saturates out and begins to look like a", - "current source. And this point is where vDS", - "becomes equal to vGS minus VT. And this way is when this equal", - "sign becomes a greater than sign, vDS becomes larger then I", - "move into this part of the curve.", - "Similarly, for various other values of vGS it will look like", - "this --", - "-- and so on. And it behaved like an open", - "circuit as before when vGS less than VT.", - "When vGS less than VT it is still behaving like an open", - "circuit. And so as I increase my vGS,", - "provided I keep my vDS greater than vGS minus VT,", - "I get current source like behavior.", - "And notice that this is increasing vGS.", - "I have purposely drawn these curves at greater distances from", - "each other to imply that it is a nonlinear relationship in that", - "if I increase vGS by some amount, the increase in vDS is", - "related to the square of vGS. It is vGS minus VT all squared.", - "So I get a family of curves of that look like this.", - "And this is in the region of operation where vDS equals vGS", - "minus VT. And this applies in this regime", - "where vDS less than vGS minus VT.", - "This region of operation is called, as you might expect,", - "the \"saturation region\".", - "We say the MOSFET has been hammered, the MOSFET has been", - "walloped, the MOSFET is in saturation.", - "So the MOSFET is in saturation. This region,", - "corresponding to this, is called the triode region.", - "This is really very simple. All we are doing is saying that", - "when vDS is increased beyond a certain limit,", - "given my vGS minus VT, the MOSFET begins to behave", - "like a current source. It cannot draw any more", - "current. It limits the current to a", - "given value like a current source.", - "But on the left-hand side of this it behaves in a resistive", - "manner. So what I would like to do is", - "--", - "What I will do is, we've plotted for you,", - "for the MOSFET, all its characteristics in its", - "full glory for a whole bunch of values of vGS and a whole bunch", - "of values of vDS. And let me stare at those", - "curves with you for a few seconds and walk you through", - "them. So what do I have here?", - "One of these curves corresponds to a given value of vGS.", - "This may be vGS equals 2 volts. This is vDS,", - "the drain to source voltage, and this is the current.", - "So focus on this curve for now. In the beginning I hid the", - "right-hand side behavior from you and showed you just the", - "resistive behavior out here. When I increase vDS to be much", - "larger the curve saturated and I got the saturation region", - "operation of the MOSFET. And notice as I increase my", - "value of vGS the saturation current also increases according", - "to a square law behavior. So these are the entire curves", - "of the MOSFET. Finally the truth comes out.", - "And notice that when vDS is less than vGS minus VT,", - "I have more or less resistive behavior.", - "But when vDS is greater than vGS minus VT I get current", - "source like behavior. So one question you may ask is", - "when do I use one model or the other?", - "When do I use the SR model and when do I use the SCS model?", - "If you want to do a real detailed analysis then you can", - "use the SR model when vDS is less than vGS minus VT.", - "And you would use this model when vDS is greater than or", - "equal to vGS minus VT. That is simple enough.", - "In 6.002, to eliminate confusion we constrain how we", - "look at things a little bit more stringently.", - "And what we do is that for our entire digital analysis,", - "for the entire digital world we focus on the SR model.", - "And I will tell you why in a second.", - "So for all digital circuits, invertors, look at power of", - "invertors, look at delay, a bunch of other things,", - "we will be using the SR model in 6.002.", - "And I will tell you why in a second.", - "And for analog -- That is for amplifier designs", - "and situations like that, we will be operating the MOSFET", - "in a saturation region. And I will talk about that in a", - "second. What I am saying here is that", - "in 6.002, when we do analog designs, we are going to", - "discipline ourselves to using the MOSFET only in this region.", - "We are going to constrain ourselves to play in only this", - "region of the playground where vDS is quite large.", - "Why? Because I am asking you to.", - "I am saying let's play in that part of the playground and keep", - "your vDS high. And so the MOSFET is going to", - "be operating somewhere in here. So we can apply just the SCS", - "model, just the current source behavior in that region.", - "There is another important reason, which I will get to in a", - "second. And for digital designs we will", - "simply use the SR model. And it turns out that this is", - "realistic because in the digital designs that you have you seen", - "and will be seeing in this course, the pull down MOSFET is", - "on, or when these pull down MOSFETs are on,", - "the output voltage is pulled down close to ground.", - "So vDS is very, very small.", - "So it does make sense that this model apply.", - "And when we talk about amplifiers, I am asking you to", - "follow this discipline. I will tell you why in a", - "second. I am saying analog designs", - "follow this discipline that I call the saturation discipline.", - "It says simply operate the MOSFET operating in saturation", - "as a current source. We will look at an amplifier in", - "a second, and I will tell you why.", - "Now let's do a MOSFET amplifier.", - "Remember my amplifier had an input port and an output port.", - "And in general in our use we are going to have a common", - "ground. And we have a VS and a ground", - "here as well. That is the power port of the", - "amplifier. The input port and the output", - "port.", - "And let me redraw the circuit putting a MOSFET in place of the", - "current source, RL, VS, vO, drain,", - "gate, source, vI.", - "So my input is vI. Again, the MOSFET output is vO.", - "And I have a resistor RL. Hey, we've seen that before.", - "It turns out this is not surprising.", - "You've seen this before. This was our primitive inverter", - "circuit. So what's different here?", - "We showed you the circuit as an inverter.", - "What's different here is that when we look at MOSFET behavior", - "as a current source, this behaves like an amplifier.", - "In other words, when vDS is greater than some", - "value then this behaves like a current source.", - "When vDS is small, in other words,", - "in the digital design when vDS was small here,", - "because when the MOSFET was on it pulled the voltage down to", - "ground, we could view this behavior as a resistor.", - "And exactly the same thing, it is an amplifier.", - "And with digital designs, I was driving it with 5 volts", - "and 0 volts and that was it, rail to rail.", - "As an amplifier, what I am doing now is looking", - "at a small region of its behavior when vDS is greater", - "than vGS minus VT. What I am saying is that for", - "amplification let's follow the saturation discipline.", - "And the reason is that when this behaves like a current", - "source, what I have shown you is that if this behaves like a", - "current source I have shown you that this expression up here", - "gives you amplification. In last lecture we plotted a", - "bunch of values for vO versus vI, and we saw that we were", - "getting amplification. For a small change in vI,", - "I was getting a larger change in vO, and that was when I had", - "the equation for a current source in there.", - "And so we know for a fact that if I can operate this as a", - "current source, with a reasonable choice of", - "values here, I am going to be able to get amplification.", - "What I haven't told you is if this is operated in the linear", - "region, in fact, you do not get amplification.", - "I won't cover that, but you can check that out in", - "your course notes as a discussion or you can try it out", - "for yourself. Replace this with the SR model", - "for small vDS and you can show yourselves that you don't get", - "any amplification. In order to get the", - "amplification we are telling ourselves let's focus on this", - "part of the playground where vDS is greater than or equal to vGS", - "minus VT. And for vGS greater than or", - "equal to VT. So when vGS is greater than VT", - "the MOSFET is on. Further, when vDS is large,", - "larger than vGS minus VT this behaves like a current source.", - "So we have now created a small playground for ourselves where", - "we can build lots of fun little amplifiers and other circuits.", - "And provided our circuits follow the saturation discipline", - "where for the MOSFET or MOSFETs in the circuit these expressions", - "are true then the MOSFETs are going to be in saturation,", - "the current source model applies, and I will be indeed", - "getting saturation. In future courses you may", - "actually see the MOSFET used in other regimes of operation for a", - "variety of reasons. But in 6.002 when we talk about", - "amplifiers and so on we will be adopting the saturation", - "discipline. And your homework problems and", - "so on will state that. Assume that the MOSFETs are in", - "saturation. What that means is that you can", - "begin to model them as a current source and simply analyze their", - "behavior accordingly. One minor nit.", - "Note that vDS for the MOSFET is the same as vO.", - "And vGS for the MOSFET is the same as vI.", - "So if you see me jumping back and forth using vOs and vIs or", - "vDSs and vGSs they are the same thing in this circuit.", - "If you are dealing with circuits with many MOSFETs then", - "you will have vDS1s and vGS1s and so on and so forth.", - "But for this simple circuit, vO and vDS are the same,", - "vI and vGS are the same. So we could go ahead and", - "analyze that circuit. What I do to analyze the", - "circuit, I am telling you this. I am telling you that the", - "MOSFET is behaving in saturation.", - "I am telling you this. We have disciplined ourselves", - "to say that in that circuit the MOSFET is in saturation.", - "As soon as we tell you that we can then go ahead and analyze", - "that circuit. And to analyze that circuit", - "what you will do is simply replace the MOSFET with its", - "equivalent model, and that looks like this.", - "Since you have been told that it is in saturation,", - "we can replace the MOSFET with its current source model.", - "And the current iDS for the MOSFET is given by K/2(vI-VT)^2.", - "And it is always good to write the constraints under which you", - "are implicitly working close by. So the constraints are one,", - "vGS is greater than or equal to VT, vDS is greater than or equal", - "to vGS minus VT. These constraints immediately", - "follow from a statement of the type we are operating under the", - "saturation discipline or the MOSFET is in saturation.", - "Let me just mark this equation as A, and we will refer to it", - "again.", - "So with this new little circuit with the MOSFET working as a", - "current source, let's go ahead and analyze our", - "amplifier. Notice that to analyze the", - "circuit I have a current source. It's a dependent current source", - "where the current depends on the square of the input.", - "So I want to go and analyze it. This is a nonlinear circuit.", - "So I can apply any one of the methods that we talked about", - "last week for nonlinear circuits.", - "To analyze it I will go ahead and use the analytical method.", - "And my goal will be to obtain vO versus vI.", - "Again, remember where are we here?", - "The MOSFET circuit operating in saturation so I can replace this", - "with a current source. It is nonlinear.", - "And so I can apply one of the two methods, the analytical", - "method or the graphical method. Let's do both and start with", - "the analytical method. The analytical method simply", - "says go forth, apply the node method and", - "solve. Simple stuff.", - "Let's go ahead and do that. Node method.", - "I have a single node here that is of interest.", - "I know the voltage vI at this node.", - "I know the voltage VS at this node.", - "So the only unknown is here at vO.", - "So I will go ahead and do that. Let me go ahead and equate the", - "currents into the node to be zero.", - "So the currents out of the node here are iDS.", - "And that was equal the current into that same node.", - "So iDS must equal VS minus vO divided by RL.", - "iDS=VS-vO/RL. For later reference,", - "let me call that B. Simplifying,", - "what I can do is, we know that iDS is given by", - "K/2(vI-VT)^2. So I replace iDS with this", - "expression and I multiply that by RL.", - "So I get K/2(vI-VT)RL. So iDS gets multiplied by RL", - "and I get vO on this side and VS remains out here.", - "All I have done is multiplied both sides by RL.", - "So it is RL iDS, taken RL iDS to this side,", - "that is here, I get the minus sign,", - "and VS stays here, vO comes here.", - "So that is my final expression. Remember this is true under", - "certain conditions. I will keep hammering that home", - "because some of the most common errors made by people is in", - "forgetting the constraints under which this was obtained.", - "And the constraint under which this was obtained is the", - "saturation discipline. And that was true when vGS for", - "a MOSFET was greater than or equal to VT and vDS for a MOSFET", - "was greater than or equal to vGS minus VT.", - "I also know that for vGS less than VT, vO=VS.", - "So when vGS is less than VT then this one turns off.", - "That's why it is the SCS model, switch current source model.", - "When vGS is less than zero it turns off and VS directly", - "appears at vO. I would like to stare at this", - "constraint with you for a second, vDS greater than or", - "equal to vGS minus VT here. And vDS is simply vO.", - "I want to rewrite this constraint in terms of iDS.", - "It will come in handy. So iDS is K/2(vI-VT)^2.", - "This is vI-VT. So vI-VT is simply square root", - "of 2iDS/K. In other words,", - "I can write iDS less than or equal to K/2vO^2.", - "So this constraint expressed in terms of iDS is simply iDS less", - "than or equal to K/2vO^2.", - "So all I've done here is analyzed this nonlinear circuit.", - "I can also analyze it using the graphical method.", - "And in order to do that, for my nonlinear circuit,", - "in order to do that, all I have to do is plot.", - "Let's have iDS here and vDS here.", - "And as we did with a nonlinear expo dweeb, what I do is I plot", - "the device characteristics iDS versus vDS.", - "The device characteristics under saturation look like this,", - "so vGS increasing. iDS versus vDS has a bunch of", - "curves that look like current sources of increasing values.", - "That simply reflects equation A.", - "And then I superimpose on top of that the expression that", - "comes up due to equation B which is iDS equals,", - "let me write that down here, iDS equals VS/RL - vO/RL.", - "That's B. And let me plot that.", - "That is a straight line relationship between iDS and vO.", - "And so when vO is zero iDS is VS/RL.", - "And when iDS is zero vO equals VS.", - "Remember, vO and vDS are the same.", - "So this is what I get. This is the straight line", - "corresponding to equation B here.", - "And, as before, we just find the point where", - "the two intersect. Let's say I am given some value", - "of vGS. And let's say I am given some", - "known value of vDS. So for that I can go ahead and", - "find out the corresponding value of iDS from this graph.", - "Just as I told you when we did the expo dweeb stuff,", - "this line here is called a load line.", - "You will be seeing that again and again and again where we", - "have the equation corresponding to the one shown here,", - "the equation written for the output loop superimposed on the", - "device characteristics. That's called a load line.", - "So I can get this point corresponding to the operating", - "point of the MOSFET for this iDS, vDS and vGS by using the", - "graphical method. In the next lecture we are", - "going to look at, given a device of this sort,", - "how do we figure out the boundaries of valid operation so", - "that the MOSFET stays in saturation?" - ] -} \ No newline at end of file diff --git a/subs/OGtElTMJidE.srt.sjson b/subs/OGtElTMJidE.srt.sjson deleted file mode 100644 index 403922af5c..0000000000 --- a/subs/OGtElTMJidE.srt.sjson +++ /dev/null @@ -1,1754 +0,0 @@ -{ - "start": [ - 0, - 4800, - 9523, - 13561, - 29000, - 34380, - 39852, - 43044, - 47330, - 52254, - 58000, - 63257, - 68247, - 71990, - 76891, - 81168, - 84465, - 89811, - 94000, - 98776, - 101576, - 106764, - 110470, - 113847, - 118705, - 124184, - 128959, - 132034, - 135352, - 139560, - 143687, - 148219, - 151462, - 156798, - 160412, - 163424, - 168673, - 172287, - 176504, - 181662, - 185657, - 190792, - 196403, - 201919, - 205818, - 212000, - 216500, - 220375, - 226625, - 231750, - 238125, - 244000, - 246615, - 250230, - 255000, - 259384, - 264153, - 269000, - 273889, - 276458, - 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For today we are going to start", - "with nonlinear analysis. Before we do that I wanted to", - "do a little bit of review.", - "I wanted to give you the past three weeks in perspective and", - "show you how all of these things fit into the grand scheme of", - "things. We began by building a great", - "little playground, and within that playground we", - "said that by enforcing upon ourselves the lumped matter", - "discipline we created the lumped circuit abstraction.", - "So within that playfield we assumed that we had dq by dt and", - "d phi by dt to be 0 so that gave us as the lumped circuit", - "abstraction. And within that lumped circuit", - "abstraction, within this playground we looked at several", - "methods of analyzing circuits, including the KVL,", - "KCL method. We also learned the method", - "involving composing resistors, the voltage dividers and so on", - "and solving circuits intuitively.", - "And we also looked at the node method, which is kind of the", - "workhorse of the circuits industry.", - "So when in doubt apply the node method and it will get you where", - "you want to go. Now, we also said that this is", - "good, here is our playground. We said hey,", - "if we focus on those circuits that are linear we come to the", - "left part of our playground. And we said that for linear", - "circuits in this part of the playground we can further use a", - "couple of techniques, a few techniques,", - "superposition, Thevenin, Norton and so on.", - "So these techniques allow you to very quickly analyze", - "complicated circuits, especially when you're looking", - "to find a single current, or voltage or some parameter of", - "interest. Whenever you see,", - "if you see a circuit containing multiple voltage sources or two", - "or more voltage sources or current sources,", - "as a first step think superposition.", - "And so these are very powerful techniques that let you analyze", - "very complicated circuits very effectively.", - "After we did this we said, oh, let me draw another", - "playground here. This is another piece of our", - "playground. And if these are linear circuit", - "then this half of the playground is nonlinear circuits.", - "And we said that if you further focus on discretized values,", - "if you discretized values and focused only on circuits that", - "dealt with binary signals, highs and lows,", - "then we came into this small regime of the playground.", - "And notice that digital circuits are,", - "by their very nature, nonlinear.", - "Remember the circuit, A, B, this was one of our NOR", - "gate circuits? And if you look at transfer", - "functions, that is if I plot, let's say for example,", - "for some combination of input values.", - "Let's say I plot v in verses v out.", - "Let's say, for example, I turned this guy off by", - "setting B to 0 and then I simply apply a low to high transition", - "at v in, then what I would see at the output is a transfer", - "function of the following sort where as v in changes the output", - "switches at some point and then stays at a low value.", - "So when v in is low v out is high and v in and high v out is", - "low. So that's kind of the v out", - "versus v in when B is set at 0. So notice that this is a", - "nonlinear curve. This is not a straight line.", - "It's a nonlinear curve. And so therefore in the digital", - "domain we see highly nonlinear functions that look like this", - "and so on. However, take a look at this", - "circuit. Suppose I focus on the circuit", - "for a given set of switch settings.", - "Let's say, for example, I focus on the circuit when A", - "and B are both 1s. For a given set of switch", - "settings, notice that I'm going to be either in this region or", - "in this region. Notice that this region is a", - "straight line. So if I focus on let's say both", - "A and B at once then I get something like this.", - "And in this situation, for a given set of switch", - "settings, notice that my digital circuit now can be analyzed", - "using linear techniques. So therefore my digital gets", - "moved into the linear domain for a given set of switch settings.", - "So if I fix my switch settings and look at the circuit then", - "each circuit, for a given set of switch", - "settings, is comprised of voltage sources and some", - "resistors and it's a linear circuit.", - "Again, I can go back and apply all my linear techniques to", - "virtually all the digital circuits that you will be", - "dealing with in 6.002. Again, remember if I fix my", - "switch settings, if I fix the inputs then the", - "output can be determined using linear techniques.", - "Because the digital circuits we're showing you in 6.002", - "simply comprise linear elements like voltage sources and", - "resistors and so on. You'll see some more later.", - "But you can apply your linear techniques and analyze them.", - "The cool thing here is that with just two weeks of stuff", - "that you've learned in 6.002, you are well on our way to", - "being able to analyze certain classes of digital circuits for", - "a given set of switch settings and many, many,", - "many linear circuits. What we will do today is focus", - "on nonlinear circuits. So we look at this space.", - "Notice again that up until now we've dealt with these three", - "methods, which apply to all circuits within this playground,", - "the lumped circuit playground. And the subset of that is the", - "linear domain. And we can analyze linear", - "circuits in this way. And digital circuits,", - "for a given set of switch settings, also fall within this", - "category. So notice that you can go ahead", - "and analyze the digital circuits using superposition or other", - "techniques like that. The next big step for us is to", - "begin our analysis of nonlinear circuits today.", - "The important thing to remember is that nonlinear circuits are", - "also within this big playground in which we are going under the", - "lumped matter discipline. So nonlinear circuits are also", - "lumped circuits. And therefore because we are in", - "that playground we can use any one of our techniques,", - "KVL, KCL or the node method to analyze nonlinear circuits.", - "So if you see a nonlinear circuit, don't get daunted.", - "Just remember this is meant to be simple stuff.", - "So let me simply write down the node equation and analyze it.", - "There is really nothing new in today's lecture.", - "I'm just going to show you a nonlinear circuit and analyzing", - "using techniques that you already know.", - "Today nonlinear circuits. And we look at several methods", - "of analyzing nonlinear circuits. We look at the \"Analytic", - "Method\". We look at a \"Graphical", - "Method\". You will look at a \"Piecewise", - "Linear Method\" in the book.", - "I won't be covering this in lecture.", - "You can read Section 4.4 for the piecewise linear method.", - "In this method you take your curves and you approximate them", - "with a bunch of straight line segments, kind of like the v", - "out, v in curve I've shown you there, and analyze the circuit", - "using linear techniques within any given straight line segment.", - "We will also do incremental analysis.", - "This is also called small signal analysis.", - "So I will cover these two today, I will introduce this one", - "today, and wrap that up during the next lecture.", - "Let's start with a simple example.", - "So I have some voltage, V, some voltage source V.", - "And I have some resistor, R.", - "And I have a fictitious device here that I labeled D.", - "Let's call this fictitious device the \"Expo Dweeb\".", - "I purposely chose a funky name because this is a fictitious", - "device. Let's call it the Expo Dweeb.", - "And let me write down the associated variables for this", - "device as follows. iD is the current flowing into", - "this terminal and vD is the voltage across this device.", - "So this is a nonlinear device.", - "And this device is characterized by the following", - "equation. Much like resistors were", - "characterized by an iV relation, V is equal to iR,", - "or i is equal to V/R. This device is also", - "characterized by the following element relationship.", - "It's a e raised to bvD. So there is an exponentiation", - "here. Again, this is a fictitious", - "device. And I'll show some funky things", - "that it does in a second. It's a very simple relation.", - "It's an exponential relation where the current relates to the", - "exponentiated value of the voltage vD across the element.", - "So I can plot iD versus vD for this element as follows.", - "Notice that when vD is 0 iD is a, so I have a here,", - "and it looks like this. It's a funny device,", - "a fictitious device. So when vD is 0,", - "I have some current flowing the device, and as vD increases I", - "get an exponential increase in the current through that device.", - "This device is funny in the sense that it is not a passive", - "device in that notice that when vD and iD are positive the", - "product is positive, which is fine,", - "which says that it is consuming power.", - "On the other hand, on the left-hand side notice", - "that the vI relation is negative, which means that when", - "I put a negative voltage on it, it can still sustain a positive", - "current. This must imply that the device", - "is producing power. But for the purpose of a", - "nonlinear analysis we don't have to worry about that.", - "Let's just do it mathematically and find out what it looks like.", - "So back to this again. I have a voltage source,", - "a resistor and my Expo Dweeb connected in that manner.", - "Now, again, reflect on this pattern.", - "A voltage source or a current source, a resistor and some", - "device. This is a very standard pattern", - "you will see again and again and again.", - "In particular, if you look at this device,", - "it's a nonlinear device here. And facing the nonlinear device", - "is a voltage source in series with a resistor.", - "And the reason I say that this is an incredibly important", - "pairing is the following. Notice that if on the left-hand", - "side I had any linear circuit and I had a single nonlinear", - "element in that circuit. Notice that by a Thevenin", - "reduction that you've learned you can take this entire mess.", - "If all you care about is the behavior of the nonlinear", - "device, for the purpose of analyzing this nonlinear device,", - "you can take this entire linear circuit, no matter how", - "complicated it is, voltage sources,", - "current sources, resistors and a bunch of other", - "funky stuff, you can boil all of that down to a Thevenin", - "equivalent, a voltage and a resistor in series.", - "So we can trick you. We can give you a complicated", - "circuit and say ah-ha, tell me what the current is", - "through this device if I apply some voltage,", - "3 volts there. What you can do is you can say", - "ah-ha, I don't care what happens here so I'm just going to", - "replace the whole thing with a Thevenin equivalent.", - "And you've done your homework now and you can calculate", - "Thevenin equivalents for circuits.", - "And simply replace this and then go ahead and solve the", - "circuit. Again, remember we are", - "engineers. We are looking for answers.", - "We are looking to build interesting systems.", - "And, in general, we like to take the simplest", - "path possible to the solution. So simplify your lives and", - "create a simple Thevenin coupled to a nonlinear device and then", - "you will be rolling. When we talk about a variety of", - "other circuits, nonlinear circuits,", - "time-varying circuits and so on in the rest of this course,", - "we will look at this pattern again and again and again and", - "again until we are blue in the face.", - "And, just remember, the reason we keep looking at", - "this pattern is that whenever you have some big linear mess", - "connected to some interesting device what you can do is if all", - "you care about is analyzing the behavior of that device,", - "you can take this linear mess and simply figure out the", - "Thevenin equivalent, or the Norton equivalent if you", - "like and replace this whole thing with its equivalent and", - "then go ahead and analyze it. So boil an arbitrarily circuit", - "down to a very simple pattern of this sort.", - "What this means is because of this brilliant Thevenin", - "simplification, going forward through the rest", - "of this course we will mostly deal with very simple circuits", - "like this, voltage source, resistor and the device.", - "That's it. Very, very, very rarely will", - "you see multiple sources and lots of resistors in a circuit.", - "It's usually going to be simple stuff.", - "And remember how we got here, by making a Thevenin", - "simplification of a linear mess. All right.", - "If in homeworks or quizzes or in real life,", - "or in many examples of real life, if you find that you have", - "to deal with a lot of grunge and a lot of mess,", - "step back and think a little bit.", - "Try to use intuition and see if you can simplify things using", - "some clever trick or method. Method 1 of analysis.", - "Let's go ahead and analyze this pattern here,", - "this template circuit, if you will,", - "a voltage source a resistor and a nonlinear device.", - "This is the analytical method. And remember the node method", - "applies, so let me go ahead and apply the node method.", - "To apply the node method, what do I do?", - "I first have to select a ground node.", - "Let me insulate this as my ground node.", - "Let me label all the nodes with their voltages.", - "So this node has voltage V and this node has label the capital", - "D. So let me go ahead and analyze", - "this using the node method. So the node method says for", - "each of the nodes in the circuit whose voltage is not known go", - "ahead and write down KCL implicitly applying the element", - "relationships to replace the current values with the voltage", - "values. Let's start with the current", - "going in that direction. Current going from the vD node", - "through resistor R, which looks as follows,", - "vD - V divided by R. That's a current going that", - "way. And the current going down is", - "iD. In general, when I apply the", - "node method, I don't write iD here but I go ahead and write", - "the element relation ae to the bvD here.", - "Then I get an equation in vD and I just solve the mode", - "voltage. However, just to make a couple", - "of extra points later, let me go ahead and do that in", - "two steps, write down this and then go ahead and write down iD", - "separately as ae to the bvD. Again, remember,", - "don't get confused here. In a node method,", - "I don't write down a second step.", - "I directly write down ae to bvD in place of iD.", - "I get one equation in vD, I go solve it.", - "Just for fun today, I'm taking two steps here,", - "writing iD and explicitly putting down iD as ae to the", - "bvD. Now, that's it.", - "I mean this is all there is to it.", - "You guys can now go ahead and analyze nonlinear circuits.", - "You get a bunch of equations, a bunch of unknowns,", - "go solve. I have two equations here.", - "vD and iD are my unknowns and I can just go ahead and solve for", - "them. Now, in general with nonlinear", - "circuits, often times it's hard to get a closed form solution so", - "you may have to use a bunch of methods.", - "You can try a closed form solution or you can try", - "numerical solutions or you can do trial and error.", - "In this case, I'll just go ahead and tell", - "you. Suppose I choose V as 1 volt,", - "R is 1 ohm and b is 1 over volt and a is \u017a amps for those", - "values, approximately vD is roughly 0.5 volts and iD is", - "roughly 0.4 volts. You can do this by using trial", - "and error or other methods. In 6.002 we don't dwell on", - "working too hard to solve equations of this sort.", - "If you cannot substitute this in here and solve it directly,", - "we don't ask you to go and learn numerical method and the", - "techniques and so on to solve it.", - "But just remember that you can use trial and error or you can", - "use back substitution and other techniques that you will learn", - "in future numerical methods classes and apply it here.", - "But suffice it to say that, for here we can stick with", - "trial and error if you like. And for these values,", - "vD and iD are 0.5 and approximately 0.4.", - "You're done. It's really that simple.", - "Yes. Oh, I'm sorry.", - "Good catch. I know there is one person", - "that's not sleeping here. Good.", - "So, as I said, there's not a whole lot to it.", - "Whether it's a nonlinear circuit or a linear circuit and", - "as long as I am inside this playground here where the lumped", - "circuit abstraction holds, I can apply my node equations", - "and then go ahead and solve it.", - "Let me show you a few more methods so we can articulate", - "your repertoire of tools for nonlinear circuits.", - "And I'd like to show you a graphical technique.", - "I personally rarely use a graphical technique to solve", - "circuits. And why am I sharing this with", - "you? It turns out that often times", - "by looking at things graphically you can get some better insights", - "into circuit behavior. You can also show cool demos", - "when you show graphs of responses kind of playing with", - "each other and so on. So this is fun for getting", - "intuition and things like that. Graphically all I'm really", - "going to do is solve those two equations graphically.", - "So I'm going to plot equation one.", - "Let me rewrite equation one as follows.", - "iD is --", - "I'm just rewriting equation one as follows.", - "V/R - vD/R. And I can also draw the second", - "guy --", - "OK, I can do this as well. I can do an iD versus vD plot.", - "And in this particular situation, you've seen this", - "already, that's my iD versus vD curve right there.", - "And I can do the same for this one here.", - "So this equation establishes the following straight line", - "relationship. It says that when vD is 0,", - "iD is V/R. So that's here.", - "And similarly when iD is 0 then vD is equal to V so I get", - "something here. So that's my straight line", - "relationship corresponding to this equation here.", - "So what I can do is I can simply solve these by", - "superimposing the two curves on the same vD, iD template here", - "and finding the intersection of the curves.", - "So I can take this curve corresponding to two and I can", - "take this curve corresponding to one, and this is V/R and this is", - "V, 0, and I can find the intersection point.", - "This curve here, for reasons that will be", - "obvious about three weeks from now, is called the load line.", - "It's called the load line. You will understand why that is", - "so in a later lecture. So I've given you a template on", - "Page 6 to boil these two down into one equation.", - "So there, again, you can substitute the values", - "for V is 1 volt and R is 1 and so on and so forth and get the", - "same kind of result as you did previously.", - "So there is really nothing new here.", - "All I've done in the second method is combined the two", - "equations graphically and found the solution by looking at where", - "the two curves intersect.", - "At the start of the lecture I also told you that you may want", - "to go and check out the piecewise linear technique --", - "-- in Section 4.4 of the course notes.", - "All right. For today let me do a third", - "method called \"Incremental Analysis\".", - "This technique is also called the small signal method.", - "I'm going to show you, before I go into the method,", - "in today's lecture what I'll do is I'll give you a motivating", - "example for why we need the small signal approach.", - "I'll give you a motivating example and show you a little", - "demo. And then I will close with", - "showing you a problem with applying a standard approach,", - "and I'll ask you to see if you can figure out a way to handle", - "it in time for next lecture. So let me give you the", - "motivation here.", - "So here is what I want to do. Many of you have seen one of", - "those electric eye garage door openers, right?", - "You have a receiver at one end and you have some kind of a", - "light beam at the other, and when you walk through it", - "stops, or rather it cuts the circuit and stops the door from", - "closing. And when no one is going", - "through it maintains a connection and lets the door", - "close. So what we did is we went to", - "Home Depot, or one of those stores, and bought a very", - "standard device that essentially produces some response when", - "light impinges on it. And my goal will be to see if I", - "can send music over the light beam using a simple garage door", - "opener device. So here is the little circuit", - "that I will do. We actually went there and", - "built this. I will also show you a demo.", - "Here is my time-varying voltage, vI(t),", - "and this is some music signal.", - "And get some music signal. And I want to connect this to", - "this device, which is a device found in garage door openers.", - "I am going to call it a LED. If you like,", - "you can view it as, this is very similar to our", - "Expo Dweeb. This is called a \"Light", - "Emitting Expo Dweeb\". That's why it is LED.", - "So what the LED does is, as I apply this voltage across", - "it, that same voltage appears across the Light Emitting Expo", - "Dweeb. And there is some current that", - "flows through the device. And for our analysis we will", - "assume that this device virtually has an identical iD", - "characteristic to the Expo Dweeb just that it emits light.", - "So when I pass a current through it, it emits light.", - "And the light intensity is proportional to the current that", - "flows through. So it emits light and light", - "intensity, LD, is proportional to iD.", - "Here is my little light emitting device,", - "which when current flows through it, itproduces light", - "because its intensity is proportional to the current.", - "And what I will do is I will stick in the receiver here.", - "Think of it as a photo resistor or some other device where I am", - "going to connect that in a circuit.", - "I am not going to spend too much time on this side.", - "I'm going to focus on the left-hand side here.", - "And let's say I have some kind of amplifier and speakers and so", - "on and so forth. Suffice it to say that when the", - "light falls on this device PR that iR that goes through here", - "is proportional to the received light intensity.", - "So if the current is proportional to the received", - "light intensity then I amplify that signal in my amplifier and", - "I get the music playing out here.", - "And notice that the following chain of dependences apply.", - "So I have an input music signal VI.", - "That gets converted to some iD. These are all time-varying", - "signals, so VI is a time-varying signal and so is iD.", - "And iD gets converted to light of some intensity LD.", - "This in turn gets attenuated somewhat and is received at the", - "photo resistor. And I get some intensity LR", - "impinging on that device there. And that in turn produces a", - "current iR and then iR is amplified and goes through a", - "speaker and so on and produces sound.", - "Notice that using this chain I've taken a music signal here", - "and I am playing it here. And just imagine that this is", - "your garage door opener device here where the light emitted is", - "being articulated by the voltage signal VI.", - "And received here. So notice that if I cut this,", - "if I stick something in here and block it then I get no", - "response here, but if I take my hand away then", - "I do get some response. But this is fine.", - "This should work. You could try this at home if", - "you'd like. If you have a garage door", - "opener, just stick a little circuit like this and it should", - "simply work. We have a problem,", - "though. The problem is that,", - "as I said, I'm using the Expo Dweeb here, the light emitting", - "Expo Dweeb, and its characteristics are as follows.", - "iD is exponentially related to the voltage vD,", - "so this is nonlinear.", - "And that's a real problem. Because this is nonlinear,", - "I am going to get a distorted output.", - "Let me show you a little wave form, a little graph to show you", - "how the distortion happens and then show you a little demo", - "showing you the distortion. Let me graphically show you the", - "kind of distortion that is happening here,", - "and I will do it by drawing the following graph.", - "So this is the vD, iD curve for our device.", - "And what I'm going to plot for you is if I have a time-varying", - "vD voltage, I just want to see what the time-varying iD current", - "looks like. And a trick to plot that is to", - "take your input voltage like so. And let's say I apply a", - "sinusoid. So I am just taking a", - "time-varying sinusoidal voltage and rotating the plot 90 degrees", - "like so, so I can see where these points correspond to on", - "that curve. So what this says is that at", - "some point here, for example,", - "where vI, at this point and time, vI is here.", - "Notice vI and vD are the same thing because vI is applied", - "across vD. vI directly applies across the", - "device, and so vI equals vD at all time.", - "So this voltage here corresponds to this voltage,", - "it corresponds to this current and then I can find out what the", - "current is for that voltage. By using the same artifice I", - "can plot the output current iD like so.", - "So for this value I get some current here.", - "And so at time T0 I start here. And notice that as this signal", - "moves up here, I can find out the", - "corresponding values of iD by looking at where a straight line", - "intersects here and plotting the values here.", - "I have a nice little graphical animation to show you this.", - "Hopefully, the laptop will work tomorrow and we can check that.", - "I am doing nothing new here. Just showing you a trick to be", - "able to plot vI versus v out relationships,", - "or vI or versus other relationships based on some kind", - "of a transfer function. So what you end up getting is", - "something that looks like this. Why is that?", - "Notice that this curve here corresponds to the signal.", - "As this signal moves from here to here, this point moves from", - "here to here and that corresponds to this iD.", - "When this moves from here to here that corresponds to a point", - "moving from this part of the curve to here,", - "and that looks like so. And then for the whole negative", - "incursion, notice that the whole negative incursion moves here,", - "so for that entire negative incursion I get an output that", - "looks like this. Notice that this device has", - "completely cut off and hammered negative going signals.", - "What it's done is that rather than giving me a nice little", - "negative spike incursion here, or excursion here,", - "what this is doing is that it is taking this excursion and", - "simply slamming it down to this value here.", - "And then again, when I go back up,", - "I get this peak here. So notice that what was a nice", - "little sinusoid out there gets hammered and squished into this", - "funny curve here. What this device is doing is", - "for positive values it tends to produce exponentially greater", - "current so I get boom, high-rising peaks corresponding", - "to these two, and for negative going voltages", - "it simply compresses them to a low positive value here.", - "And that's what I see here corresponding to negative", - "excursion. So notice that what this will", - "do, if I view sound, if I input sound here,", - "and sound has negative going excursions it will simply", - "scrunch them. But more or less let the", - "positive things through. And that is going to give rise", - "to a bunch of distortion in my signal.", - "So I would like to show you a little demo.", - "Actually, we've gone ahead and built a little device like this.", - "We have an honest to goodness little device costing,", - "I don't know, 50 cents or $1 or something,", - "which is a little voltage, it's a device that emits light", - "proportional to the current flowing through it.", - "I have a receiver. And I am going to play some", - "music, and you will listen to the output here.", - "And hopefully you should see a bunch of distortion because of", - "that effect that I showed you.", - "And what I will do is, before we do that,", - "you will see two curves up there.", - "The yellow, I believe is the vI, is the input,", - "and the green, I believe, is a signal", - "proportionate to -- The other way around.", - "Oh, I see. So green is the input.", - "So green, the lower one is the input and the upper one is the", - "distorted output. So we are going to play some", - "sound through it, music through it and you can", - "listen, through a little CD player.", - "So a couple of things. The good news is that it works.", - "However, I doubt that music artists will come to my studio", - "to record if this is the quality of what I produce.", - "Do notice that there are hardly any negative going excursions in", - "that curve up there, right?", - "All the negative ones have been like scrunched up down into a", - "flat line there, and that's the reason I get", - "this distortion. And just to prove to you that I", - "am indeed using a garage door opener device and not faking it", - "here, I am going to just shut the signal off by stopping the", - "light using a piece of paper here.", - "So notice that this device here is the little device that has a", - "light beam going through the center, and I am going to take", - "this piece of paper, can you turn it up?", - "So let's have some fun with this.", - "If I were to put this piece of paper halfway down,", - "I should get half the intensity, right.", - "So my sound should diminish in volume a little bit.", - "Maybe that will work. Let's see if it works.", - "Nothing to do with 002 but it's just fun.", - "Louder. You can make it loud.", - "Too much coffee. My hand is shaking.", - "I guess you did see the lowering of volume,", - "right?", - "OK. Just way too much coffee,", - "and so my hand was shaking too fast imposing its own sine wave", - "on top of the signal. What did I show you?", - "This was garbage, right?", - "We had a nice little signal input, and the output was", - "completely distorted because I was playing sound over this and", - "this is what happened. Switch to Page 9.", - "Now, this is what I would have liked to have happened.", - "On Page 9 what I would have liked to see happen is this.", - "Suppose I had a light emitting device that looked linear,", - "a straight line where the current was linearly related to", - "vD. Then what I would see,", - "if I had a sinusoid here then I would get a sinusoid here.", - "No distortion there, right?", - "If only things were like I wanted them, if I had a linear", - "device, but I don't have a linear device.", - "I have an Expo Dweeb. Now you know why I call it a", - "dweeb. Well, I'd like a linear device", - "and it's exponential. But this is what I would like.", - "And if I had this I wouldn't show it to you today.", - "If I had this my music would go through without any distortion", - "and I wouldn't have to run cables through my attic.", - "I could just use my garage door opener to play signals from my", - "bedroom and living room and so on, right?", - "So the key thing here is how do I get this?", - "And what I would like you to do is think about it yourselves.", - "What I am given is something like this.", - "This about it yourselves, you know, what would you do?", - "See if you can come to me before lecture tomorrow or", - "Thursday and tell me the answer, OK?" - ] -} \ No newline at end of file diff --git a/subs/PzBZENXgN7g.srt.sjson b/subs/PzBZENXgN7g.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/PzBZENXgN7g.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/Q3IF4g9eH34.srt.sjson b/subs/Q3IF4g9eH34.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/Q3IF4g9eH34.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - 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2958111, - 2961370, - 2965814, - 2968185, - 2972481, - 2976925, - 2980627, - 2984625, - 2988623, - 2992103, - 2997000 - ], - "text": [ - "We have put some of the quiz stats here.", - "The mean was about 75%. And I must tell you that that", - "is very impressive. I guess MIT undergrads never", - "cease to amaze me. And this was not an easy quiz.", - "This was a relatively hard quiz.", - "And that average implies that you guys did well on a", - "relatively hard quiz. Good.", - "Let's get back to our final lecture on amplifiers and small", - "signal circuits. And as always let me start with", - "a review. Very quickly --", - "-- we came up with a notation to represent small signals.", - "And our notation looked like this.", - "Our total variable was small and capital, and this was a DC", - "bias and this was a small signal.", - "This is also called the operating point.", - "And the small signal is also called the incremental signal.", - "In general, if you have some function, some variable of", - "interest in the circuit, say a total variable V out,", - "let's say it relates to some input variable as F of VI.", - "So mathematically we can find out V out by simply finding the", - "slope of this function at the operating point and then", - "multiplying it by the incremental change in the input.", - "Gold standard math. So we do the slope of this", - "function and evaluate it at the operating point.", - "So this would give us the slope of the function.", - "And multiply that by small VI, which is incremental change.", - "This is standard math. What this will tell you is", - "given a small change in VI this function gives you,", - "this expression gives you the small change in V out.", - "And in lecture we have pretty much used this method so far,", - "used the math to get to where we wanted it to be.", - "And then the way we provided biasing and so on was for our", - "amplifier in particular we had a bias voltage,", - "some small signal value, VS.", - "And this was output which was also given to be some output", - "operating point plus a small change, which was a change in", - "the output voltage. So what we have done here is", - "mathematically computed small V out.", - "And what I am showing you here is to get the same effect in a", - "circuit is you build your circuit and replace what used to", - "be a total variable with a DC bias plus a small change.", - "And then you will get your output here.", - "And this output will relate to this input using this", - "expression.", - "So this is more review. To continue on with the math", - "review, for our amplifier VO was given to be VS-K/2(vI-VT)^2 RL.", - "So this was the output versus input relationship for the", - "amplifier. And mathematically I could get", - "the small change in the output VO by simply differentiating", - "this function with respect to VI, evaluating that function,", - "at capital VI and multiplying by the small change in the", - "input. And the resulting expression", - "that we got for small VO --", - "-- was simply minus K, this was our DC value,", - "and RL times small VI. So we derived all of this the", - "last time. So nothing new so far.", - "So my small signal output was some function given by", - "K(VI-VT)RL times small vi. And notice that this is how VI", - "relates to VO. And this is a constant with", - "respect to VI. V capital I is a DC bias,", - "so this is a constant. So therefore this is the linear", - "relationship that we had set out to get.", - "This term here, for reasons we will see today,", - "this term here K(VI-VT) is called gm.", - "Transconductance. We will look at it in more", - "detail a little later.", - "Even more review.", - "So I can draw the transfer function and plot VO versus VI.", - "Another way to graphically view what is going on is by plotting", - "the load line curve for this circuit, so this is VI.", - "And I said we draw that by first plotting the --", - "These were our MOSFET curves. And we know that at some point", - "the MOSFET gets into saturation, so this curve was iDS=K/2 VO^2.", - "And to the right side of the curve the MOSFET is in", - "saturation. And we said we will adhere to", - "the saturation discipline and operate in this regime.", - "When the MOSFET gets into this region it is in its triode", - "region. And then we could draw the load", - "line here. The load line codified the", - "following relationship, iDS=VS/RL-VO/RL.", - "This was a load line. So I have superimposed a load", - "line on the device characteristics,", - "and I am going to show you a little demonstration based on", - "that at this point. So these curves were drawn for", - "increasing values of VI. And if I choose some operating", - "point here then this point would correspond to some bias,", - "this bias point would correspond to some input voltage", - "VI, a corresponding output bias VO and a corresponding current", - "iDS. So iDS capitals,", - "VO capitals, VI capitals represent the", - "operating point values for our little circuit.", - "So far there is nothing new. One thing we stopped the last", - "time by pointing out that the gain of our amplifier,", - "this is the gain, -K(VI-VT)RL.", - "That is the gain A of the amplifier.", - "That gain related to VI. A gain was proportional to", - "VI-VT. So therefore if I increased VI,", - "I would get more gain. So the question is how do we", - "choose a bias point? And in our particular example,", - "let's say we are free to play around with VI.", - "So we play around with VI and I can choose various bias points.", - "So where do you set the bias point?", - "What are the various characteristics of the circuit", - "that relate to my bias point? Well, first,", - "of course, is gain. The gain depends on how I", - "choose VI. I will show you that in a", - "moment. The second important thing,", - "in other words, if I choose a bias point that", - "is a small VI then my gain is going to be smaller.", - "If I choose a bias point that's at a much higher value of VI,", - "I get a bigger gain. The second important", - "consideration is operating range.", - "Notice that if I choose a bias point here then as the input", - "changes -- Notice VI in this graph goes up", - "or down, and I would be traversing and following", - "different lines here in my MOSFET characteristic.", - "And as VI increases the operating point would come up", - "here and so on. So if about this operating", - "point I varied my input voltage VI then, so let's say about this", - "operating point, if my input VI,", - "my small signal VI varied about a small range then", - "correspondingly the output value would vary about this part of my", - "load line. So notice now that the", - "operating range, how far can VI vary before the", - "MOSFET goes out of its saturation discipline?", - "Well, on the low side my VI can come down to here.", - "And we looked at the operating ranges for an amplifier.", - "And I can come all the way down to VT.", - "At that point the output will come here.", - "Similarly at the high end VI could get up to a high value.", - "And we computed that value in the last lecture.", - "And the corresponding value of the input would be here.", - "So in some sense I can traverse all the way from here to here", - "and have the MOSFET remain in saturation.", - "Remember we are not talking about linearity right now,", - "just about the valid operating range based on my definition", - "which is that the MOSFET should stay in saturation.", - "So if I chose my operating point here then I get this range", - "here. And, on the other hand,", - "if I chose my operating point to be here, for negative", - "excursions of the input signal I have a very small amount before", - "I hit cutoff. So if I chose my operating", - "point here then for negative traversals of VI about the", - "operating point I very quickly hit cutoff.", - "So if I want symmetric swings then this is the best that I can", - "do in terms of the valid input operating range if I want", - "symmetric swings given that this is my bias point.", - "On the other hand, if I chose my bias point", - "somewhere here, or very carefully chose my bias", - "point then my input can vary on a much wider region and still", - "get symmetric swings. And so therefore the choice of", - "bias point also influences the maximum swing range of my input", - "signal. I shouldn't call this operating", - "range. I should call it input swing", - "range. We defined the valid input", - "operating range as the range for which the amplifier satisfied", - "the saturation discipline. So the two key issues,", - "gain and the input swing. Let me show you a quick demo", - "and try to point out on a graph some of the characteristics that", - "relate to the matter we have been talking about so far.", - "So what I show here are these curves for the MOSFET.", - "This is VO and this iDS. This is the zero point.", - "Ignore this line down here. This line up here corresponds", - "to the output voltage VO. What I am going to do now is,", - "through some careful circuit hacking, I'm going to show show", - "you a load line and show you the bias point, and show you how the", - "bias point can be moved up and down by changing the input", - "voltage which changes the corresponding output voltage.", - "It is hardly visible out there.", - "Is it there? OK.", - "It is not really clear, but notice that as I increase", - "my input, I am increasing my input.", - "My output keeps coming down. And I hope your eyesight is", - "better than mine because I don't see a dot up there.", - "I am amazed. This is the first time this has", - "happened to me. That's OK.", - "All right. As you can see,", - "as I change the input value the output operating point changes,", - "and the dot out there traverses, articulates a load", - "line. I guess I have to believe that", - "there is a dot out there. Next what I will do is show you", - "some more fun stuff. What I will do is instead of", - "having just a dot by having a DC voltage, let me apply an input", - "sinusoid. So if I apply an input sinusoid", - "at some bias then I should see an articulation of the", - "corresponding region of the load line corresponding to the input.", - "So, as you can see here, now the bottom line,", - "here is my input and this is my output.", - "And notice that this the region of the load line articulated", - "when the input is of this magnitude.", - "Now let's have some fun. As I increase my input,", - "you can see that a larger portion of the load line is", - "articulated, right? There you go.", - "And as I decrease my input a smaller region of the load line", - "is articulated. Let's leave it here for a", - "moment. And what I will do next,", - "this is the region here that we are looking at,", - "let me increase the bias. If I increase the bias,", - "if I increase VI, what do you think should happen", - "to this line here? Well, if I increase the bias,", - "the line should go up, right?", - "Because remember the dot? The dot is in the middle of", - "this thing here. If I increase the bias this", - "should move up here. So that line moves up.", - "Do you expect anything else to happen to that line?", - "Pardon? It increases,", - "exactly. If I increase the bias point to", - "here then this must also increase because my gain has", - "increased. Let me do that.", - "So let me increase the input bias.", - "Indeed notice that the region of the load line articulated is", - "larger now. Let me decrease the bias.", - "And notice that because the gain is smaller the little", - "segment shown is also smaller. I have shown you two things so", - "far. One is that I as I increase my", - "bias the line indeed rises up corresponding to a higher value", - "for the input operating point. And the second is that I get a", - "larger swing in the output as I increase the bias.", - "Just to show that for those like me who were visually", - "challenged in terms of viewing that little dot up there,", - "let me get some audio so you can actually hear the sinusoidal", - "tone. It is a big annoying.", - "As I reduce the bias the gain is decreased.", - "As I increase the bias you can see that the gain is increased", - "and the tone is louder. Let's have some more fun and", - "let's play some music now. And what I am going to show you", - "with the music -- The reason I play the music is", - "not just for fun. Well, it's 85% fun and 15%", - "learning. Can we turn it on for a second?", - "What I would like to do is, as we play the music,", - "the reason I am playing the music for that 15% is so you can", - "listen to distortion. I want you to listen to the", - "distortion. That is when the articulation", - "is here you are not going to get much distortion.", - "But as I get into cutoff you should be getting a bunch of", - "distortion. Similarly, as you get into the", - "triode region you should also be getting distortion because the", - "amplification from being somewhat nonlinear here becomes", - "highly nonlinear at those two points.", - "So let's just play the signal. So volume increases,", - "or rather the amplitude increases by increasing the", - "bias. Now you should hear the volume", - "go down and distortion.", - "So notice now that the bias point is way down here.", - "So the gain is very low, and plus there is a distortion", - "because of cutoff. Now what I will do is blast it", - "up here, and you will see that the volume has gone up but then", - "you see distortion again. Let's see if you can stand the", - "volume here.", - "Even the CD doesn't like that.", - "Notice that as I went up here the volume kept increasing", - "because the gain kept increasing, but as I got into", - "the triode region I began to lose my gain because,", - "remember, the amplifier doesn't have gain in the triode region,", - "MOSFET in its triode region, and we also get a bunch of", - "distortion out there. Finally, it turns out that as", - "people are building amplifiers --", - "I think this was in the mid to late `50s and `60s and so on.", - "They said man, electrical engineers are not", - "going to get their thing right. So they invented a new kind of", - "music which was much more tolerant to distortion.", - "And I will play that music for you.", - "It is called hard rock. I challenge you to tell me it", - "is distorting.", - "Sounds good to me.", - "OK. All right.", - "That'll do it. Thank you.", - "I hope there are no hard rock musicians in here who will come", - "and beat me up after lecture or something.", - "All right. Believe it or not most of that", - "was review. There is nothing new today", - "besides some fun and games and so on.", - "I will give you a breather for five seconds before jumping into", - "something even more fun.", - "I want you to look at the middle board here.", - "And, as I told you in the beginning of 6.002,", - "engineering is about building useful systems.", - "Engineering is not about showing off at math or saying", - "man, I am really cool in math and stuff.", - "Engineering is about building useful systems,", - "and you want to find the simplest, easiest,", - "cheapest way to get there. Unlike deep areas of math and", - "theory and so on, the beauty is in the", - "simplicity. So the aesthetics are in how", - "simply can we make things and still get to where we want to", - "be? All through the course what you", - "will be seeing happening again and again and again is when", - "things begin to get too grovelly in terms of math,", - "we will step back and say oops, we are engineers,", - "remember? Let's find a much simpler way", - "to do it and use intuition. So time and time and time", - "again, I am going to take you on a simpler path where you can", - "solve things by inspection by pure intuition.", - "Most circuit designers do that. So take a look at this.", - "I don't like this nasty differentiation here.", - "That's getting into late high school calculus and so on.", - "Let's avoid the math and let's see if you find some way of", - "doing it that is even much more simpler.", - "And that is what I will do next and show you what is called the", - "small signal circuit view. A purely circuit way of", - "developing the small signal model.", - "So let me just start by drawing the large signal equivalent", - "circuit for you. I will draw it here for reasons", - "that will be obvious at the end of the class.", - "All right. This is the large signal", - "equivalent circuit model for our MOSFET amplifier.", - "VS and here is my current source.", - "iDS relates to the square of VI minus VT.", - "So stare at that for a second. And that is a nonlinear", - "circuit. iDS relates to the square of VI", - "minus VT. Let me start by making the", - "following claim. Let me shoot from the hip here", - "and make the following grand claim, and then I will show you", - "how I can prove that claim. The grand claim I am about to", - "make says the following. A bunch of little devices here.", - "It is a nonlinear circuit. Just suppose for a moment we do", - "a Gedanken experiment. Suppose I replace each of my", - "circuit elements here with its linearized element equivalent.", - "In other words, here is a VS source,", - "here is a dependent current source, let me replace them with", - "their linear equivalent circuit models.", - "In other words, with their corresponding small", - "signal element models. And I will show you what those", - "are in a second. The resistor has a", - "corresponding small signal element.", - "The dependent current source has a corresponding small signal", - "behavioral element model. And what I am going to do is", - "keep the same circuit connections and simply pull out", - "the large signal model for the element and replace it with a", - "small signal element model. And by the nature of the small", - "signal model they are all going to be linear.", - "So what I am going to be left with is a linear circuit with", - "simple linear circuit elements in there.", - "And then once I have a linear circuit, I should be able to", - "analyze that linear circuit using methods 1,", - "2 and 3, superposition, Thevenin, node method and so", - "on. And certainly the intuitive", - "methods like superposition and Thevenin, which make life a lot", - "easier for me with linear models, and thereby get the", - "function that I am looking for very quickly.", - "Again, my claim is that I can replace each of these large", - "signal models by just small signal equivalents and then just", - "analyze the resultant circuit. And I claim that I should be", - "able to get the same answer. That's a claim.", - "All right? So what I will do is give you", - "an informal proof for why I can do that.", - "And I also ask you to refer to Section 8.2.1 of the course", - "notes to go through the foundations of the small circuit", - "model in more detail. The intuition is that,", - "remember KVL and KCL? I can write down KVL and KCL", - "for every loop in that circuit and every node in that circuit.", - "If I do KVL and KCL, I will end up with something", - "like this. For the input loop I get VI", - "something or the other applying KVL.", - "For the output loop I get V out something or the other.", - "And then applying KCL I get some other equation in iDS.", - "So here are my KVL and KCL equations for that circuit.", - "Now, KVL and KCL are simply a different representation of the", - "circuit because within those KVL and KCL is encoded the topology", - "of the circuit. Remember each KVL equation", - "represents a loop and each KCL equation represents how nodes", - "are connected together. So KVL and KCL equations encode", - "within them the topology of my circuit.", - "What I do next is, say, I replace each of these", - "with the bias plus the small signal, so I get the bias plus", - "the small signal and keep the equations the same.", - "All I have done in my big set of KVL, KCL equations,", - "I have simply replaced the total variable with the large", - "signal variable and the small signal quantity.", - "Then comes a key trick. The key trick is that because", - "the bias point variables, they are a valid solution to", - "the circuit. The circuit is in this", - "quiescent state, and those are valid solutions", - "to circuit. So therefore I can cancel them", - "out. So the VI, the large signal", - "values can be cancelled out leaving just small signal", - "variables in there. So from the KVL,", - "KCL equations I can cancel out the large signal values,", - "the DC bias points because they satisfy the KVL and KCL", - "themselves. In other words,", - "I could have written VI plus V out and so on.", - "Since they are satisfied I just strike out the large signal", - "variable from both sides of each of these equations,", - "so what is left is the same KVL, KCL equations but with", - "small variables in place of the big variables.", - "What that should tell you, this informal proof should tell", - "you is that the small signal variables should then satisfy", - "the same form of the KVL, KCL equations that the total", - "variables satisfy. And because the KVL,", - "KCL equations are a reflection of the topology of the circuit,", - "what that says is that the small signal variables must also", - "satisfy KVL and KCL. And since these arrive from the", - "small signal elements that says that I can replace the big", - "elements with the small elements and KVL and KCL will hold for", - "the resulting circuit. This is a very quick breeze", - "through, an informal proof to show that I can replace the big", - "elements with the corresponding little element models and then", - "simply apply linear techniques. Refer to Section 8.2.1 for more", - "foundations and more discussion about the foundations for why we", - "can do this. That brings up the small signal", - "circuit method. The circuit method for small", - "signal analysis has three steps. The first step is find", - "operating point by using LS. First you analyze your large", - "signal circuit and find the operating point.", - "You have to do this, because remember,", - "the small signal models depend on the operating point values.", - "Remember the gain of our amplifier depended on the bias", - "point. Second step is develop small", - "signal models of elements. Second step is take each of the", - "elements in your circuit and find their equivalent small", - "circuit model for each of the elements.", - "Third step is replace original elements with their small signal", - "model elements. Third step is simply take the", - "large elements and replace them with their small signal", - "equivalent models. Then analyze resulting circuit,", - "and that circuit will be a linear circuit.", - "So let's do an example. I will just use the amplifier", - "as an example of this method. And convince you that you are", - "going to get the same expression at the end, but just so,", - "so simply without even the smallest amount of grubby math.", - "Three steps. The first step is to find the", - "operating point using the large signal model.", - "And let me just do that here. I get my V out =", - "VS-K/2(VI-VT)^2 RL. Let me just write down that out", - "here. Don't worry about copying that", - "down. It is on the last page of your", - "notes. The first step of the method", - "simply applies the large signal model and finds out the behavior", - "of that circuit to find out what the bias point values are.", - "The second step is to develop the small signal model of my", - "elements. How do I go about developing", - "the small signal models of elements?", - "Let's start with the MOSFET. The large signal model for the", - "MOSFET looks like this.", - "Here is my Vgs. This is my gate.", - "This is my drain. This is my source.", - "And I know my iDS to be K/2(Vgs-VT)^2.", - "So this is the large signal model for the MOSFET,", - "again in saturation. I am talking about all of these", - "models are under the saturation discipline.", - "So Vgs relates to iDS in the following way for the MOSFET.", - "That is iDS, is K/2 and that is my square", - "law relationship. So what is a corresponding", - "small signal model? I go ahead and start with this.", - "The corresponding small signal model simply says that iDS", - "relates to Vgs in the following way.", - "All I have to do is find a small signal equivalent where I", - "need to find out, given a small change in the", - "input Vgs, what is the small change in the iDS?", - "So I can apply my standard trick to a much simpler", - "expression here, which is iDS simply,", - "I differentiate this function with respect to Vgs.", - "So I don't completely eliminate the math here,", - "but it is a much simpler problem here.", - "At Vgs equals the bias point times small vgs.", - "I can find the small change in iDS corresponding to a small", - "change in the input using this expression.", - "That gives me iDS as simply K(Vgs-VT) vgs.", - "I call this gm, and I will tell you why in a", - "second. So what does this expression", - "say? This expression says that if I", - "have a small change in Vgs then this will be my small change in", - "iDS. Notice that the resulting small", - "signal model is also a dependent current source.", - "It is a voltage controlled dependent current source.", - "So the output is the current, and it is a dependent current", - "source and it depends on the input voltage.", - "The good news is that notice that this one,", - "this expression here gm is a constant related to the bias", - "point values. Therefore, notice that the", - "small signal model for the MOSFET in saturation,", - "not surprisingly, is a linear voltage controlled", - "current source according to the following expression.", - "So iDS=gm Vgs. Gm is a representation for", - "K(Vgs-VT) and is called a transconductance.", - "It is called a transconductance because it, in some sense,", - "deflects the conductance properties of this based on the", - "input. So it is a transconductance.", - "So this value is called Vgs. Therefore, I can build the", - "small signal model as follows. Vgs is a voltage controlled", - "current source and iDS is simply gm Vgs.", - "So this is my gate, drain, source.", - "So that is the small signal model for my MOSFET.", - "As a next step what are the other elements in my circuit?", - "Let's see. I have a voltage source and I", - "have a resistor, so let me find out the", - "corresponding small signal model for a DC supply VS.", - "This is Page 7. I will do it mathematically for", - "you, but often times it is always good to do a sanity check", - "using intuition. Let me ask you,", - "the large signal for a DC supply looks like this.", - "The element law for a voltage source is VS equals some capital", - "VS. It is a constant voltage.", - "So what do you expect to be the small signal model for a voltage", - "source? In other words,", - "for a small change, suppose I have a small change", - "in the current, by how much should the output", - "VS change? It shouldn't change.", - "It is a voltage source. So what does intuition tell you", - "is a small signal model for the voltage source?", - "A short. So the key here is that a", - "voltage source behaves like a short circuit for small", - "perturbations. In other words,", - "if I change the current flowing through it by a small amount", - "somehow, the output is still going to held at VS.", - "In other words, small signals are simply going", - "to scoot through this voltage source without having any impact", - "whatsoever on the voltage. Or mathematically I could also", - "do small vs is del by del IS of VS evaluated at IS equals some", - "capital IS times small IS. And therefore VS equals zero.", - "What that means is that the small signal model for my", - "voltage source is simply a short circuit.", - "So in a small circuit voltage sources appear like a short", - "circuit. Finally, I have a resistor,", - "my resistor R. Let me find out its", - "corresponding small signal model.", - "The large signal model looks like this R, VR,", - "IR. And I know that VR is simply", - "RIR. And to find the small signal", - "equivalent I do del of IRR divided by del IR for IR", - "calculated at some constant value times small IR.", - "What I am looking to do is to find out what is the change in", - "the voltage across R for a small perturbation in the current?", - "Again, let me exhort you to rely on intuition to at least", - "sanity check your answers. So what do you think this", - "should look like? It's a resistor and I have a", - "small change in the current, by what do you expect the", - "voltage to change? Think about,", - "for the next five seconds, what the small signal model for", - "this should look like and then I will go ahead and write down the", - "answer.", - "So differentiating I simply get RIR.", - "In other words, for a resistor the small signal", - "model is the resistor itself.", - "So what I have done so far, let me just take you through", - "where we are right now, give you the big picture there.", - "I began by suggesting that looking to find an even simpler", - "way to do small signal analysis. I gave you an informal proof to", - "show that if I had small signal element models for all of my", - "elements, I could simply replace them in the circuit and then do", - "a corresponding linear circuit analysis phase to get the result", - "I am looking for. There are three steps to the", - "method. As a first step we began by", - "finding small signal models for each of our elements.", - "For the nonlinear MOSFET the small signal model was a linear", - "dependent current source. For a voltage source the", - "corresponding small signal model was a short circuit.", - "Again, that makes sense intuitively if I change the", - "current through a voltage source by a small amount.", - "By how much does the voltage change?", - "It is a voltage source, silly.", - "The voltage doesn't change. So the small signal V,", - "the small change in the voltage is zero, and that is the same", - "thing as a short circuit. For a resistor by how much does", - "the voltage change if I change the current by a small amount?", - "Well, it will change by R times the current change,", - "and that is the property of a resistor, R.", - "As a final step what I would like to do, on Page 8,", - "I'd like to very quickly draw for you the small signal circuit", - "and then analyze it. This is the large signal", - "circuit. That is a large signal circuit.", - "And let me draw the small signal circuit.", - "And the method says simply pluck out, gouge out each of", - "these elements. And simply replace each of", - "these nasty nonlinear elements with the corresponding small", - "signal linear equivalents. So let's do that.", - "Remember, for the input you replace input with its small", - "signal voltage because I am telling you that it's sourcing a", - "small change in VI. So that is VI.", - "And then I replace a short for VS.", - "I replace an R for RL because it is an RL itself for the small", - "signal model. And then for the dependent", - "source, we discovered that the dependent source was a linear", - "dependent source given where ids=gmvi.", - "Remember, this was my small VO. Here you go.", - "I have a small signal circuit here where I have simply created", - "that by replacing each of the big elements by little", - "rinky-dink elements. Now these are all linear", - "elements so I can do a really simple linear analysis.", - "What method shall we use? Well, this is so simple.", - "I will just go ahead and use the node method.", - "So applying the node method at the node with voltage VO,", - "what I will do is the current going up, VO divided by RL", - "equals the current going down iDS.", - "And so the current going up is VO divided by RL and the current", - "going down is -- Oops, I should have done this.", - "The total current going out is zero, so the sum of these two is", - "zero. That is my good old node method", - "here. And I know that iDS is simply", - "gmvi equals zero. So right there I have the", - "relationship between VO and VI. So VO is simply minus gmviRL.", - "And remember gm was simply K VI minus VT.", - "We are done, OK?", - "What have we here? I created a linear circuit", - "which simply comprised small signal models for each of my big", - "elements. And then I simply did a", - "straightforward linear analysis using any one of the linear", - "techniques I knew about. This is simple enough so I", - "apply the node method. And I've got the equation at", - "this node, simplified it and I directly got the answer.", - "In one or two steps I directly gave you the output as a", - "function of the input. It can't get any simpler.", - "Thank you." - ] -} \ No newline at end of file diff --git a/subs/RAxyscAwETM.srt.sjson b/subs/RAxyscAwETM.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/RAxyscAwETM.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/RJTIDCzcKPo.srt.sjson b/subs/RJTIDCzcKPo.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/RJTIDCzcKPo.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/RsJ1eg7XNVs.srt.sjson b/subs/RsJ1eg7XNVs.srt.sjson deleted file mode 100644 index 5636ac4fb2..0000000000 --- a/subs/RsJ1eg7XNVs.srt.sjson +++ /dev/null @@ -1,1934 +0,0 @@ -{ - "start": [ - 0, - 11000, - 15900, - 18350, - 23716, - 29783, - 34486, - 41473, - 45144, - 49644, - 56750, - 61746, - 66103, - 70080, - 75384, - 81256, - 84760, - 90064, - 93250, - 96342, - 100770, - 105031, - 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Loud and clear.", - "OK. Let's get started.", - "Before I begin, just a couple of announcements.", - "Brad Buren is one of our students here and he needs a", - "note-taker. It's a paid position.", - "So if you are interested you can stop by after class and see", - "him. He's sitting right here out", - "there, OK? Second, just a reminder that", - "6.002 does have prerequisites. And the prerequisites are 8.02", - "and 18.03. So with that let me start off", - "with the usual. Do a quick review of what we've", - "done so far. So we started out life looking", - "at the laws of physics and Maxwell's equations and so on.", - "And those were way too hard so we said let's make life easy for", - "ourselves. So we chose to play in this", - "playground in which we said we shall adhere to the lumped", - "matter discipline. OK?", - "The LMD. So we are in that playground.", - "So this entire course, and for that matter large parts", - "of EECS are within that playground, within which the", - "lumped matter discipline applies.", - "So as soon as we jumped into the playground,", - "the LMD playground, we could take Maxwell's", - "equations and abstract them out into two very,", - "very simple rules. And the very simple rules were", - "KVL and KCL. KVL simply said that I can sum", - "the voltages in any loop in a circuit and the result then", - "would be zero. Similarly, I can sum the", - "currents that enter or exit any node and the sum will also be", - "zero. So what you can now do is,", - "if you feel like, you can go around and brag.", - "Oh, yeah, we use Maxwell's equations in everyday life and,", - "yeah, it's good stuff. And the key is that this is", - "really an encapsulation of Maxwell's equations within this", - "playground that we are in. So I talked about the first", - "method of circuit analysis in the last lecture.", - "And that method simply took the, wrote KVL for all the", - "loops, wrote KCL for all the nodes and wrote element vi", - "relationships. And together gave you a big", - "bunch of equations. And you sat down and grunged", - "through the equations and you solved for branch voltages and", - "currents. So we reviewed a second method", - "of circuit analysis. And I'll simply call it circuit", - "composition. The basic idea behind this", - "method was to learn some simple rules of how resistors add and", - "conductances add and so on and so forth and look at a circuit", - "and simplify the circuit by making series simplifications", - "when the resistors are in series and so on and so forth,", - "and compose it and play around with it till we end up with the", - "current, the voltages that we are looking for.", - "This is the intuitive method. And so a section in Chapter 2,", - "I believe, of the course notes discusses several examples using", - "this method and attempts to make a little bit formal the", - "intuitive approach that is applied in this method.", - "So we then looked at the node method.", - "And the node method was simply a particular way of applying KVL", - "and KCL. Node method,", - "remember? We took a ground node.", - "Then we labeled the nodes of the remaining voltages with", - "respect to that ground. Then we wrote KCL for each of", - "the nodes. And when we wrote KCL for each", - "of the nodes, remember, KVL was implicit in", - "this expression that we used for each of the currents that were", - "exiting each node. So if Ej was a node voltage,", - "then Ej minus Ei multiplied by the conductance Gi was the", - "current that was going through one of those,", - "I should call it Gij. This is a conductance that", - "connects nodes i and j. That gave us the KVL that fed", - "into the same system. So these are three methods.", - "The node method, by the way, is sort of the", - "workhorse of the 6.002 industry. And for that matter for all of", - "the circuits industry. When in doubt,", - "apply the mode method, you'll be OK.", - "That applies to linear circuits, nonlinear circuits,", - "what have you. What I'm going to do today is", - "go through two more methods. So notice that the first few", - "lectures of this course, the first three lectures simply", - "comprise transitioning you from the world of physics to the", - "world of EECS. And then two lectures on giving", - "you a bag of tricks. So we start you off with the", - "sort of tools, your mallets and chisels and so", - "on and so forth. And these five methods are your", - "tools. We'll look at two methods", - "today. One method is called the method", - "of superposition and the second method is called the Thevenin", - "method. And these methods apply only to", - "linear circuits. So we look at the subset of", - "circuits that are linear, and these two methods apply to", - "only those circuits. These are methods that combined", - "with intuition really enables you to solve very interesting", - "circuits very, very quickly.", - "So let me do an example using a usual node method.", - "And then jump into introducing the superposition methods and", - "Thevenin methods using that same example.", - "So let me draw you an example circuit here.", - "So, again, I'm using this example, I will use this example", - "to introduce the method of superposition and the Thevenin", - "method. So what I'm going to do is", - "start off the usual way and analyze the circuit using a", - "method that you know now, the node method.", - "And what I'll do is write down the node equations for this by", - "applying the node method. So if you recall the node", - "method. I choose a ground node.", - "I'm going to choose this node. It's got both the voltage", - "source connected to it, and it's also got many other", - "edges impinging on it. So I'm going to choose that as", - "my ground node and I'm going to label the other nodes with their", - "voltages. So this is an unknown.", - "I'll label it as e. I guess we just have one", - "unknown e. And I know the voltage of this", - "node, and that is simply V. Since it's V,", - "there's a voltage source between the ground node and that", - "node. So what I can do next is that I", - "can write down the node equation for this node and then go from", - "there. So let me go ahead and do that.", - "So let me sum up the currents going outside,", - "going outwards. So I have e minus v divide by", - "R1, I have e minus zero divide by R2, and I have minus i equals", - "zero. This is a node equation.", - "The first thing I want you to observe is that this equation is", - "linear in V and i. What I mean by linear is that", - "you don't see terms like Vi or V-squared and things like that.", - "It's some constant times V plus some constant times i equals", - "some other constant. So that's quite nice.", - "So I'm going to rearrange the terms in the following manner.", - "I'll move the known sources to the right-hand side and collect", - "the coefficients of e on this side, so I get one by R1 plus", - "one by R2 over here.", - "So stare at this for a moment and notice again here I have e,", - "my unknown node voltage, there is some constant", - "multiplier, and that equals some function of V summed up with", - "some function of i. And, again, notice that this is", - "a linear combination of V and i. No multiplication terms and so", - "on and so forth. This is a pretty standard form", - "in which we will represent equations quite often.", - "And just to label it, this is often labeled G as the", - "conductance matrix. Of course this is e,", - "our unknown node voltages, and this is a linear sum of", - "sources. So this is a very standard way", - "that we will represent equations.", - "We did that last week as well, or rather on Tuesday where I", - "took a conductance matrix, multiplied that by a column", - "vector of unknown node voltages and equated that to some linear", - "combination of my source voltages.", - "The reason the circuit is linear is that I have only", - "linear elements in the circuit. I don't have any nonlinear", - "elements. And because of that I can", - "rewrite this in the following manner.", - "I'm just going to express e as a function of V and i and bring", - "it over to this side. So it's some function of i.", - "So I get R1 R2 divide by R1 plus R2.", - "And I bring R1 R2 to this side. That's what I get.", - "So stare at this for a few seconds, very common form.", - "My unknown node voltage is equal to this stuff on the", - "right-hand side. The stuff on the right-hand", - "side has a term multiplying the source voltage V and some other", - "term multiplying the current I. And if I were to put this in", - "sort of symbol-like form my unknown node voltage is some", - "constant times V1 plus some constant times,", - "is of the form constant times the source current,", - "constant times the source voltage and so on.", - "The units of As and Vs are different because in this case A", - "has no units because V is a voltage.", - "And so is e. In this case V has units of", - "resistance. So that V times i gives me a", - "voltage. So stare at this equation for a", - "few seconds and this should help us build up some insight that", - "will allow us to write down the answer almost by inspection.", - "I'm going to show you a method now, in a few minutes,", - "which will allow you to write down the answer e just by", - "starring at the circuit without having to go through node", - "equations and so on. The more and more methods I", - "teach you, the more you will be able to do a lot of this", - "completely by yourselves. In this particular example it's", - "a relatively simple circuit but these methods would be", - "particularly useful when you have more complicated", - "situations. But before I go on let me spend", - "a few minutes pontificating on linearity.", - "So that's a linear circuit. And this equation gives me the", - "unknown node voltage e as a linear sum of source voltages", - "and source currents. Linearity implies two", - "properties, the property of homogeneity and also gives vice", - "to the property of superposition.", - "Let's do homogeneity first. What this says is if I have a", - "circuit, some circuit and I feed it some sort of inputs,", - "A, then let's say my output is S.", - "If you're feeling hungry think of these as apples and the", - "circuit converts them into applesauce.", - "So what homogeneity says is that what I can do is if I take", - "each of my apples and instead of feeding it an entire apple what", - "if I give it three-quarters of an apple?", - "Say I multiple all my inputs by some constant alpha,", - "three-quarters. What that says is that at the", - "output instead of getting one full bottle of applesauce I'm", - "going to get three-quarters of a bottle of apple sauce.", - "So if I proportionately reduce all the inputs and if this is a", - "linear circuit then so shall my output be reduced in the same", - "proportion. So that's homogeneity.", - "Next, let's look at superposition.", - "The property of superposition says the following.", - "The same kind of circuit. If I feed it apples then I get", - "applesauce. I take the same circuit,", - "and this time around if I feed the circuit a different set of", - "inputs, say blueberries. And let's say my output,", - "oops, let me do it this way. So as my output I get blueberry", - "sauce, if such exists. So apples applesauce,", - "blueberries give me blueberry sauce.", - "Then what I'm going to get if I mix up the two,", - "so let's say I take my circuit, the same circuit with a set of", - "inputs and in this example one output.", - "Let's say I mix up my inputs and some of my inputs in the", - "following way, here I feed an A1 plus B1 and", - "here A2 plus B2 and so on then at the output I am going to get", - "a mush of apple sauce and blueberry sauce.", - "All this says is that if I apply just apples I get", - "applesauce. If I apply just blueberries I", - "get blueberry sauce. Then if I were to figure out", - "how this blender would have worked had I fed in the", - "combinations of apples and blueberries, then for the", - "purposes of understanding that blender all I could have done", - "was taken by two outputs and just mixed them up together", - "myself and that's exactly what I'd get.", - "So if I sum up the inputs my outputs would also be the sum of", - "the outputs with the inputs applied by themselves.", - "So let me take this here and munge around with hit for a few", - "seconds and get something interesting out of it.", - "So notice two inputs, two inputs, outputs.", - "In your notes I've given you another template for the next", - "set of scribbles I'm going to make here.", - "So use the next set of templates on page three.", - "What I'm going to do here is something very simple,", - "set one output to zero and feed a voltage V1.", - "So that's feed a voltage V1 and set the other output to zero.", - "And let's say I get Y1 as an output.", - "And in this case I set the first voltage to zero and feed a", - "different voltage V2 on the second input.", - "And let's say my output is Y2. This is just a particular", - "application of the superposition principle I just outlined.", - "Apply V1 set one output to zero.", - "Apply V2 set the original output to zero.", - "Then what I'm going to find is that the answer will simply look", - "like this, just replace for As and Bs what I just did and we", - "get V1 and zero here and we get zero and V2 here.", - "And as my output I'm going to get exactly the sum Y1 plus Y2.", - "This is simply a particular application of superposition", - "where what I'm saying is the following.", - "If you look at this circuit here effectively what have I", - "done? Effectively what I've done is", - "apply the voltage V1 on one input and a voltage V2 on the", - "other input. V1 here.", - "V2 here. And the output is Y1 plus Y2.", - "What I'm saying is look backwards now.", - "What I'm saying is that the whole components of the output", - "Y1 plus Y2 could individually be derived in the following manner.", - "I could get the component Y1 by simply applying one of the", - "voltages and setting the other to zero.", - "I can get the other component Y2 by setting yet another input", - "to zero and applying the voltage V2 to get Y2.", - "And sum then up and that's my answer.", - "This will become a lot clearer with an example.", - "Again, remember if I have a bunch of inputs applied to a", - "circuit, V1, V2 and so on, and I get some output then what", - "this is saying is that I can alternatively find out the", - "answer by applying just one voltage, setting all the others", - "to zero, measuring the output, apply a second voltage,", - "set all inputs to zero, measure the output and sum of", - "applesauce and blueberry sauce and there you get the answer.", - "Let's do an example. And before we go into that I", - "talked about setting voltage sources and current sources to", - "zero. First of all,", - "what does it mean to set a voltage source to zero?", - "This is the same as this. Setting a voltage source to", - "zero is simply replacing the voltage source with a short,", - "and setting a current source to zero simply implies an open", - "circuit. So when I say zero that source,", - "if it's a voltage source short it, if it's a current source", - "open it.", - "I can take any two nodes in the world and measure the potential", - "difference across them. So there may be some potential", - "difference across these set by the circuit that I haven't shown", - "you on this side. There might be some other", - "circuit that is controlling the voltage of these two nodes.", - "The same with the short. What's V going to be?", - "But there is a V. It's zero.", - "So that's method four, method of superposition.", - "And this method says that the output of a circuit --", - "Again, remember I'm focusing on linear circuits.", - "Remember, I have this playground where LMD applies.", - "And within that playground I'm playing in the south goal area.", - "In the south goal area, in that subset of the", - "playground circuits are linear. So in that part of the", - "playground superposition applies because there circuits are", - "linear. So the output of a circuit is", - "determined by summing up the responses to each source acting", - "alone.", - "Now, in this statement here this source stands for", - "independent source. I haven't talked about", - "independent versus dependent sources.", - "We'll talk about dependent sources a few weeks from today.", - "And just so you don't get confused, for dependent sources", - "you will be looking at Section 3.3.3 of your course notes to", - "see how superposition works with dependent sources.", - "But remember we haven't covered dependent sources yet.", - "We will be covering them about two weeks from now.", - "So let's go back to our example and apply the method of", - "superposition to an example. So the method says sum up the", - "outputs of each of the sub-circuits where I'm applying", - "one source acting alone. So let me just do this here.", - "Let me start with the circuit. And let me start with shutting", - "I off. So I have voltage V --", - "I have R2. And I'm shutting I off.", - "So I have replaced this with an open circuit.", - "So I is zero. Let me call the node voltage eV", - "to reflect that component of the node voltage that arises due to", - "V acting alone. And you should look at this", - "pattern here and very quickly be able to write the answer for", - "patterns like this voltage, the two resistors.", - "That's called a resistive divider.", - "It will appear again and again and again.", - "And eV is simply V times R2 divided by R1 plus R2.", - "That's still my ground node. So the voltage here is simply", - "this voltage divided by the two resistors to give you the", - "current multiplied by R2 to give you the voltage across this R.", - "Remember this pattern. You apply voltage divider", - "patterns probably more times than any other pattern that you", - "might imagine. So that's with the V acting", - "alone. Now, let me do I acting alone.", - "So for I acting alone --", - "And what I do this time around is replace this with a short,", - "replace the voltage source to the short.", - "And let me call this voltage eI for the component of the voltage", - "due to the current I. And eI, in this case,", - "is simply given by yet another pattern here,", - "the current across a pair or resistors is simply the", - "effective resistance multiplied by the current so it's i and the", - "effective resistance is R1, R2 or R1 plus R2.", - "That's eI. That's a component that node", - "due to the current I. Now, so the method says that.", - "Then take these components, sum them up and there you have", - "the answer. So E is simply ev plus ei.", - "The components of V and I acting alone,", - "just simply V times R2 divided by R1 plus R2 plus R1,", - "R2. There we go.", - "Fortunately, the fates have been kind to us", - "and the answer is the same as the answer we obtained with the", - "node method. No surprise here.", - "So this is actually an incredibly simple method.", - "So you can take a very complex circuit.", - "What have you really done here? You can take a very complex", - "circuit and you can solve a very complex circuit by breaking it", - "down into many simple individual sub problems.", - "You will do this in EECS time and time and time again.", - "Whether it's in software systems or hardware systems or", - "what have you, you're often times building", - "complicated systems. Remember doom on this side?", - "And the way and when you put these things together,", - "let's say a large software system, is you don't write the", - "whole piece of software starting main and grunge down.", - "You build a lot of little components and tie the", - "components together. In the same manner here you", - "take a big circuit and you find its behavior for each source", - "acting alone. Lots of little inky dinky", - "simple little circuits. And you will see examples in", - "your homework where you're given a big circuit or because it set", - "all the Is to zero and the other Vs to zero the whole circuit", - "almost vanishes and all that you're left with is a little", - "resistor or two. So this is the very,", - "very powerful method. I'd like to do a little", - "demonstration for you. And what I'm going to show you", - "is the demo is a vat of water. Actually, I'll tell you what it", - "is in a second. But assume it is salt water for", - "now. I'll apply two voltages.", - "In this case I'm going to apply a sinusoid.", - "That's not very good. A sinusoid and a triangular", - "wave. And what I'm going to do is", - "measure the response at this site.", - "Now, this is a vat of salt water.", - "And I'm going to tell you it behaves like a linear system.", - "If you view each little particle, or each little", - "cubic-centimeter or whatever of water, it'll behave like little", - "resistor. So this vat of salt water", - "behaves like big distributed resistor in the following", - "manner.", - "And so on. This of this big mesh of little", - "resistors, but it's all resistors.", - "It's a linear circuit. So I'm going to apply two", - "voltages, a triangular and a sinusoid, and we're going to", - "observe the output. And what do you expect to see", - "there? You will see the superposition", - "of the two, which is you'll see a sinusoid.", - "And then you'll see the jagged triangular thing articulating", - "the sinusoid pattern. What I'm going to do right now,", - "don't put any water yet. This is the vat of nothing", - "right now. It's all empty.", - "Can we show the screen on this side?", - "The oscilloscope screen?", - "OK. Oh, there you go.", - "So this is the screen of the oscilloscope now.", - "Notice that I have a sinusoid and I have a triangular wave and", - "the output is zero. And the reason is there is", - "nothing in this vat. It's empty.", - "So previously when I taught this course I would get", - "saltwater and pour saltwater. Then we discovered a much", - "better source of water that conducted electricity like one", - "real mean fluid. Cambridge water.", - "It just works very pleasantly. It just conducts electricity", - "like nothing at all. And I've been thinking of using", - "Charles River water next time and see what happens,", - "although there we'd probably get some biological organisms", - "doing strange things at you. But go ahead.", - "Our friendly demonstration expert, Lorenzo,", - "will pour some water into the vat.", - "And you should begin seeing the output being a superposition of", - "the two. So as he pours,", - "there you go, do you see that?", - "So you do see the sinusoidal articulation and the jagged wave", - "form. And just to have some more fun,", - "what I can do is increase one of the voltages.", - "And you'll see --", - "Now you know what would have happened if I had used Charles", - "River water. So my output keeps increasing", - "as I increase the corresponding wave form.", - "I could do this, this is fun.", - "So let me pause there and go onto the next topic.", - "So that little demonstration showed you that even something", - "as simple as this physical entity vat of water behaves like", - "a linear system, and we can model that linear", - "system as a set of resistors. Unbeknownst to you,", - "right now, in the past ten seconds I introduced a new", - "concept. It's called subliminal", - "advertising. So one of the things we do in", - "EE a lot is model real systems. So often times if I wanted to", - "look at the behavior of salt, behavior of a vat of water,", - "I can model it as a set of resistors for certain kinds of", - "activities. Just hold that thought for some", - "time later in your careers. All right.", - "That's method four, the superposition method.", - "Remember, it is methods like this that will make your life", - "really, really, really easy.", - "If you find that you are having to do a lot of grunging homework", - "or something, just step back and think", - "superposition, think Thevenin or think", - "composition rule. There must be a simpler way", - "usually. Let's do the next method.", - "This is called the Thevenin method.", - "To derive this method let me start by applying superposition", - "to some circuit. So let's say I have some", - "arbitrary network N. Assume it's a linear network", - "and the network has a whole bunch of goodies in it.", - "It has a bunch of resistors, it has a bunch of voltage", - "sources, and it has a bunch of current sources.", - "Many current sources. Many voltage sources.", - "Many resistors. Some jumbled voltage sources,", - "current sources and resistors. And I look at two nodes in this", - "network. Here are two nodes in the", - "network, two points in the network were elements connect.", - "I'm looking at those two nodes and all I want to do is the", - "following. I want to figure out if I take", - "a rinky-dinky little current source and apply it there,", - "all I want to figure out is what is V and what is I.", - "There is this mongo box out here, a black box of resistors,", - "voltage source and current sources, too many to count.", - "I pick two nodes, apply a current source,", - "and all I care about is what is the voltage that I will measure", - "by applying it here. Notice the current here will be", - "I because the current here is I. And I apply it here.", - "I want to measure what the voltage is.", - "Now, with the insight you've obtained from superposition,", - "you should be able to jump up and state the form of the", - "answer. So by superposition we know the", - "following. We know that the effect of the", - "circuit will be the same as the sum of components being added", - "up. Sum of component,", - "sum of component, a bunch of components added up.", - "Each component will be the response of one source acting", - "alone. So if I can figure out the", - "effect of one source acting alone and put that down here,", - "and do the same thing for all the sources, that's what I will", - "get. So for the source Vm it's a", - "linear circuit. So I know that my answer is", - "going to be, in the final answer is going to be a Vm term and", - "it's going to be multiplied by some alpha M term.", - "I know that. It's a linear circuit so I know", - "that the answer shall have a term Vm multiplied by some", - "constant. Simple, I know that.", - "Similarly, the same is true for, oh, this is the term Vm.", - "And what I can do is I can measure just this effect by", - "setting all the other sources to zero.", - "So I can set all the other current sources to zero and all", - "voltage sources, except for this one,", - "and I can get that answer. So, similarly,", - "for every voltage source I am going to get a term.", - "So for every single voltage source, M1, M2,", - "M3 and so on I'm going to get such a term and they're all", - "going to sum up. Similarly, I'm going to get a", - "term for In. And I know there will be an In", - "term, and I know it's going to be some constant beta", - "multiplying In. In this example of ours here,", - "in this example, remember alpha was this and", - "beta was this constant here. There's some constant beta,", - "some constant alpha. And because I have a whole", - "bunch of current sources there's going to be such a term for each", - "one of them. And each one of these terms,", - "Vm, In will be the voltage I would see here if I set all the", - "other Vms to zero and I set all the other current sources,", - "except for that one to zero. What am I missing?", - "Is that it? The response here,", - "V here. Am I missing anything here?", - "Is that it? Now, don't all yell at once.", - "What am I missing? Current source i,", - "exactly. So if I have a current source i", - "then there's an effect of this current as well.", - "And so I write down i there, too.", - "It's going to be some constant multiplying I.", - "And that constant is going to look like a resistor,", - "right, because this circuit contains current sources,", - "voltage sources and resistors. If I've shorted all my voltage", - "sources and opened all my current sources,", - "what's left in here? Just a whole caboodle full of", - "Rs. It's just going to look like", - "some resistance R. And that's what I get here.", - "So this is what V is going to look like and that's a form.", - "So let's take a look at these components.", - "Let's focus on the easy part first.", - "What does this look like? This component looks like an I,", - "it looks like a current and has some resistance.", - "What is that resistance given by?", - "Supposing I gave you this network and this currency source", - "and I asked you tell me R. How would you measure R?", - "What you would do is open all the current sources,", - "short all the voltage sources, put a ohmmeter in there and", - "measure the resistance R. That's R.", - "OK, so we understand this term. What about this term here?", - "Can someone tell me the units of this term here,", - "this big thing here? Voltage.", - "This is a voltage. This is a voltage.", - "iR is a voltage. So this does behave like a", - "voltage. And it behaves like some", - "voltage V. So notice that as far as this", - "current I is concerned the rest of the universe looks like a", - "resistor and a voltage source behaving in some manner.", - "And let me just call it Vth for now, and you'll know why in a", - "second.", - "The voltage has a form, some voltage plus Ri.", - "So, in other words, as far as this I is concerned", - "this whole network here N full of all the nice stuff is", - "indistinguishable to this I here.", - "So my I is sitting out there injecting a current into two", - "nodes. If I am i, I'm looking at this,", - "this network looks no different than a voltage source in series", - "with the resistor R. Notice that the equation for", - "this simple circuit is this, so I is given by V minus Vth", - "divided by R. Just remember.", - "It's a circuit. In other words,", - "Agarwal sitting here cannot tell the difference if I'm", - "measuring the voltage here between a circuit that looks", - "like a Vth in series to the resistor or this huge mess of", - "voltage sources and current sources and so on.", - "Now, we will talk about Vth and R.", - "R is called the resistance of the network as seen from the", - "port with all the sources shut off.", - "And similarly Vth, what is Vth?", - "Vth is the open circuit voltage.", - "In other words, if I apply the voltage here", - "this is the response of all the current sources and all the", - "voltage sources acting together. So it's as if I took this out", - "and simply measured my V here as if I didn't exist,", - "correct? Because this is the component", - "of i. So if I opened i and measured", - "V, I would get that big term on the left-hand side.", - "That's my Vth. So that inspires the next", - "method called the Thevenin method.", - "In this method what I'm going to do is take some circuit,", - "I'm on Page 9, with a mess of stuff.", - "It's a big mess of stuff. And if I care to look at its", - "impact on something else that I add from the outside then as far", - "as the outside world is concerned this is", - "indistinguishable from a circuit that looks like this.", - "So what I can do is if I want to figure out what's happening", - "here then, for the purpose of my analysis, this simple network", - "here with R and Vth becomes a surrogate for this entire mess.", - "So for the purpose of finding out the behavior at this point,", - "I can take this huge mess and replace it with its Thevenin", - "surrogate or Thevenin equivalent.", - "This is called the Thevenin equivalent of this big network.", - "Let me do an example that will make the method completely", - "clear. Again, remember in EECS,", - "most of our lives are about how can we make things so simple as", - "being able to be analyzed by inspection?", - "And so this is a method that takes you further down that", - "path. So let me use the same circuit", - "that I've been using before, my voltage V,", - "R1, R2. This is an R.", - "I'm 55 minutes fast so we have another three or four minutes.", - "So this is my circuit. And let's say all I care about", - "is finding out i1. That's all I care about.", - "And what I'm going to do is I'm going to box this up and see if", - "I can replace that with its Thevenin equivalent.", - "So I'm going to box that up.", - "What I'm saying is that I'm going to box it up and replace", - "it with this Thevenin equivalent.", - "I don't know what Vth and R are at this point.", - "I'm just calling it Rth for fun.", - "I don't know what these two values are, but if I knew what", - "these two values were I can determine I really trivially as", - "follows. I can get i1 as simply V minus", - "Vth divided by R1 plus Rth. So if I knew Vth and Rth,", - "I can write down i1 by inspection in that manner.", - "So next, finally, how do I get Vth and Rth?", - "You get Rth by looking at this network and shutting off all the", - "voltage sources and measuring the resistance there.", - "So I short my voltage source, that's R1.", - "Oops, wrong way. I need to look this way.", - "So looking this way, that's what I get.", - "So what's Rth? Rth is simply R2.", - "So I have opened my current source.", - "Similarly, for Vth, remember all I want to do is", - "look at the two nodes, step back, put a voltmeter", - "there, measure the voltage, that's my open circuit voltage.", - "So the way I do it is I take the circuit and simply measure", - "the voltage there. That's R2.", - "That's my current capital I. And I simply want to measure", - "the open circuit voltage here, which is what?", - "Just simply if I stand back and I kind of gingerly measure the", - "voltage here without disturbing anything, I simply get IR2.", - "So Vth is IR2 and Rth is R2 and here is the formula for the", - "current in this branch when I apply a voltage source and a", - "resistor R1 to this little circuit here.", - "OK, let's pause and let me summarize this in about ten", - "seconds. I had this circuit here.", - "I wanted to find out i1. So what I said I'd do is take", - "this complicated mess, well, it's not a complicated", - "mess but assume it is, and replace with it a", - "resistance Rth got by turning off all the sources.", - "And the voltage in series, Vth, which I get simply by", - "pulling this thing out, taking my input,", - "this part out and simply measuring the open circuit", - "voltage out there, Vth.", - "And then I replaced the whole network with this new network", - "that they call the Thevenin network, and voila,", - "I get the answer in a second." - ] -} \ No newline at end of file diff --git a/subs/SMVp8kv_rlg.srt.sjson b/subs/SMVp8kv_rlg.srt.sjson deleted file mode 100644 index b0d89f501d..0000000000 --- a/subs/SMVp8kv_rlg.srt.sjson +++ /dev/null @@ -1,152 +0,0 @@ -{ - "start": [ - 180, - 2190, - 6270, - 6900, - 10280, - 13270, - 14500, - 17120, - 21170, - 26140, - 29450, - 33330, - 36300, - 39110, - 40960, - 45450, - 47030, - 50360, - 52660, - 56320, - 57970, - 59910, - 63260, - 63900, - 67040, - 70980, - 75460, - 80410, - 81910, - 86060, - 88590, - 92730, - 95200, - 97660, - 99650, - 100850, - 102080, - 105240, - 109550, - 111640, - 115310, - 116480, - 119270, - 120560, - 122710, - 125160, - 126070, - 128780 - ], - "end": [ - 2190, - 6270, - 6900, - 10280, - 13270, - 14500, - 17120, - 21170, - 26140, - 29450, - 33330, - 36300, - 39110, - 40960, - 45450, - 47030, - 50360, - 52660, - 56320, - 57970, - 59910, - 63260, - 63900, - 67040, - 70980, - 75460, - 80410, - 81910, - 86060, - 88590, - 92730, - 95200, - 97660, - 99650, - 100850, - 102080, - 105240, - 109550, - 111640, - 115310, - 116480, - 119270, - 120560, - 122710, - 125160, - 126070, - 128780, - 132100 - ], - "text": [ - "All right, this is the sub circuit.", - "And what I've done here is I've have to turn the current", - "source off.", - "So notice that out here, I create an open circuit.", - "And that is the result of my current source", - "being turned off.", - "And this is my usual ground note.", - "And let me call this node voltage, with the voltage", - "source acting alone, as ev. So ev is the partial response of", - "the circuit to the voltage source acting alone.", - "Now how do we go about solving for ev?", - "Notice that we have a known pattern here.", - "We have a voltage source connected to a pair of", - "registers, R1 and R2.", - "And ev is simply the voltage across R2.", - "Now, this is a known pattern.", - "So one thing you should keep in mind is that in circuits,", - "and electronics, we use patterns a lot.", - "Whenever we see a pattern, we can directly go and write down", - "what the output response is going to look like.", - "What I'm going to do is throughout this course, as we", - "see more and more patterns, I'm going to alert you to", - "these patterns.", - "So right here is a voltage divider pattern.", - "So for the voltage divider pattern, I can write down ev.", - "I can write down ev as being some fraction of the source", - "voltage v. And by the divider action, we simply R2 divide by", - "R1 plus R2.", - "So it is simply the voltage across R2, and that is given", - "by R2 divided by R1 plus R2.", - "And this is a known pattern that you'll find very helpful", - "as you analyze circuits very quickly.", - "Next, let's look at I acting alone.", - "Before we do that, what do we have so far?", - "Again, recall, this is the circuit", - "we're trying to analyze.", - "We are trying to get the voltage e.", - "And so far, we have computed the partial voltage ev, due to", - "the voltage source acting alone.", - "As a next step-- again, this is still step one of the", - "superposition method--", - "let's look at the partial response of the circuit due to", - "the current acting alone.", - "To get the response for the current acting alone, I need", - "to build a circuit in which the voltage", - "source is turned off.", - "I'll let you think for a couple of seconds as to what", - "the circuit will look like before I draw it out for you." - ] -} \ No newline at end of file diff --git a/subs/SaieZYN_WR0.srt.sjson b/subs/SaieZYN_WR0.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/SaieZYN_WR0.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/T2NRdHHQlOA.srt.sjson b/subs/T2NRdHHQlOA.srt.sjson deleted file mode 100644 index 442bd545f2..0000000000 --- a/subs/T2NRdHHQlOA.srt.sjson +++ /dev/null @@ -1,167 +0,0 @@ -{ - "start": [ - 160, - 6070, - 11030, - 12260, - 15910, - 20200, - 21230, - 25235, - 28170, - 32990, - 36420, - 39500, - 43190, - 48010, - 53840, - 56590, - 60500, - 64310, - 68250, - 70030, - 73220, - 77210, - 80920, - 84820, - 86620, - 89910, - 93140, - 97560, - 99070, - 102100, - 104730, - 109310, - 110310, - 115590, - 117910, - 121150, - 124740, - 127830, - 130419, - 135490, - 140610, - 144660, - 149890, - 153040, - 155790, - 160590, - 162220, - 169490, - 174110, - 178340, - 183420, - 188440, - 191370 - ], - "end": [ - 6070, - 11030, - 12260, - 15910, - 20200, - 21230, - 25235, - 28170, - 32990, - 36420, - 39500, - 43190, - 48010, - 53840, - 56590, - 60500, - 64310, - 68250, - 70030, - 73220, - 77210, - 80920, - 84820, - 86620, - 89910, - 93140, - 97560, - 99070, - 102100, - 104730, - 109310, - 110310, - 115590, - 117910, - 121150, - 124740, - 127830, - 130419, - 135490, - 140610, - 144660, - 149890, - 153040, - 155790, - 160590, - 162220, - 169490, - 174110, - 178340, - 183420, - 188440, - 191370, - 193410 - ], - "text": [ - "PROFESSOR: OK, so i1 is very quickly calculated by taking", - "the difference of V and VTH and dividing that by the sum", - "of the two resistances.", - "So the current i1, flowing in this direction, is given by V", - "minus VTH divided by R1 plus RTH.", - "And there I have it.", - "Notice that by converting the arbitrary network N into the", - "Thevenin equivalent, I turn this into a really trivial", - "problem where I could write down i1 simply by inspection.", - "Finally, before we move off the topic of the Thevenin", - "network and the Thevenin method, it is worthwhile", - "staring at this pattern here comprising the voltage source", - "in series with the resistance and the equation v equals vTH", - "plus RTHi that governs the vi of the Thevenin pattern.", - "So it's worthwhile looking at this graphically as well.", - "So I'm going to show you a little graph here and plot the", - "iv relation for this Thevenin pattern.", - "And usually the way you draw these iv relations is you try", - "to find out an open-circuit voltage.", - "In other words, try to find out of the voltage when the", - "current is 0, so open-circuit voltage when i is 0.", - "So in this case, when i is set to 0 and there's no current,", - "then the open-circuit voltage here is simply", - "vTH so v equals vTH.", - "So in other words, when the current is 0,", - "my voltage is vTH.", - "So I found one point on the iv relation for the Thevenin", - "equivalent pattern.", - "Next, let me find out the short-circuit current.", - "And for the short circuit, v is set to 0.", - "So in this case, I apply a short circuit here, and I'm", - "going to measure the current.", - "So the current in this case, i is given by minus", - "vTH divided by RTH.", - "Notice that because vTH is positive here, the current", - "flows down in this direction and is given by vTH divided by", - "RTH, and that is in a direction opposite to i.", - "And so therefore, I get the minus sign.", - "So my current is given by minus vTH divided by RTH.", - "And so for 0 volts, I get some current here, and that is", - "given by vTH divided by RTH.", - "And so this voltage here is my open-circuit voltage, and this", - "current here is my short-circuit current, OK?", - "So this is my short-circuit current, and that's my", - "open-circuit voltage, and my iv relation is drawn by simply", - "connecting the two points.", - "And the slope of this curve is given by 1 divided by RTH.", - "So here again, to very quickly summarize, I've drawn the iv", - "relation for this definite pattern, which has a vTH in", - "series with an RTH and found two points on the iv relation.", - "One is on the voltage axis, and one is on the current axis", - "by measuring the open-circuit voltage and the short-circuit", - "current, and then drawing a line through them." - ] -} \ No newline at end of file diff --git a/subs/T6jJuBoPtK4.srt.sjson b/subs/T6jJuBoPtK4.srt.sjson deleted file mode 100644 index 5114ef81c4..0000000000 --- a/subs/T6jJuBoPtK4.srt.sjson +++ /dev/null @@ -1,260 +0,0 @@ -{ - "start": [ - 320, - 4820, - 6840, - 9100, - 10110, - 15230, - 17310, - 21890, - 24700, - 31260, - 35190, - 37900, - 39250, - 42630, - 47040, - 49210, - 49810, - 52180, - 55380, - 57000, - 58760, - 60610, - 63910, - 68520, - 70220, - 73780, - 75760, - 81070, - 85540, - 87860, - 93830, - 97170, - 99230, - 100240, - 102810, - 103740, - 107310, - 108200, - 110340, - 115060, - 115916, - 119090, - 121720, - 125850, - 128570, - 132100, - 135865, - 138510, - 140960, - 145040, - 145890, - 149280, - 155300, - 156500, - 159910, - 164370, - 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215290, - 218540, - 221000, - 222200, - 226790, - 231260, - 235700, - 236820, - 237880, - 239760 - ], - "text": [ - "SPEAKER 1: All right, so to do KCL at e2, let's start with", - "the current leaving this node.", - "Remember, my usual habit is to sum the", - "nodes leaving the node.", - "So the current heading in this direction will be e2 minus e1", - "divided by R3.", - "So current going left from that node will be e2 minus e1", - "divided by R3 or multiplied by G3.", - "Then the current going up will be e2 minus V0 times G4.", - "And the current leaving the node and going down", - "will be e2 times G5.", - "Have I missed anything?", - "Aha, there is a current here that's coming into the node.", - "And so therefore, the current leaving the mode is minus I1.", - "And all of that sums up to zero.", - "There you have it.", - "So I've written KCL for the two nodes.", - "And I've substituted the device laws as I've been", - "writing it so I don't have this", - "intermediate current variable.", - "So just stare at the beauty of this.", - "Notice that I have two equations, one and two, and I", - "have two variables, e1 and e2, two unknowns and two equations", - "and that's it.", - "OK, so let me go on to step four of the node method.", - "The step four of the node method is simply to go ahead", - "and solve for the node voltages, e1 and e2.", - "So I have my two equations which reflect the KCL at node", - "e1 and KCL at e2.", - "So now it's simply juggling it on with some math and trying", - "to collect all the coefficients of e1 and those", - "of e2, collect them all and just write", - "them a little cleanly.", - "So let me move all the constant terms to the", - "right-hand side.", - "And I will move the variables, or the unknowns, to the", - "left-hand hand side.", - "So let me start with e1.", - "So notice that e1, I multiplied by G1, so", - "I write that down.", - "Multiply by G3, so I write that down.", - "And multiply by G2, so I write that down too.", - "So I get e1 times G1 plus G3 plus G2.", - "And then I collect the terms in e2.", - "And there's only one here, which is minus G3.", - "And the constant terms are here, V0 G1.", - "And I'm going to move that to the right-hand side and write", - "that down as V0 G1.", - "For the next set of steps, I go ahead and do e1 for the", - "next equation.", - "I get minus G3.", - "And then for e2, I go ahead and get a G5, and I get a G4,", - "and I get a G3.", - "So it's G3, G4, and a G5.", - "And I can move the constant terms, which is V0 G4, and I", - "want the right-hand side.", - "And in this case, they both become positive as they move", - "to the right.", - "And I get a I1 here.", - "Good, there you go.", - "So I end up with two equations and two unknowns.", - "And notice I have by e1 times something plus e2 times", - "something equals a constant.", - "And then again, that e1 times something plus e2 times", - "something is another constant.", - "So I two equations and two unknowns.", - "And see how remarkably simple this is.", - "This is basic high school math to solve a pair of", - "simultaneous equations in order to get the answer.", - "And just to be a complete here, let me go ahead and", - "complete it for you.", - "So supposing in step four number four you've gone and", - "solved for the node method, and by solving the node method", - "you get the values of e1 and e2.", - "So let's say you've gone and solved the simultaneous", - "equations for step four and you have e1 and e2.", - "Then, to complete your circuit analysis you need to find the", - "branch voltages.", - "And so you can go ahead and find all the v-i's and i-i's.", - "So in this case, one of my branch voltages is v1 i1.", - "So I just do a couple of quick examples just to show you that", - "it's pretty simple.", - "So what is v1 here?", - "Well let me pause and have you do it." - ] -} \ No newline at end of file diff --git a/subs/TXJIhDHtHSI.srt.sjson b/subs/TXJIhDHtHSI.srt.sjson deleted file mode 100644 index 87e6a1e158..0000000000 --- a/subs/TXJIhDHtHSI.srt.sjson +++ /dev/null @@ -1,2099 +0,0 @@ -{ - 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Good morning.", - "In the last lecture I did a little demonstration for you", - "where I showed you a pair of inverters.", - "And showed you that the output of the first inverter looked", - "weird, certainly not like anything we have seen thus far.", - "It looked like a slow rising transition like this.", - "And using that motivation we have begun our study of RC", - "circuits. And in particular for today the", - "lecture is titled \"Digital Circuit Speed\".", - "We are going to look at the fundamentals of digital circuit", - "speed. And it all boils down to an RC", - "delay. By the end of the lecture,", - "I am going to show you two numbers that you can look at a", - "circuit and obtain by observation, multiply them out", - "and you will get a good idea of the speed at which a circuit", - "will run. It is pretty amazing.", - "So as a quick review -- The relevant section for this", - "is Chapter 10.4. As a review,", - "we said to understand things like this we need to develop the", - "foundations for RC circuits. And the example I covered was", - "that of a very simple circuit that looked like this --", - "An RC circuit of this form. And I also showed you that for", - "an input of the form, input that steps from zero to", - "VI at time T equal to zero. And assuming that the capacitor", - "state at time T equals zero was zero.", - "What this means is that the capacitor starts from rest,", - "so at time T=0, oops, this is VI,", - "I'm sorry. So we assume that the capacitor", - "starts from rest. At time T=0 I apply a VI step,", - "capital VI. And then I want to look at how", - "the voltage across the capacitor behaves.", - "And we did a bunch of analysis. And at the end of the day,", - "in the final demo in the lecture last time I showed you", - "that the capacitor would behave like this.", - "It would start off at, oops.", - "I am sorry. This should be,", - "let's assume that started off at VO.", - "We get a different equation for zero.", - "So let's say the capacitor started off at VO,", - "in which case VC at time T=0 is VO as expected.", - "And we showed that the output would look something like this.", - "After a long period of time this would come up to VI and", - "this rise had a time constant of tau=RC.", - "So we wrote the equation for this waveform.", - "And this is the case when VI is greater than VO.", - "I would like you to stare at the circuit and this result here", - "to get more intuition on what is going on.", - "At time T=0, VC starts off at VO as expected", - "because I am telling you that is the case, that is initial", - "condition. It starts off at VO.", - "Then this one steps to VI. There is no infinite transition", - "anywhere here, and so the capacitor holds its", - "voltage at VO, at time T=0.", - "And then the VI here, which is greater than VO,", - "begins to charge the capacitor up, charge it through this", - "resistor. And so therefore the capacitor", - "charges up. After a long period of time,", - "from the basic foundations of capacitors, we know that the", - "capacitor appears like a long-term open circuit to DC.", - "This is a DC voltage VI. So it appears like an open", - "circuit. So after a long period of time", - "VI appears at the end. And from here to here I have an", - "exponential rise that is typified by an equation of the", - "form -t/RC. This kind of waveform rising", - "from a smaller value to a higher value is typified by this", - "expression. We saw the expression when we", - "developed the equations last time.", - "On the other hand, if the input was such that VI", - "was smaller than VO, so let's say VI was smaller", - "than VO then what will happen is that the capacitor voltage would", - "start off at VO, because I am telling you that", - "is the initial condition, and would then decay in this", - "manner to the final value of VI which is the input.", - "Instead of going up this way it decays down to the final value", - "applied to the circuit. Again, the time constant is RC.", - "But this is typified by a form, this is exponential rise and", - "this guy e^-t/RC is an exponential decay.", - "The key thing to remember is that when you have RC circuits", - "of this form, the waveforms that you get are", - "either each of the e^-t/RC or 1-e^-t/RC.", - "So you can now begin to see how waveforms such as that come", - "about. We will do an example and sit", - "down and compute the inverter delay.", - "And notice that this waveform here is very typical or", - "corresponds to this waveform that we see here.", - "Here I am starting at VO. And assuming this axis starts", - "off at zero, this one starts very close to zero and then", - "rises up to some final value. So far I have reviewed some", - "material for you that I covered the last time.", - "As a second step, I would like to give you a much", - "more intuitive approach -- -- that doesn't involve solving", - "any differential equations. And the reason I do this is", - "that most experienced circuit designers do not sit down and", - "write differential equations each time they see an RC", - "circuit. When you are starting out and", - "you see an RC circuit, you say node method and you", - "write the differential equation, but experienced people don't do", - "that. They look at it and they can", - "sketch the waveform out by inspection.", - "And I will show you how to do that.", - "It is indeed incredibly simple once I give you some intuition.", - "Throughout the rest of this course, I will be showing you", - "many such examples where initially I develop the", - "foundations of stuff and then show you an intuitive approach", - "that very quickly lets you either get the final answer or", - "at least sanity check the answer that you have gotten.", - "And this is how experienced circuit designers deal with", - "stuff. How many people here have seen", - "this movie Bend it Like Beckham? So you know this Beckham", - "character doesn't think about how he is going to curve the", - "ball. He just does it and it happens.", - "He doesn't sit down writing differential equations to find", - "out the projectile trajectory and all of that stuff.", - "You just kind of do it. These series of intuitions I am", - "going to give you is going to be in line with the Bend it Like", - "Beckham kind of intuition. And this one in particular I", - "would like to do in honor of one of your recitation instructions", - "Professor David Perreault. And so this piece of intuition", - "is going to be termed \"Practice it Like Perreault\".", - "Watch what I do with the other names.", - "Professor David Perreault is really a world expert in", - "designing really incredible power supplies for very,", - "very small chips and so on. He doesn't start writing", - "differential equations to do this stuff.", - "He looks at it and sketches it out.", - "Let me show you how he would do this.", - "Suppose I have my circuit like before, VI, R and C,", - "and I am telling you that VC(0)=VO.", - "And my input VI is a step that looks like this.", - "VI is a step. How would Professor Perreault", - "do this? Let's do it completely by", - "intuition. No math here.", - "All right. We know that I have told you", - "that this guy starts off at VO. I am telling you that.", - "You know it is going to start at VO.", - "And there is no impulse or huge infinite transition,", - "and so the capacitor starts off at VO.", - "We also know from basic capacitor properties that after", - "a long period of time, in the steady state,", - "this is but a DC voltage. If you apply a DC and here is", - "my capacitor. After a long period of time", - "this guy is going to look like an open circuit.", - "It is going to charge up to some value and then is going to", - "look like an open circuit. Because if it didn't,", - "you would keep charging it and its voltage would keep", - "increasing. That doesn't happen,", - "it looks like an open circuit. So it looks like an open", - "circuit in the long run. The voltage across it must be", - "capital VI. If I don't have current flowing", - "in the circuit then the only way that can happen is --", - "This open circuit. Capital VI appears across the", - "capacitor. Well, after a long period of", - "time I know that the output must look like this.", - "In this case, I have assumed VI is greater", - "than VO. So you have two points of your", - "curve, VO and VI after a long period of time.", - "And, as I told you earlier, with capacitors you get two", - "kinds of curves. Two things.", - "What you do is go zoop. There you go.", - "You're done. And this has an exponential", - "rise. This is with the form", - "1-e^-t/RC. So we can write an equation for", - "that as follows. VC we know has something to do", - "with minus t/RC. This is of that form,", - "so there has to be that term in there somewhere.", - "And I start off with VO. At time T=0 this is one and", - "this is one, so this term becomes a zero.", - "At time T=0 that becomes a zero so I get VO here.", - "I am going to make sure this stuff stays zero at time T=0,", - "so I start off with VO. Now, as time wears on what", - "happens here? This voltage here,", - "VI-VO, if you look at this difference.", - "That is exponentially decaying over time.", - "And so therefore all I have to do here is write VI-VO.", - "There is the answer. I know the form of the curve.", - "I am just fitting an expression that meets this form.", - "This starts off at VO. When time T=0 this second", - "expression is zero and so it is VO.", - "And this difference here decays down to zero.", - "And this difference here, VI-VO is multiplied by this", - "term here and that is what I get.", - "And you can confirm this. At time T=0 this is zero.", - "At time T infinity this goes to zero, this goes to zero leaving", - "a one, and VO and minus VO cancel and I get a VI.", - "Virtually any such simple voltage source,", - "current source, resistor, capacitor,", - "circuit for most inputs like steps and so on can be analyzed", - "in this manner. Initial value,", - "final value, it's simple.", - "And just to show you that this is simple, I am going to label", - "this expression this way. It is of the form 1-e^-t/RC.", - "Just remember that. Now, by the same token,", - "what if VI had been smaller than VO?", - "Then that is simple, too.", - "I would have had my VI being here.", - "VI would have been here. And that is of the form.", - "In this particular situation, here is my VI,", - "my starting value and I do this.", - "And just to label that, let me label that this way.", - "I just told you that for RC circuits you go this way or you", - "go this way. So it is down here.", - "I get some kind of an exponential decay.", - "And, like before, think of this one.", - "This one has VI as a base value here.", - "And the difference between the two is VO minus VI.", - "And that difference decays. So I have a VI out here,", - "and this difference decays so I get VO-VI and that decays in", - "this form. So I get an exponential decay", - "of this difference here. Just stare at it for a while", - "longer. You should be able to just go", - "and knock it off like this, just like Professor Perreault", - "would. No differential equations.", - "Just write it down by looking at the curve.", - "Let's keep these two in mind, OK, these forms?", - "One is the 1-e^-t/RC form and the e^-t/RC.", - "Both have a time constant RC. Let me just make this a dashed", - "line just to be on the safe side here.", - "That is our first piece of intuition.", - "And, as I pointed out before, in problems you face in life or", - "in ones that we give you, feel free to use the intuitive", - "method. Or what you can do is apply the", - "mathematical method and then check your answer by using your", - "intuition. What I would like to do next is", - "apply what you have learned so far to figure out what we set", - "out to figure out, which is the delay of my", - "inverter. I had promised you that by the", - "end of this lecture I was going to close the loop on that little", - "demo. I was going to close the loop", - "for you on this little circuit that we had looked at,", - "one inverter driving another inverter.", - "This was A, this was inverter X, and this was my node B.", - "The green curve you see out there, the middle one has a", - "transition shown up there. And what I am going to do next", - "is use the results we have gotten so far to compute a", - "number. We are going to compute a delay", - "number both for a rising transition.", - "We will call that delay DR for rising transition.", - "And we will compute a delay for the falling transition DF.", - "Remember, that this is the input that falls down sharply.", - "The intermediate node B rises much more slowly.", - "And because this rises much more slowly this guy here falls", - "a little after this transition here, and so there is a delay.", - "And I am going to apply what we have learned so far and do an", - "example for you and figure out what that delay is.", - "This is an absolute foundational calculation done in", - "building digital circuits all the time.", - "It is remarkable that something so simple is used in designing", - "even the most complex of circuits to obtain very quick", - "ideas of what my delay will look like when I have some subcircuit", - "driving some other piece of subcircuit.", - "Let me just draw a few equivalent circuits for you.", - "The internal circuit looks like this.", - "This is my inverter X, A, my node B.", - "And notice that I have this capacitor CGS.", - "Since I am interested in this node, let me show you that,", - "this capacitor explicitly, it is because of this capacitor", - "here that arises because of this MOSFET here between the gate and", - "the source. And that capacitor gives rise", - "to this RC thing that we are seeing.", - "This is RL, this is RL, VS, VS.", - "And let's say, just as up there,", - "at time T=0 I get a transition like so, a falling transition", - "from say 5 volts to 0 volts at the node A.", - "This is VA here. That is shown up there.", - "And VB --", - "We had expected that VB would look like this.", - "We expected VB to be instantaneous and looking like", - "that, but instead because of the capacitor VB looks like this.", - "And remember, again, this is of the form", - "1-e^-t/RC. And we will write down the", - "answers by inspection. From this let me draw the", - "connection to circuit delay by showing you another little graph", - "here t, VB, zero. And what I am going to show", - "you, this is 5 volts. And so the output goes like", - "this from close to zero to 5 volts.", - "It is close to zero. Because, at least with the", - "inverters we have been seeing in lab and so on,", - "the RON for the inverter is very, very small compared RL.", - "So it is virtually zero down here.", - "And so what is the delay? I mentioned there are two", - "delays of interest. One is the rising delay.", - "That is the logical value at the end, if I wait a long enough", - "period of time, is a logical one.", - "Delay is simply defined as starting from here how long does", - "this output take to get to a valid one?", - "At what voltage here can I say that this transition corresponds", - "to a logical one? At what voltage here can I say", - "that that represents a valid one?", - "Any ideas? Yes.", - "It depends on the discipline, bingo.", - "So it depends on the discipline.", - "Now let's get more specific. Since it depends on the", - "discipline, at what value based on something in the discipline", - "can I say this thing is a logical one?", - "This is an output remember. VOH, bingo.", - "There is some VOH somewhere. And it takes some amount of", - "time to get to a valid logical one output, ergo there is your", - "delay. This is tR.", - "And I call this the rising delay of the inverter X.", - "It is interesting that the rising delay of inverter X,", - "based on our model, depends on the parameters of", - "this inverter and the parameters of whatever it is driving.", - "So remember that the delay is not necessarily just the", - "property of the inverter itself, but it depends on the context.", - "If I stick my inverter before another inverter like this,", - "it is the capacitance on that inverter by our model that tells", - "me what the delay is going to look like, of course in addition", - "to RL. And we will do the math in a", - "few seconds. By the same token,", - "if I had this wire connecting not to one inverter but going to", - "ten other inverters, I expect to have a capacitance", - "equal to ten times CGS. And so therefore this thing", - "should rise even more slowly, correct?", - "The more capacitance on here the slower it rises up.", - "Simple. If I put more and more load on", - "this line by putting more and more MOSFETs on that line,", - "more and more inverters this will rise slower.", - "In our example I just have one, so let's go ahead and compute", - "the delay. This is called the rising delay", - "of X. That says that for this node", - "here to go from its output value to a valid one,", - "which is VOH how long does it take?", - "Notice that if this capacitor was zero then you would have", - "seen an instantaneous transition.", - "If you have an instantaneous transition then notice that the", - "rising delay was zero. That was the model we had", - "looked at up until learning about capacitors.", - "So let's go ahead and compute the number.", - "I can draw an equivalent circuit for computing a rising", - "delay. The equivalent circuit for the", - "rising delay looks like the following.", - "The VS voltage source, with a resistor RL and a", - "capacitor CGS, because when I turn this guy", - "off, this guy has gone off, and so as far as the rise time", - "of this node is concerned I can look at this circuit,", - "ground through CGS through RL through VS back to ground.", - "And just for simplicity, let me draw this in a form that", - "we understand.", - "CGS. Let me use this as my ground", - "node. And this is the voltage VB.", - "And this is RL. And V is simply VS once that", - "transition happens. My other equations here,", - "VI=VS. And what is VB(0)?", - "VB(0) is at what value does this node start out?", - "Notice that for simplicity here if this RON is much,", - "much smaller than RL, then this node would be very", - "close to ground. So I will just go ahead and say", - "that VB at T=0 is approximately zero.", - "And then what I want to find out is what does the value look", - "like for time starting from zero and then going forward?", - "Well, we have become experts at this now.", - "Let's do the intuition here. Start off with zero.", - "That's good. Because my initial value is", - "zero, I start off here. What is the final value?", - "After a long time, since this is a DC voltage,", - "what would be the value at VB after a long time?", - "Pardon? VS.", - "If I wait long enough then it is going to be at VS.", - "This is greater than the initial value,", - "so we're done. That is my 1-e^-t/RC form.", - "It took me three seconds there. It's pretty cool.", - "We could add the expression for this.", - "And the expression was I take my starting value,", - "which is zero, and I add to that this", - "difference VS and I multiply that by this form.", - "There we go. And remember I get this from", - "that rising form up here. V0=0, this is zero,", - "so it is simply VI times that, and VI=VS.", - "I really would like you to get this intuition.", - "If I had two choices, one is that you understand the", - "intuition and are able to sketch that versus in your sleep be", - "able to solve the differential equation and get to the answer.", - "I would much rather you get the intuition, if it is one or the", - "other. It is very simple.", - "Start off at zero, I go chuck, and boom,", - "I get to VS and this is my 1-e^-t/RC form.", - "I need to compute tR. And tR is the time that this", - "takes to get to VOH.", - "For what value of time, for what T, does VB reach VOH?", - "I want to find tR. What's tR?", - "From that equation, that simply tells me the", - "trajectory of VB as a function of time.", - "And so I need to find out what is T for which VB is VOH?", - "I write VOH=VS (1-e^-t/RC). So after a rise time my output", - "is going to be VOH. And so let me go ahead and find", - "tR. Let's see.", - "I bring this to this left-hand side and divide VOH by VS,", - "and then I move things around and what I end up getting is", - "-tR/RC and on the other side I get ln(1-VOH/VS).", - "Divide VOH by VS, that is this,", - "move this to the other side, and move e^-t/RC to this side.", - "And take logarithms on both sides.", - "This is what I get. tR is therefore -RLCGS", - "ln(1-VOH/VS). That is my rise time.", - "You can just do this by inspection.", - "It is just so awfully simple. Just to give to some intuition", - "with numbers and so on. Let's say that RL=1K,", - "VS=5 volts, VOH=4 volts, CGS=0.1 pF.", - "This happens so often that we often time call it \"puff\".", - "0.1 puff. It is pF, it's called puff.", - "If it is nF, I don't know why they didn't", - "call it \"nuff\". They just call it nanofarads.", - "TR for these numbers gets to be one times ten to the three times", - "point one times ten to the minus twelve for pico-farads", - "ln(1-4/5). And if you do the math you get", - "this down to 0.16 nanoseconds. This means that if I had an", - "inverter like that droving another inverter then my output", - "transition would be delayed by 0.16 nanoseconds.", - "Trust me, when Intel builds microprocessors or when Broadcom", - "builds its cable modem chips, they have to do this one way or", - "the other using a computer tool or by hand for virtually every", - "little subcircuit in their chip. That is how you get the delays", - "or some approximation thereof. What I want you also to do is,", - "for no particular reason, I will just compute for you the", - "following quantity RLCGS. The time constant of that", - "circuit for no reason at all. I am just going to compute it", - "and stick it here. And RLCGS 1 K times 1 pF is", - "simply 0.1 nanoseconds. I am just writing it and", - "sticking it there for no particular reason.", - "The next step let's do the falling delay,", - "DF. That is the rising delay.", - "And, although I didn't show this to you in the demo,", - "there is a corresponding delay of the fall time.", - "It doesn't fall instantly, but rather it falls rather", - "slowly. Let's draw the equivalent", - "circuit for when the node X falls.", - "Notice that in my inverters here, this node starts off being", - "at VS. This is high.", - "And this is going to fall because when I turn this", - "transistor on it is going to pull this node to ground or it", - "is going to fall down. And what is the equivalent", - "circuit? The equivalent circuit is that", - "ground through capacitor to this node.", - "At this node I have RON connecting to ground and I have", - "RL connecting to ground through VS.", - "Let me draw that little circuit for you.", - "Remember life begins and ends on storage elements,", - "so I will draw them first. My storage element CGS.", - "That is VB. And, as I said,", - "this is node X, it goes from RON to ground,", - "and it also goes through RL through VS to ground.", - "And in this particular situation VB of zero for the", - "following delay, VB starts off at VS so VB of", - "zero is VS. And the final output I am not", - "sure yet. What is the final value of the", - "voltage at this node? I don't know that yet.", - "I need to compute that. So what I will do is whenever", - "you see something like this, a capacitor connecting to", - "linear stuff, or a nonlinear element", - "connecting to linear stuff. For no apparent reason you", - "should at least think about what?", - "Think Thevenin, exactly.", - "And then see if you can use the Thevenin method to simplify your", - "life. Capacitor, a bunch of stuff", - "here, I need to find out the initial value.", - "Oh, I know that. That is VS.", - "Done. I need to find the final value", - "using my intuitive method. For the final value,", - "I could do it just by looking at this, but I wanted to throw", - "in Thevenin. Hey, let me try to the Thevenin", - "equivalent and see if that makes my life any easier.", - "VTH. The Thevenin method says that", - "you can replace this circuit here with a Thevenin equivalent", - "of the sort for the purpose of determining what happens at this", - "node given that that is linear.", - "So I need to find out that for the purpose of determining what", - "happens at the node X. I have to replace this with its", - "Thevenin equivalent. And I now need to find out RTH", - "and VTH. So I get RTH by looking in", - "here, shorting this guy and looking at the resistance.", - "So I look in like this, then I short this guy here and", - "I get RL in parallel with RON because this one shorts to", - "ground. So RTH is simply RL in parallel", - "with RON. This is a convenient notation", - "for RL being in parallel with RON.", - "And you all know the value of that.", - "It is another one of our very simple patterns like voltage", - "divider and so on. Resistances in parallel can be", - "computed as RL RON divided by RL plus RON.", - "What is VTH? VTH is the open circuit voltage", - "here. If I take out this capacitor,", - "I want to find out what the voltage here is.", - "Ah-ha, voltage divider. VS, the voltage divider here,", - "RL and RON. I could write this down as VS", - "times RON/(RL+RON). Remember you will see again and", - "again and again and again in 6.002 or any circuit stuff that", - "you do, you will see them all over Thevenin.", - "Voltage dividers, current dividers,", - "resistances in series, resistances in parallel,", - "RC thing-a-ma-jigs like this. So if you just remember those", - "10 to 15 intuitive patterns then you are pretty much set for", - "life. It just comes on again and", - "again and again. Parallel resistors.", - "Voltage dividers. You should be able to write", - "down a voltage divider in your sleep.", - "So this is what I have. Let me now write down", - "intuitively what I expect the node X to do just by inspection.", - "Let's see. What is the initial value of", - "the voltage across the capacitor, intuitive method?", - "This is how Professor Perreault would do it, remember?", - "He would start off by saying ah-ha, initial value is VS", - "because I am told it is VS. I start off with VS.", - "And so I start off here. What is the value after a long,", - "long time based on this circuit here?", - "V Thevenin. After a long time this is a DC", - "voltage because that is a DC voltage.", - "The capacitor looks like an open circuit after a long time.", - "And VTH appears there so it is simply V Thevenin.", - "And then when you see those two, boy, I love doing this,", - "you go like this. That is the coolest part.", - "And then I am done. It is so simple.", - "Three seconds or less, I am able to tell you what the", - "delay of an inverter is purely by intuition,", - "completely intuitively. I mean I haven't done any", - "solving. It is just by observation.", - "Took this circuit, made my life easy,", - "Thevenin, looked at RTH, VTH and then sketched it by", - "inspection. Again, if you find that things", - "are really, really, really simple don't be", - "surprised. Once you get some conceptual", - "understanding things are indeed very simple.", - "You can eliminate a lot of math just by staring at things", - "attempting to build up the intuition.", - "As a next step what I can do is write down the expression for", - "VB. And I write down the expression", - "from a falling transition. How do I do it?", - "What was it? What is the method?", - "I take the lowest value of interest here.", - "That is VTH. And then I add to that this", - "difference decaying exponentially.", - "And that difference is simply VS-VTH.", - "And that decays exponentially. This form is the e^-t/RC form.", - "And, boom, I am done. Many of you are wondering,", - "Professor Agarwal, if life was so simple,", - "why on earth did you have us mess around with those", - "differential equations to get here?", - "You show us differential equations and then you don't use", - "them anymore. Well, that is a good question.", - "The answer to that is that you need to understand the", - "foundations. Once you understand the", - "foundations you can find simplifying techniques to get to", - "where you need to be, but you need to understand the", - "foundations. You need to at least see why", - "things are the way they are at least once.", - "Understand the foundations and then find intuitive ways of", - "getting your answers. So now my falling delay here", - "is, I start off with VOS and I need to get all the way down to", - "what value to compute. At some point here,", - "this is a valid one, at some point VB becomes a", - "valid zero for the output. And that is when I stop my tF", - "block. What is the value here for this", - "to be a valid zero? Don't all yell at once.", - "VOL. I simply had to figure out what", - "is the value of time, this is Page 7,", - "for which this expression decays down to VOL.", - "So it is VTH+(VS-VTH) e^-tF/RC. Then I simplify this.", - "How do I do that? VOL-VTH.", - "Then I divide that by VS-VTH. So VOL-VTH.", - "Divide that by VS-VTH. Take logarithms on both sides", - "and then multiply by RC. So I get tF is -RC log of that.", - "This is R Thevenin and this is CGS.", - "How did I get this? VOL-VTH divided by VS-VTH.", - "Take logs on both sides. And then multiply throughout by", - "-1/-RC and I get my tF. Done.", - "Let's do it for the same set numbers, just that we add an RON", - "of 10 ohms. I will do this for RON of 10", - "ohms and compute the value for you.", - "tF=-RTH. RTH is RON parallel RL.", - "This is 10 ohms. That is 1K.", - "So 10 ohms in parallel with 1K is approximately 10 ohms.", - "So let me just use approximately 10 ohms.", - "1 pF, that is RC times ln of VOL.", - "Oh, I need to give you a VOL. Let's say my discipline has VOL", - "being 1 volt. And so therefore I end up", - "getting a VOL-VTH divided by VS-VTH.", - "Since RON is much, much, much smaller than RL,", - "since RON is 10 ohms and this is 1K, most of VS will drop", - "across RL. This is a hundred times", - "smaller. Compared to VOL,", - "which is 1 volt, VTH is very,", - "very small. VTH will be on the order of", - "0.05, and so therefore I simply write down VOL here and say VTH", - "is approximately zero, and I get VS-VTH.", - "This is approximately 5. So let me just say this is", - "approximately. And if you do it you will get", - "1.6 pico-seconds. Again, just for fun,", - "let me write the corresponding RC time constant for the", - "circuit, which is RTHCGS. So RTH is approximately 10 ohms", - "and CGS is 1 pF, so this is 1 picosecond.", - "Now you will understand why I have been writing this time", - "constant down. It turns out that the time", - "constant is a very, very important number.", - "So you see an RC circuit, and you compute its time", - "constant for an RLC connection like this, it is the series", - "resistance times the capacitor. The time constant is a very", - "important number. And usually the circuit delays", - "are in the neighborhood of the time constant value.", - "In this case this is 1 pS. That is 1.6 pS.", - "And in this case we had 0.1 nS and 0.16 nS.", - "So the time constant itself is a good indicator of what your", - "delays are going to be like. If you have no time,", - "you are sloshing your cereal down in the morning and you need", - "to know how long the delay of the inverter very quickly,", - "you have three seconds. Just do the RC and that is a", - "good first approximation. What I would like to do next in", - "the last three or four minutes is set up a little demo for you", - "for your recitation, and then your recitation will", - "cover it.", - "This is a true story. This really,", - "really happened. In this West Coast school,", - "which shall remain nameless, they had a chip,", - "they built a chip. And the chip had a bunch of", - "pins, as you might imagine. And the pin,", - "as you have a trace on a board, a wire on a board there are", - "some capacitance attached to wires, between the wire and", - "ground. And that is a capacitor.", - "And they just called it a load capacitance.", - "It could have been 0.1 pF or 0.01 pF or something like that.", - "What they found when they built this chip --", - "What they found was that the voltage here they expected to", - "look like this, this computer science", - "abstraction and so on, zero to one transition,", - "boom, it should look like this. But for the reasons we saw", - "today the observed transition was much slower and looked like", - "this. So the students said ah-ha,", - "let's speed up this chip. We can speed up the chip by", - "looking at the RL and RON of my driving inverters.", - "And if I make RL small -- Notice if I make RL small my", - "delay is small. If I make RON small my falling", - "delay is small. So let's make really small RLs", - "and RONs and let's all have fun. Unfortunately,", - "what they observed was that by making RL and RON both small,", - "the RC time constant small they expected to see a much sharper", - "rise time. And this was the original.", - "But what really happened was -- They expected this to get", - "faster and kind of look like this, but what happened was", - "disaster struck. What they observed was", - "something like that. This is a real-life story.", - "And so instead of getting something like this they go", - "something like this. And why is that a problem?", - "That is a problem because notice when I expect to be at a", - "zero, I got some spikes that went higher than VIL into the", - "forbidden region and did bad things to me.", - "So let me show you a little demo and show you that that's", - "exactly how the circuit is behaving.", - "Notice that this is what I expect but this is what I see.", - "Look at the purple curve here. Notice these spikes that are", - "showing up there. This is true.", - "They saw it happen. And why is this happening?", - "It turns out that what was happening was that the two pins", - "were next to each other. And I will show you a little", - "demonstration here. Let's see if you can figure out", - "why this was happening. Think of these as two pins and", - "the pins are close together. I am just modeling the two pins", - "with a role of wire. And what I am going to do is --", - "I am going to separate the wires and keep them far apart.", - "It is like keeping my pins far apart.", - "Hey, guess what happened? Those nasty spikes went away.", - "But then I cannot keep my pins 1 meter apart on a chip.", - "Your laptops are going to look 20 yards long.", - "You want the pins to be very close to each other so that you", - "can have many pins on chips and therefore have very small", - "systems. But then look,", - "I get the spikes. Any idea why that is happening?", - "Why is that when the pins are close together I get those", - "spikes? Any ideas?", - "Somewhat? We just learned about", - "capacitors, so this must have to do with capacitors.", - "There is this parasitic capacitor between the pins,", - "exactly. Here is what is happening.", - "Here is what I expect. I expect a nice square wave at", - "the output. But instead I have a pin next", - "to me. And I have a faster wave form", - "driving it. And so therefore there is a", - "parasitic capacitor here. And because of that I get", - "something called \"crosstalk\". And the model for crosstalk is", - "some resultant resistance with the parasitic capacitor and I", - "get those spikes. And the 6.002 experts saw the", - "solution. They said how do we fix this", - "problem? 6.002 experts said the way we", - "fix this problem if it is slow it may be better.", - "Instead of having sharp transitions let me drive it with", - "slower transitions. Let's switch to the demo again.", - "You will see this in recitation, but I will show you", - "the demo very quickly. I have a sharp transition of", - "the input, which is that yellow thing out there.", - "I am going to make the transition slower.", - "Switch to a triangular wave. And you will notice the spikes", - "go away. Oh, no.", - "That is the wrong one. The other one.", - "There you go. The moment I switch to a slower", - "transition boom, the spikes go away.", - "You want to switch back to square?", - "There you go. The 6.002 experts saw the", - "solution. Slower transitions.", - "And you will do this example in detail in Section tomorrow.", - "Thank you." - ] -} \ No newline at end of file diff --git a/subs/TbsD4Bemwg0.srt.sjson b/subs/TbsD4Bemwg0.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/TbsD4Bemwg0.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/TwQScW8yLek.srt.sjson b/subs/TwQScW8yLek.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/TwQScW8yLek.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/UJu_O4HwP_0.srt.sjson b/subs/UJu_O4HwP_0.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/UJu_O4HwP_0.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/UuML_lIpPVo.srt.sjson b/subs/UuML_lIpPVo.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/UuML_lIpPVo.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - 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Good morning all.", - "Today we embark on another new chapter in what we do.", - "And the topic is going to be --", - "We will talk about this thing called an Operational Amplifier.", - "Before I get into the lecture, I want to point out a couple of", - "things. One is that you are going to", - "hear about two big words in today's lecture.", - "Two big and incredibly important words.", - "And I want to mention those words to you right now so that", - "when I come to them in lecture you can say OK,", - "I better pay really close attention, these are important", - "words. All right.", - "One of them is abstraction. The second one is feedback.", - "Two incredibly important concepts.", - "Abstraction, you have been seeing a couple", - "times during this course, once in the beginning where we", - "abstracted out Maxwell's equations by focusing on a", - "smaller playground and simply using KVL, KCL in place of those", - "equations. A big abstraction.", - "It turns out that almost all of EECS is based upon abstractions", - "at various levels. In the first lecture,", - "I also showed you the layer upon layer of abstraction that", - "we built to be able to build interesting systems.", - "The second big thing is feedback.", - "And I am going to relate this to anti-lock breaks in cars.", - "And so, you can wait and see how we do that.", - "It's an incredibly important concept.", - "Before we dive into the amplifier abstraction,", - "let me first talk about something that you know.", - "Start with something that you know and then lead up into the", - "operational amplifier and its circuits.", - "You know about the MOSFET amplifier.", - "The MOSFET amplifier that you know about looked like this.", - "It was based on a MOSFET.", - "There was a VS supply. There was a vI input,", - "a vO output and, as I said, a VS supply.", - "So, this was a MOSFET circuit that you've seen before.", - "One way of viewing this is that this circuit has three major", - "ports. This here is the input port", - "with voltage vI. This here, between the drain", - "terminal and the ground, is the output port.", - "I take the output between the drain terminal and ground.", - "And, finally, we have a third port,", - "which is this one. It is called the power port.", - "I apply VS between this terminal here and the ground", - "terminal. And that gives us the power", - "port. This device here was a three", - "port device. Input port or control port,", - "output port and a power port. And so we looked at the circuit", - "and did a whole bunch of analyses of it.", - "Then what I can do at this point, now that you've seen", - "this, it's often times interesting to think about", - "abstracting this out into some kind of a building block.", - "Much like in software, you write a procedure and you", - "abstract out the internal details of the procedure in the", - "procedure declaration and in the call that you make.", - "In the same way, we can take this little device", - "here and abstract that out into the following abstraction.", - "We could abstract that out as a device that looks like this.", - "I have my input port, I have my output port and I", - "have my power port. So, I can apply VS here.", - "Notice that I've taken these six terminals here,", - "one, two, three, four, five and six,", - "and put a box around it. And just exposed the terminals", - "to you. And I need to tell you a little", - "bit more about the internal properties, but suffice it to", - "say that you can begin working with this little block.", - "An even simpler version of this for many applications might just", - "look like this, vI and vO where there is a", - "ground that is shared among them that is implicit in this", - "picture. And vI and vO can simply be the", - "node voltages at these nodes. This is a progressively more", - "abstract representation of this amplifier.", - "What we can do is, provided we know,", - "we can abstract out the relevant properties of this", - "block and expose them outside. And the relevant properties", - "might well be that, let's say here the properties", - "may be that I in is always zero. I can also express to you the", - "gain of this amplifier. I may also be able to tell you", - "the Thevenin equivalent for the output.", - "There are some properties that I can give you that will let you", - "use this building block abstractly.", - "Today, what we will do is introduce a powerful abstraction", - "of a type of amplifier. This is called the operational", - "amplifier or \"op amp\" for short. What I am going to do is give", - "you a slightly more involved building block than the one I", - "have shown you there. But suffice it to say that the", - "idea is going to be the same. This building block looks like", - "this. This building block has an", - "input port. This building block also has a", - "port in which to connect power or the power port.", - "And the way I am going to connect power,", - "I am going to connect a plus VS supply here.", - "That is going to be my ground node.", - "And I am going to connect a minus VS supply to this node", - "here. So, these voltages are both VS.", - "I want to apply a plus VS here and a negative VS out here.", - "And I am going to take the output between the ground node", - "and the output node of the operational amplifier and call", - "that a vO. This is the output port.", - "So, input port and output port and a power port.", - "Think of this as a pattern where I have an input port", - "across which I connect the input.", - "I have a power port across which I connect a plus VS,", - "minus VS supply, and then I take the output", - "terminal and take a ground terminal, which is defined by", - "external components of my circuitry, and use this as my", - "reference node. Remember ground is just a", - "reference node. I am going to use this as a", - "reference node. These two are equal in", - "magnitude. And take this as my output.", - "And when I do something like this, I can build an even", - "simpler, so this is an abstract differential input amplifier.", - "In other words, this amplifier is going to", - "amplify whatever I apply at the input.", - "A slightly more abstract representation of this looks", - "like this. vOUT and plus/minus vIN.", - "This is a slightly more abstract representation where,", - "remember, we are going to draw this again and again,", - "maybe at least 38 or 39 times in this course.", - "And, remember, each time you draw it,", - "remember that there is an implicit power port,", - "a plus/minus supply that is connected which we don't show.", - "And I remember when I first learned about it a long time ago", - "there was a confusion in me initially.", - "How does this work? Where is the power coming from?", - "Just remember that power comes from a plus/minus supply,", - "and we just don't show that in this abstraction.", - "Now, the details, a lot of details are in Chapter", - "16 of your course notes. That's the reading for that.", - "The other thing is that there are some other key properties of", - "this amplifier. And let me discuss those very", - "quickly. First of all,", - "I can draw a circuit model for the amplifier.", - "Make some room for myself here. And this is a circuit model for", - "what we call the ideal operational amplifier.", - "And the circuit model is going to look like this.", - "This is an abstract device. And, in terms of analyzing how", - "this behaves in a circuit, I am going to show you this", - "abstract circuit that looks as follows.", - "Some input v is applied at these two terminals here.", - "And this terminal is called my v plus terminal and this is", - "called my v minus terminal, so this corresponds to these", - "two terminals. I am telling you that the", - "current going in is going to be zero, so i plus is going to be", - "zero and i minus is going to be zero.", - "i plus is the current in here and i minus is the current into", - "the v minus terminal, and both these currents are", - "going to be zero in this device here.", - "The output is going to look like this.", - "Let me just call it vOUT to be consistent with this here.", - "And taken with ground as my reference.", - "The output is simply Av. In other words,", - "what I am doing is I am going to model this as a device that", - "has a dependent source at its output.", - "And the dependent source here is a voltage controlled voltage", - "source. It is a dependent source,", - "it is a voltage controlled voltage source such that the", - "output voltage is A times the voltage v across its input.", - "This is actually very simple. Think of these three terminals", - "I have shown you here. I applied input across these.", - "And the output is going to be A times whatever I applied.", - "And A is going to tend towards infinity.", - "A is going to be huge. And specific values for A might", - "be a hundred thousand or a million or things of that sort.", - "Huge A in this abstract amplifier.", - "In addition to that, the other properties are that", - "it is going to have infinite input resistance.", - "That means looking in this looks like an open circuit.", - "The fact that this is open here implies the infinite input", - "resistance across this port. What about the output here?", - "Remember, this is a voltage source.", - "And we have a zero output resistance, which means that no", - "matter how the load affects this, as I apply a load this is", - "going to behave like an ideal voltage source and keep holding", - "the voltage constant based on whatever the function I", - "establish here. And A is virtually infinite.", - "Let me pause there for a few seconds and just dwell on this", - "so you just understand what the basic device is.", - "Following this basic definition, I am just going to", - "build a whole bunch of fun little circuits.", - "The analysis will be pretty straightforward,", - "but this is a big conceptual leap here where there is some", - "circuitry inside. Containing resistors,", - "MOSFETs, a whole bunch of stuff in there.", - "I am not telling you what is inside it.", - "Much like I could build an abstract amplifier,", - "I could put an abstract box around the amplifier you saw", - "earlier, I want to put a box around some circuitry.", - "I am not telling you what the circuitry is.", - "And, if you are curious, you should look at page 581 of", - "your course notes. There is an example solved.", - "The example is for a differential amplifier.", - "This is the small signal analysis chapter.", - "That differential amplifier that's solved in that example is", - "usually the first stage in an operational amplifier circuit.", - "That differential amplifier is the first stage at the input.", - "And that differential amplifier, as the name implies,", - "amplifies not a single voltage but amplifies a differential", - "voltage. Note that this guy amplifies", - "the voltage difference between these two terminals.", - "That's v here. And v is simply the same as v", - "plus minus v minus. It's the node voltage here", - "minus the node voltage here. That is what's amplified.", - "It amplifies a difference. Therefore, it is called a", - "difference amplifier or a differential amplifier.", - "And so that input stage is what is inside the op amp.", - "It's got a bunch of other circuitry like level shifters", - "and so on. And at the output it has got a", - "buffer. At at the output it has", - "something that is reminiscent of the source follower circuit that", - "you learned about in recitations, solved an example", - "in the course notes and in your homework as well.", - "And you solved a variant of the source follower on your quiz as", - "well in problem two. So, a circuit that looks like", - "that appears at the output. Remember, for the source", - "follower, the resistance looking in from the output was very,", - "very small. You have seen some of the", - "pieces that go inside the amplifier, but we will deal with", - "this as a building block and simply represent it using this", - "abstract little circuit. To dwell on this a little", - "longer, this little device here is the workhorse of the analog", - "industry. Much like your primitive gate", - "abstraction, your inverter and NAND gate and so on,", - "much as your primitive inverter or NAND gate was from the", - "foundations of the digital industry.", - "Remember we learned how to build this little abstract", - "device called a NAND gate or an inverter?", - "We noticed that those form the foundations of very complicated", - "microprocessors. Those were the building blocks", - "of the digital industry. In the same way,", - "this little beast here is the building block of the analog", - "industry. Just to give you an analogy", - "from software, think of this abstract little", - "device as a library routine from a library of functions when you", - "program in C++ or whatever. Can someone give me an example", - "of an incredibly popular routine that we use all the time that", - "may be called the workhorse of the software industry?", - "Pardon? An abstraction,", - "an abstract procedure. One example might be something", - "like a printf. Printf is an abstract name for", - "a procedure that goes and does something for you.", - "It is amazing how we take the lowly printf for granted.", - "I stick my printf into my program, it includes the", - "standard IO library and it goes and prints a value.", - "You won't believe how complicated the printf is.", - "As you go into learning more advanced software subjects,", - "implementing the printf is a nightmare.", - "It is horrendously complicated. Just imagine.", - "You give it a string and it has to go and print that on your", - "terminal or on your Windows system or whatever.", - "Think of the complicated steps it has to go through.", - "But, as far as you're concerned, it's simple.", - "Just print out something and you're done.", - "The same way. Think of this as the printf of", - "the analog business. It is really simple,", - "and the analysis is going to be incredibly simple,", - "it will be mind-bogglingly simple, but inside it,", - "heavens forbid if you look inside it.", - "Tell you what, go into to S-T-D-I-O dot in one", - "of the library routines and just pore through printf.", - "The world's worst horrendous macros are in there.", - "I mean it is just nasty. The same way inside the op amp,", - "it is nasty. You don't want to go there.", - "Much like in your C programming in your classes,", - "you were able to use printf without fully knowing how it was", - "implemented. Probably some MIT god or some", - "key graduate implemented it, but once it was implemented you", - "just used it based on simple abstract rules as to how it", - "behaved. You didn't have to know what", - "was inside it to use it. The same way with the", - "operational amplifier. So, just think of printf when", - "you see this and just imagine how simple it is going to be to", - "use it. You may think that I spend way", - "too much time, ten minutes dwelling on this", - "abstract concept, but I like to dwell on things", - "that I think are incredibly important.", - "The concept of abstraction is very important.", - "And it's not just in software. The concept of abstraction", - "pervades all of EECS. And if I were to give you a", - "project to say go and ask every professor what is the one word", - "that you think best describes all of EECS?", - "Just pick one word. Go ask every single professor", - "you know. What is a single word?", - "If you were to characterize all of EECS with just one word,", - "what might that word be? In my mind, it is the A word,", - "abstraction. It is all over.", - "If you do a grep on all the words used by all your", - "professors in your four years here, I promise you the first", - "one will be know. And the second one will be", - "abstraction. Check it out.", - "See if what I am saying is true or not.", - "It is all over the place. In 6.001, how many times do you", - "think the word abstraction was used in 6.001?", - "It's all over the map. It's the A word all over.", - "Imagine your shock when you see it being used in 002 because the", - "same concept applies. We build more complicated", - "systems by abstracting out the details of lesser objects,", - "and then using those to build the more complicated systems.", - "Abstraction is a very powerful mechanism of dealing with", - "complexity. Next step is how do I go about", - "using the op amp? Let me show you how it looks on", - "a scope. What I am going to do is apply", - "input to the op amp, I am going to look at the", - "output, place the resistor RL to ground and look at the output.", - "And here I am going to apply a plus VS and out here a minus VS.", - "Again, remember that a plus VS simply looks like this and a", - "minus VS simply looks like this. It's just an inverted VS", - "applied here so I get a minus VS at this input.", - "First of all, what I would like to do is as I", - "change vIN, I am going to plot for you how vOUT looks.", - "vIN and this is vO. I am going to plot vIN in terms", - "of microvolts and vO in volts. vIN is going to have a very", - "very small, the scale is going to be in microvolts because", - "remember the gain of this is huge.", - "It's on the order of ten to the sixth.", - "It's huge. Small changes in vIN are going", - "to cause massive changes in vO. I have a very fine scale on the", - "X axis. What is going to happen if I", - "somehow magically make vIN exactly zero?", - "If I short these two terminals, if this was a completely ideal", - "op amp, which it never is, if it's a completely ideal op", - "amp, then my output should be zero.", - "As I increase my vIN the output should be A times vIN.", - "For some small value of vIN, small v, let's say one", - "microvolt, the output should be one volt.", - "A is a constant so this would look like a straight line.", - "And let's say my supply voltages are 12 volts minus 12", - "volts, if this were an ideal amplifier and I didn't have to", - "worry about the supply, this would just go on extending", - "forever. But I have a plus 12 volt", - "supply and a minus 12 volt supply.", - "My output cannot go past those limits.", - "And so, therefore, my output kind of flattens out", - "at these two points. And it is called hitting the", - "rails. Output goes up and you hear a", - "thunk sound and you hit the rails.", - "When you play with op amps in your next lab,", - "if you listen really, really carefully you may hear", - "it. So, this saturates out.", - "Not surprisingly, this region where the output", - "saturates at the supply is called the saturation region.", - "Remember, don't confuse it with-- It's not the same as your", - "saturation in the MOSFET. It is a totally different", - "thing. It is just happenstance that we", - "call this saturation. And if you would like to think", - "about it, you can think of it as the thunk region.", - "That's probably more appropriate to distinguish it", - "from the saturation region in the MOSFET.", - "And, not surprisingly, this one is called the active", - "region. And it is in this region that", - "we use the op amp. Here it has hit the rails and", - "is kind of dangling out there. It's not much use to us.", - "It's in this active region that we use it because this is where", - "the gain is seen. Now, it turns out that this is", - "a very high gain device. It is very skittish.", - "This gain is kind of a really funny thing.", - "It's dependent on a bunch of factors.", - "This could be temperature dependent.", - "This gain here and this curve is just completely skittish.", - "It could depend on temperature. It could depend on time of day.", - "It could depend on what medication this amplifier is on.", - "It could depend on its mood swings.", - "Who knows what? This is kind of unstable.", - "And A in particular is highly unstable.", - "It is going to be big, that's for sure,", - "but it could be ten to the six, on a rainy day it might be two", - "times ten to the six. If it feeling sleepy it may be", - "point five times ten to the sixth.", - "It is big but I cannot rely on it.", - "Let me show you an example. I want to show you this curve", - "for this MOSFET, apply an input and plotting the", - "output. What I will do is take a look", - "at this curve. Then what I am going to do is", - "use a heat gun to heat the op amp and you are going to see", - "this vary all over the map. If you still remember last", - "week, some of you may remember that from some place in a", - "similar situation where the gm for the MOSFETs you were given", - "was also dependent on temperature and stuff like that.", - "It is a very common occurrence. And that is certainly the case", - "for the MOSFET.", - "Let's apply input. Let's do this.", - "This is vIN versus vOUT for the amplifier.", - "Notice that this is plus 12 volts, this is minus 12 volts.", - "It is about two volts per division.", - "This axis here is in microvolts, I believe.", - "For a very small change, for a few tens of microvolts,", - "I have an incredibly high gain. Notice that this has an", - "incredibly high gain here. The gain is the slope of this", - "line, almost a vertical line. What I am going to do next,", - "is to have some fun, is I am going to heat the op", - "amp. To show you that A is kind of", - "really skittish and also the fact that it doesn't quite hit", - "zero, it does all kinds of weird things, I am going to heat the", - "op amp. And then let's take a look at", - "how that curve fluctuates.", - "What you saw there was that the op amp began to behave really", - "weirdly as I heated it. Instead of doing this it", - "sometimes did this really weirdly, like getting an offset", - "from the center and so on. And it does a bunch of other", - "weird things, but we won't go into those", - "details. It's not relevant for this", - "course. But the point is that the gain", - "and the offset at the input are dependent on temperature.", - "And we look for ways to make it less dependent on temperature.", - "As the next step, what I would like to do is", - "build a circuit. This is model equivalent of", - "your Hello World program. We are going to use the printf", - "and build a small program on the printf.", - "You don't have to worry about how printf is implemented,", - "just that we can build very highly interesting circuits with", - "this horrendously complicated function based on a simple", - "abstraction of the device. The circuit that we will build", - "is called a noninverting amplifier.", - "From now on, I am not going to show you the", - "plus/minus VS. I am not going to show the", - "power port, but it is in there. It's hidden under the", - "abstraction layer. This is my op amp.", - "And I am going to build the following circuit.", - "This is my v plus and this is my v minus.", - "What I am going to do is for the v plus I shall apply a vIN.", - "Let me talk a little bit about ground as well.", - "Ground is commonly taken as the point at which I connect my VS", - "and minus VS supply. It is kind of at the midpoint.", - "And if VS and minus VS are very carefully tuned then the output", - "is also going to be at that same ground reference when the input", - "is zero. So, the ground is defined as", - "the point at which I connect my plus/minus VS supplies.", - "I apply my vIN out here. Then what I am going to do,", - "here is my output vO. I am going to have a resistive", - "divider to ground here and label these R1 and R2.", - "And what I am going to do here is feed this back to the input,", - "to the v minus input. I am going to sample the", - "voltage here and feed that into here.", - "So, this is my abstract model and this is my Hello World", - "program. What we are going to do is", - "simply analyze how this little program behaves.", - "So, my equivalent circuit model.", - "The way to analyze these is after one or two of these", - "examples, you will be able to directly analyze this just by", - "looking at it, by inspection.", - "But, much as we did for the other pieces,", - "let me grunge through drawing the equivalent circuit and", - "grinding through the analysis, and then show you the much", - "simpler way of doing it. And even here,", - "even with this grinding analysis, it is going to be", - "pretty simple in any case. So, I will replace the op amp", - "with its equivalent circuit model.", - "Its equivalent circuit was v plus, v minus.", - "So, that was the equivalent circuit model of the operational", - "amplifier, just this piece. I draw that for you.", - "Then what I am going to do is I connect my v in here.", - "And, remember, I have an R1,", - "R2 resistive divider here. And this one gets connected to", - "this terminal there. I also know that i plus is", - "zero. I also know that i minus is", - "zero. All I've done is simply", - "replaced the amplifier with its equivalent circuit.", - "Let's go ahead and analyze that circuit now.", - "Let's go ahead and analyze that circuit.", - "And it's going to be pretty simple, actually.", - "What I am going to show you is the hard way of doing it.", - "I will show you a much easier way, but the hard way itself is", - "pathetically easy. What I want to do is find vO in", - "terms of vIN. And there will be a bunch of", - "other factors thrown in, including things like R1 and", - "R2, A and stuff like that. Let's go and analyze it.", - "vO, let's look at that circuit. By the way, let me take 30", - "seconds and make a little speech at this point.", - "When you see circuits like this, and I saw this happen in", - "quiz two as well, for some reason,", - "when you see a new kind of circuit, don't completely go", - "berserk or freeze or whatever. There is just no reason to.", - "You know the node method. The node method is the", - "workhorse of our business. When in doubt apply the node", - "method. It will simply work.", - "Don't freeze. Don't think oh,", - "man, I need to apply a pattern that I know already.", - "I must have seen this somewhere.", - "When in doubt boom, apply the node method.", - "This circuit here, all I have here is one unknown", - "node voltage. I know the voltage of v plus,", - "I need to compute the voltage vO.", - "There are two unknowns, vO is an unknown and the", - "voltage here at v minus is another unknown.", - "This is a very simple circuit involving a dependent voltage", - "controlled voltage source, and you need to find out vO and", - "v minus using the node method. Just apply it.", - "It's simple. Don't freeze.", - "Just look at it and say I can do it and apply the node method.", - "It will simply work. So, let's do that.", - "What I can do here is vO is A times v plus minus v minus.", - "This is actually really simple. And then, if I take v plus", - "here, I know v plus is simply vIN so I will just make that", - "substitution right away. So, v plus is simply vIN.", - "What is v minus? v minus here is vO --", - "What is v plus? I'm sorry, v minus.", - "v minus is simply the voltage that is between R1 and R2.", - "Notice that no current flows in to the v minus node.", - "There is no current flowing in. Voltage at v minus is simply", - "the voltage given by the resistive divider,", - "which is vO times R2 divided by R1 plus R2.", - "Stare at that for another second.", - "The voltage at this node here is simply given by the resistive", - "divider. Because no current is flowing", - "in this direction. And no current flows in because", - "I am telling you there is no current there based on my", - "abstraction. I am telling you i minus is", - "zero. That voltage is simply the", - "voltage at this resistive divider.", - "And so I can simplify it further and write this as vO.", - "So I get, there is a one here. And I move this thing over to", - "this side so I get one plus A times R2 divided by R1 plus R2.", - "And that is equal to AvIN. And simplifying it some more,", - "I get vO is AvIN divided by one plus AR2 divided by R1 plus R2.", - "Notice how simple this is, and this is the hard method.", - "All I have done is analyze the circuit using the basic circuit", - "analysis principle that you learned the first week of the", - "course, and I have the output for you.", - "I just noted very carefully what the relationships were", - "between the various elements in the abstraction.", - "Notice here that I am told that A is extremely large.", - "A is on the order of ten to the six and so on.", - "And suppose it is the case that, let me write that down", - "again. vO is AvIN, one plus AR2,", - "R2. Suppose R1 and R2 are more or", - "less comparable and A is ten to the six, it's a huge number,", - "so this whole number is much, much greater than one.", - "If it is much huger than one, what I can do is I can then", - "write this as follows. I can say that this is more or", - "less equal to AvIN divided by AR2 divided by R1 plus R2.", - "I am ignoring the one here. As soon as I do that,", - "notice I can cancel out A and I get vO to be approximately equal", - "to vIN times R1 plus R2 divided by R2.", - "Notice now that when the gain is very large the output is a", - "function of the input multiplied by some number.", - "The beauty of this thing here is that when A is very large,", - "or this expression is very large, A cancels out and there", - "is no A in this relationship. This means that even though the", - "basic amplifier was very skittish, the output here", - "relates to the input based on components that I have control", - "over. These are soldiers in my army.", - "I control them. So, to give you a sense of some", - "numbers here, suppose A was ten to the six.", - "And I choose R1 to be 9R. And R to be some R.", - "Then vO is ten to the sixth vIN divided by one plus ten to the", - "six R divided by 9R plus R. So, that is ten to the six vIN", - "divided by one plus ten to the six divided by ten.", - "All right. If I ignore the one here,", - "the ten to the six and ten to the six cancel out,", - "this ends up giving me 10vIN. So, I get a really nice", - "amplifier whose output is simply ten times the input and", - "determined solely by some resistor values.", - "Let me show you another quick demo this time and show you the", - "amplifier again, but with resistors connected", - "like that. And then I show you that I want", - "to heat the amplifier to the wazoo, the op amp to the wazoo,", - "but vO is going to be absolutely rock solid.", - "Let's try that out.", - "This time around, this is the transfer function,", - "the vO versus vIN. And notice that this time", - "around I have similar scales on the X and Y axes,", - "and this has a slope of 10. This is the point where the", - "amplifier saturates at plus 12 volts, and this is minus 12", - "volts, and this point here is a zero.", - "So, this is vIN, vOUT, plus 12,", - "minus 12 and this slope is 10. What I am going to do now is", - "heat the op amp to the wazoo and this ain't going to change", - "because it's my external resistors that control it", - "independent of the value of A, provided A continues to be very", - "large. I am just articulating the", - "vOUT, vIN curve. And let me start heating the op", - "amp.", - "Notice that it's pretty stable. It doesn't change because it is", - "independent of the amplifier values.", - "What I have done now is by connecting these resistors in", - "this way, I have a nice amplifier with a gain of ten.", - "The question you may ask yourselves is why?", - "There is this little sucker in there that wants to shoot things", - "up by ten to the sixth. Wants to knock things off the", - "one rail or the negative rail. Why is it that it's behaving", - "like a docile lamb here and giving us a nice little factor", - "of ten gain no matter what I do to it?", - "Why is it doing that? What is the intuition behind", - "it? I will draw something on the", - "board, but for the next ten seconds I want you think about", - "it. See if you can come up with", - "some insight as to why is it doing that.", - "Why is it exactly ten? Why isn't the ten to the sixth", - "kind of killing me somehow? Why am I getting exactly ten no", - "matter what happens? See if you can come up with", - "some intuition and then I will show you how it works.", - "I will redraw the circuit in the meantime.", - "Let me see if I can give you some intuition.", - "This is my circuit, and let's say this is R and", - "this is R. As an example,", - "let's assume that the input is 5 volts, vIN is 5 volts.", - "If R and R are equal, what should the output be?", - "It's R and R, so it's R1 plus R2 divided by", - "R2, right? It's 2R divided by R,", - "so it has a gain of two. My amplifier has a gain of two", - "because R1 plus R2 divided by R2, which is my gain,", - "is R plus R divided by R equals two.", - "So, this will be 10 volts. If that is 10 volts this is", - "going to be 5 volts, correct?", - "This R and R, voltage divider,", - "this is five, so I get 5 volts here.", - "This is v plus. This is v minus.", - "I get R and R, 5 volts here,", - "that's how the circuit looks. Now let's understand what is", - "going on. And listen very carefully.", - "This is going to be a key insight that I hope you will", - "carry with you for the rest of your lives.", - "This is really, really key.", - "What you are going to see is, I think, the third big ah-ha", - "moment in 6.002. Like small signal analysis,", - "like the frequency domain stuff we saw, I think this is the", - "third big one in the next 30 or 40 seconds, things that are", - "completely either not necessarily intuitive but are", - "just spectacular in terms of what they can do for you.", - "Let's see. Let's suppose that because I am", - "heating it, let's suppose that A suddenly tends to increase.", - "It wants to increase because I have heated it.", - "A is saying I want to get out this mold here and starts to", - "break through its shackles here. Let's say, as a Gedanken", - "experiment, that it tries to shoot up this to 12 volts.", - "It tries to push it up higher. This is just a Gedanken", - "experiment. The up arrow says that the", - "increase in A is trying to push up vO momentarily.", - "Let's see what happens. It is trying to push up vO", - "momentarily, so let's say this goes to 12 hypothetically.", - "If that goes to 12, what should this volt node go", - "to? Six, exactly.", - "This goes to 6 volts. If that goes to six,", - "what does v minus go to? 6 volts again.", - "So, v minus goes to 6 volts. Now at the input I have 5 volts", - "at v plus and 6 volts at v minus, so where should the", - "output go? The output should go down", - "because the voltage of the negative terminal is higher.", - "And so the output is A times v plus minus v minus.", - "And because this has gone down, this has gone up here it is", - "going to try to pull the output down.", - "That is going to pull the output down let's say to 9 volts", - "or something. Cachunk, there is a big battle", - "going on here. A has gone up,", - "it has boosted it up to 12, but the moment that goes to 12,", - "this goes to 6, this goes to 6,", - "and the op amp output has to go down to 9 volts now because this", - "input is higher here. If this goes to 9,", - "this goes to 4.5. If that goes to 4.5,", - "this goes to 4.5. What happens now?", - "If this goes to 4.5, what happens?", - "It wants to go back up. Can't it make up its mind?", - "This guy wants to go back up now because v plus is higher", - "than v minus. What am I seeing here?", - "This whole circuit here behaves like my little son,", - "my 9-year-old. If say do this,", - "he wants to do the exact opposite.", - "So, there is a trick in how you make them do things for you.", - "Look at this. Because of this arrangement of", - "the circuit when A tries to push the output up,", - "the rest of the circuit tries to pull it back down to where it", - "used to be. If the circuit tries not to", - "follow the true path, the rest of the circuit tries", - "to whack it into shape so it follows a true path.", - "And what's happening is because, in this arrangement,", - "I have fed back a portion of the output to the negative", - "input. I have fed back some of the", - "output to the negative input. And by providing this feedback", - "of a portion of the output to the negative input,", - "I have arranged it in a way that I have something called", - "negative feedback. What negative feedback does is", - "that if this wanted to go wild and crazy, the circuit provides", - "it with some negative feedback like you just saw.", - "Feedback, a big word. If you take a poll of all the", - "EECS faculty, I suspect that feedback would", - "rank at least as the ninth or tenth most important word in the", - "EECS. If abstract is number one,", - "I think this would rank like a nine or a ten or something.", - "So, that's the reason why it worked.", - "In the last couple of minutes, let me give you some insight,", - "based on something that you know, on how feedback works.", - "This is a road here. Let's look at anti lock breaks.", - "This is my tire. And let's say I have a set of", - "disk brakes here. As the car is moving forward,", - "if I apply the brakes the tire stops rolling,", - "but if I apply the breaks too hard it can lock up the tire and", - "the whole car can skid. The way anti lock breaks work", - "is as follows. There is a controller that sits", - "here. And there is a little person", - "looking at the wheel and seeing is it turning.", - "So, this is a feedback. And it is saying is it turning?", - "Yes. Or, is it not turning?", - "No. All this person watching the", - "tire is doing is saying is it turning or is it not turning.", - "That is it. That is a negative feedback.", - "And so, if it is no and if it is yes.", - "If it is yes then what this does is it applies the brakes", - "even more strongly. It is turning so I can apply", - "more brakes. But if it says oops,", - "it stopped turning, what it does is it simply", - "releases, the controller releases the brakes.", - "And when the controller releases the brakes this one", - "tends to loosen up a little bit and the tire starts turning", - "again. So, this way you are constantly", - "keeping the tire in its region of critical friction so that it", - "is constantly moving. And static friction applies to", - "how hard you can brake and it doesn't start skidding.", - "In fact, if you take your car out, and I don't say you do", - "this. Let's say go onto the Charles", - "River in the dead of winter and you drive on the lake and you", - "slam your anti lock brakes on, on an icy patch,", - "you will notice that there is a constant sound that looks like", - "something is vibrating in there. That is exactly what is", - "happening. Oops, the tire is locked.", - "Release the brakes. The wheel is turning.", - "Jam the brakes on. That is exactly what is", - "happening. The same way as out there,", - "you notice that oops, the output is going up,", - "pull it down, oops, it's going down,", - "pull it up. So, there is constant negative", - "feedback that is keeping the output stable.", - "A very important concept. And I will ask your recitation", - "instructors to cover the very simple method that is on page 9." - ] -} \ No newline at end of file diff --git a/subs/V1_MS_lrPsY.srt.sjson b/subs/V1_MS_lrPsY.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/V1_MS_lrPsY.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/WRHqCrSE-Rk.srt.sjson b/subs/WRHqCrSE-Rk.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/WRHqCrSE-Rk.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/WT-qzgaKeGI.srt.sjson b/subs/WT-qzgaKeGI.srt.sjson deleted file mode 100644 index c8e6558868..0000000000 --- a/subs/WT-qzgaKeGI.srt.sjson +++ /dev/null @@ -1,1841 +0,0 @@ -{ - "start": [ - 9000, - 11571, - 17000, - 24138, - 28000, - 34000, - 39311, - 42950, - 47475, - 52885, - 56131, - 60435, - 63657, - 68371, - 71200, - 74028, - 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Let's get moving.", - "Good morning.", - "Today, if everything works out, we have some fun for you guys.", - "I hope it works out. We'll see.", - "What I am going to do today is a very major application of the", - "frequency response and the frequency domain analysis of", - "circuits. And this application area is", - "called filters. The area of filters often times", - "demands a full course or a couple of full courses all by", - "itself. And filters are incredibly", - "useful. They're used in virtually every", - "electronic device in some form or another.", - "They're used in radio tuners. We will show you a demo of that", - "today. They're also used in your cell", - "phones. Every single cell phone has a", - "set of filters. So, for example,", - "how do you pick a conversation? You pick a conversation by", - "picking a certain frequency and grabbing data from there.", - "They are also in wide area network wireless transmitters.", - "Do we have an access point here?", - "I don't see one, but you've seen wireless access", - "points. Again, there they have filters", - "in them. So, virtually every single", - "electronic device contains a filter at some point or another.", - "And so, today we will look at this major, major application of", - "frequency domain analysis. Before we get into that,", - "I'd like to do a bit of review. The readings for today", - "correspond to Chapter 14.4.2, 14.5 and 15.2 in the course", - "notes. All right.", - "Let's start with the review. We looked at this circuit last", - "Friday --", - "-- where I said that for our analysis, we are going to focus", - "on this small, small region of the playground.", - "And what's special about this region of our playground is that", - "I am going to focus on sinusoidal inputs.", - "And, second, I am going to focus on the", - "steady state response. How does the response look like", - "if I wait a long, long time?", - "And then we said that the full blown time domain analysis was", - "hard. This was, remember,", - "the agonizing approach? And then I taught you the", - "impedance approach in the last lecture, which was blindingly", - "simple. And, in that impedance", - "approach, what we said we would do is --", - "I will apply the approach right now and in seconds derive the", - "result for you. But the basic idea was we said", - "what we are going to do is assume that we are going to", - "apply inputs of the form Vi e to the j omega t.", - "Wherever you see a capital and a small, there is an implicate e", - "to the j omega t next to it. I'm not showing you that.", - "And what I showed last time, and the class before that was", - "once you find out the amplitude --", - "Once you find out the multiplier that multiplies e to", - "the j omega t, it's a complex number,", - "you have all the information you need.", - "And once you have this, you can find out the time", - "domain response by simply taking the modulus of that,", - "or the amplitude and the phase of that to get the angle.", - "And that gives you the time domain response.", - "So, our focus has been on these quantities.", - "The impedance method says what I am going to do is replace each", - "of these by impedances. And then the corresponding", - "impedance model looks like this.", - "Instead of R, I replace that with ZR.", - "And instead of the capacitor, I am going to replace that with", - "ZC. And this is my Vc.", - "ZR is simply R and ZC was going to be one divided by sC where s", - "was simply a shorthand notation for j omega.", - "Based on this, once I converted all my", - "elements into impedances, I can go ahead and apply all", - "the good-old linear analysis techniques.", - "I will discuss a bunch of them today.", - "As an example, I could analyze this using my", - "simple voltage divider relationship.", - "Vc is simply ZC divided by ZC plus ZR times Vi.", - "And that, in turn, is, well, let's say I divide", - "this by Vi so I can get the response relation,", - "is ZC divided by ZC plus ZR. And ZC I know to be one by j", - "omega C, plus R. And multiplying throughout by j", - "omega C, I get one divided by one plus j omega CR.", - "It's incredibly simple. This is simply called the", - "frequency response. And it's a transfer function", - "representing the relationship between the output complex", - "amplitude with the input. We can also plot this.", - "Notice that in our entire analysis we have not only", - "assumed sinusoidal input, but we're also saying that let", - "us look at this only in the steady state.", - "So, we will wait for time to be really, really large,", - "and then look at the response. And so, therefore,", - "we will plot the response not as a function of time,", - "but rather we are going to plot the response as a function of", - "omega. What we are going to say is I", - "am going to input a sinusoid and my output is going to be some", - "other sinusoid. And since I'm waiting for a", - "long time to look at the output, time doesn't make sense", - "anymore. Rather, my free variable is", - "going to be my frequency, so I am going to change the", - "frequency of the input that I apply.", - "And so, I am going to plot this as a function of omega.", - "This represents a completely complimentary view of circuits,", - "the time domain view and then there is a frequency domain", - "view. The frequency domain view says", - "how did this circuit behave as I apply sinusoids of differing", - "frequencies? I can plot that relationship in", - "a graph like this, and this relationship is simply", - "given by a parameter edge the transfer function,", - "it's a function of omega. And I can also plot the", - "absolute value of that. And let's take a look at what", - "it looks like. So, I can look at functions", - "like this and very quickly plot the response.", - "I am going to do a whole bunch of plots just by staring at", - "circuits and staring at expressions like this.", - "And you will see a number of them today.", - "First of all, the way you plot these is look", - "for the values where omega is very small and when omega is", - "very large. When omega is very,", - "very small this term goes away. And so, for very small values", - "of omega the output is simply one.", - "Vc by Vi is simply one. This part goes away.", - "What happens when omega is very, very large?", - "When omega is really large, this part dominates,", - "is much greater than one. If I ignore one in relation to", - "this guy and take the absolute value of that then I simply get", - "one divided by omega CR when omega is very large.", - "So, when omega is very large, I get a decay of the form one", - "over omega CR. I know the value for small", - "omega, and it looks like this for very large omega.", - "And, if you plot it out, this is how it's going to look", - "like. Let's stare at this form for a", - "little while longer. And let's plot some properties", - "off it. First of all,", - "you notice something else. When omega CR equals one then,", - "in other words, when omega equals one by RC,", - "notice that the output is given by one plus j.", - "And the absolute value of that is simply one divided the square", - "root of two. So, in other words,", - "when omega is one by RC -- When omega is one by CR then", - "the output is one by square root two times its value when omega", - "is very, very small. So, that is one little piece of", - "information. If you look at the form of", - "this, I would like you to stare at it for a few minutes and try", - "to understand what this represents.", - "This says that for very low frequencies the response is", - "virtually the same as the input in amplitude.", - "In other words, if I apply some very low", - "frequency sinusoid of some amplitude then the output", - "amplitude is going to be same as that amplitude.", - "And that's a one. Now, it also says when I apply", - "a very high frequency, at very high frequencies it", - "decays. So, this graph which says I am", - "going to pass low frequencies without any attenuation,", - "without hammering it, but I am going to clobber high", - "frequencies and give you a very low amplitude signal at the", - "output but pass through, almost without attenuation,", - "the input at low frequencies. And so this is an example of", - "what is called a low pass filter or LPF.", - "What this is saying is that this little circuit here acts", - "like a low pass filter. It's a low pass filter because", - "it passes low frequencies without attenuation but kills", - "high frequencies. If I take some music,", - "and you will do experiments with this in lab.", - "When is lab three? People are doing lab three", - "right now, right? Lab three is going on right now", - "and early next week as well. And, in lab three,", - "you will play with looking at the response to music of", - "different types of filters. If apply some music here,", - "you will see that the output will pass low frequencies but", - "really attenuate high frequencies.", - "You will hear a lot of the low sounding base and so on but", - "attenuate a lot of the high frequencies.", - "All right. The other thing that I", - "encourage you to do is Websim has built in pages for a large", - "number of such circuits. You can go in there and play", - "with the values of RC, or L for that matter,", - "for a variety of circuits. And, if you click on frequency", - "response, you actually get both the amplitude response and the", - "phase as well. You can play with various", - "values of RLC and see how the frequency response looks like", - "for each of the circuits. As a next step,", - "what I would like to do is just give you a sense of how", - "impedances combine. This won't be very surprising", - "given that they behave just like resistors, but it's good to go", - "through it nonetheless. Suppose, just to build some", - "insight, suppose I had two resistors in series.", - "All right. R1 and R2.", - "And this was my A and B terminals respectively.", - "And let's say the complex amplitude of the voltage was Vab", - "across this. Then I could relate,", - "let's say Iab was the current, I can relate these resistances.", - "Or, I could relate Vab and Iab as follows.", - "Simply Vab divided by Iab equals R1 plus R2.", - "I know that. And the same thing applies to R", - "viewed as an impedance. It's still impedance R,", - "and so this one still goes ahead and applies.", - "The second thing I can try is the circuit of this form.", - "A, B, and I have an R1 and an L in this case.", - "And what I can do is, in the impedance model,", - "I can view this as an impedance of value j omega L.", - "And I can also combine them to get the impedance between A and", - "B. Much as I got a resistance", - "between A and B, I can get an impedance between", - "A and B as Vab divided by Iab. And that will be given by ZR1", - "plus ZL, and that is simply R1 plus j omega L.", - "Similarly, I can do an even more complicated circuit.", - "So, resistance. And here I have a capacitor in", - "series with the resistance, and then I apply inductor to", - "it. This is A, B,", - "Iab and plus, minus Vab.", - "And let me call this R1 and let me call this R2 and this is C", - "and L. I can go about combining these", - "in much the same manner that I combine my resistances in the", - "series parallel simplifications. I can define an impedance Zab", - "between the A and B terminals as ZR1 plus Z of this combination,", - "impedance of this combination, which is simply impedance of C", - "and that of R2 in parallel with each other.", - "I get Zc in parallel with ZR2. Notice that this notation", - "simply says that look at the impedance of the capacitor in", - "parallel with a resistor. And then, finally,", - "I add to that the series impedance of the inductor ZL.", - "Exactly as you would have done for resistances,", - "if all of these resistances you would have said R of this piece", - "plus the R of the parallel combination plus the R of", - "whatever was here. This time around we have", - "impedances. And replacing this with the", - "values, this is R1. I know for ZL it's j omega L.", - "And so, for ZL, parallel ZR2 it is given by", - "ZCZR2 divided by ZC plus ZR2, which is simply R1 here and j", - "omega L. And let me just substitute the", - "values here. I know that ZR2 is simply R2,", - "ZC is one by j omega C, and then one by j omega C plus", - "R2. And I can go ahead and simplify", - "that further and get my impedance Zab.", - "Notice how simple analysis has become.", - "Using this technique, using the impedance method", - "we've managed to convert our analysis from solving", - "differential equations to going back to algebra.", - "A large part of what we do in circuits is see how we can get", - "back to really simple algebra and try to be clever about how", - "we do things. So, this is as far as analysis", - "is concerned. In the next five minutes,", - "I want to give you some insight into how you can build different", - "kinds of impedances.", - "And I won't go into too much detail but give some insight", - "into how you can get a sense for the kind of filters you want to", - "design. Or, at the very least,", - "given a filter, how can you very quickly get", - "some insight into what kind of filter it is,", - "how it performs, what its frequency response is", - "and so on. And, this time around,", - "this piece of intuition will be in honor of Umans.", - "And back to our Bend it Like Beckham series,", - "I call this \"Unleash it like Umans\".", - "What experts in the field do is they don't go about sitting", - "around writing differential equations, but rather use a lot", - "of insight into how to solve these things.", - "And so in honor of Umans, I will label this unleash it", - "like Umans. Let's get some insight into how", - "the response of various elements look like.", - "Let's take, for example, I have some impedance Z.", - "Let's say this could be a resistor, it could be an", - "inductor or it could be a capacitor.", - "Let's take a look at what the frequency response of just these", - "elements look like. In other words,", - "what are the frequency dependents of Z itself?", - "Let me just plot the impedance of each of these elements as a", - "function of frequency. Let me just take the absolute", - "value of their impedance. Notice that it's a complex", - "number. For the inductor it's j omega", - "L. And let me take the absolute", - "value omega L in that case and plot it for you.", - "And use that to develop some insight.", - "Let's do a simple case first. If Z is a resistance of value R", - "then no matter what the frequency my value is going to", - "be R. If I have an inductor of value", - "L then the impedance is going to look like j omega L,", - "and so I am going to omega L for that.", - "And the dependence of that simply says that for low omega", - "the impedance is very small. For omega zero the impedance is", - "zero and it increases linearly with omega.", - "So, it's omega L for the inductor.", - "Impedance increases linerally as I increase the frequency.", - "What about for the capacitor? For the capacitor,", - "the impedance is one divided by j omega C.", - "And so, therefore, I get the dependence being", - "related to omega C. Which says that for very high", - "frequencies impedance is very low, but for very low", - "frequencies the impedance is very high and I get a behavior", - "pattern that looks something like this.", - "It goes as one by omega C. As omega is very large,", - "my impedance is very small. If omega is very small,", - "my impedance goes towards that of an open circuit.", - "This is not surprising. You've known this before,", - "right? That a capacitor behaves like", - "an open circuit for DC. An inductor behaves like a", - "short circuit for DC. Notice that zero frequency here", - "corresponds to DC. The capacitor looks like an", - "open circuit for DC, very high impedance.", - "The inductor looks like a short circuit for DC,", - "very low impedance. And the opposite is true at", - "very high frequencies. While R is a constant", - "throughout. Let's use this to build some", - "insight into how our circuits might look.", - "Let me do this example.", - "Let's say I have a Vi and I measure the response across the", - "resistor.", - "So, I measure Vr divided by Vi and take the absolute value and", - "take a look at how it's going to look like.", - "I want you to stare at this for me and help me with what the", - "response is going to look like. Let's take incredibly high", - "frequencies. At very high frequencies,", - "this has a very high frequency, what do the capacitor look like", - "to very high frequencies? Is it an open or is it a short?", - "A short circuit. At very high frequencies the", - "capacitor looks like a short circuit.", - "Then Vi simply appears across the resistor,", - "which means that at very high frequencies the output is very", - "close to the input. At very low frequencies what", - "happens? At very low frequencies the", - "capacitor looks like an open circuit.", - "If this looks like an open circuit then very little voltage", - "will drop across this resistor here because most of it is going", - "to drop across the capacitor. What is going to happen is,", - "for very low values, I am going to be looking at", - "something out here. And, because of that,", - "my response looks like this. And this is of a different form", - "than the one you saw earlier. In this case,", - "I pass high frequencies but attenuate low frequencies.", - "Not surprisingly, this is called a high pass", - "filter.", - "You need to begin to be able to think about capacitors and", - "inductors in terms of their high and low frequency properties.", - "And, if you develop that intuition, once you develop the", - "intuition about capacitors and inductors and their frequency", - "relationship, that will be a big step forward", - "in 002. If you get that insight,", - "you will go a long way in terms of knowing how to tackle", - "problems and being able to quickly sketch responses.", - "Yes.", - "In the case of, if we get something like j", - "omega L, what you can do is take the limit as omega goes to zero.", - "If it is omega L then notice that it is going to start", - "linear. And, on the other hand,", - "if when you get very high frequencies, for example,", - "if you get one by something omega C then this is a", - "hyperbolic relationship, so it is going to go ahead", - "looking like this. So, you can take a look at a", - "lot of these functions at their very low values and see how they", - "look like at that point. All right.", - "The next one I would like to draw for you is something that", - "looks like this.", - "Let's say, for example, I have an inductor L and a", - "resistor R and I want to see what that looks like.", - "In this particular example, I have H, take the absolute", - "value. So, what is this going to look", - "like? I am going to look at the value", - "across the resistor here. Here what I am going to find is", - "that at very low frequencies this guy is a short circuit.", - "Since this guy is a short circuit, all the voltage drops", - "across the resistor so it's going to look like this.", - "And, at very high frequencies, what I am going to find is that", - "the inductor is going to appear like an open circuit.", - "And so, therefore, all the voltage is going to", - "pretty much drop across the inductor.", - "It will be R divided by something plus omega L.", - "So, at high frequencies this guy is going to taper off to", - "zero and is going to look like this.", - "And this is back to my low pass filter.", - "Just to go back to a question asked earlier,", - "how do you know what this looks like?", - "I can very quickly write down the expression for H of j omega.", - "This is simply going to be R divided by R plus if this is VR.", - "VR is simply R divided by one by j omega C.", - "I multiply it out by j omega C in the numerator and the", - "denominator. I'm going to find j omega C", - "here and I am going to get one by j omega C here.", - "And what is going to happen with something like this is that", - "as omega becomes very small then I am going to ignore this.", - "When omega becomes very small, I can ignore this with respect", - "to one, and I get R j omega C. Given that, is what I've drawn", - "here correct or wrong? This goes away with respect to", - "one. I am left with R j omega C,", - "right? For very low frequencies.", - "Given what I have drawn here, is that correct or is that", - "wrong? Well, it's hard to say.", - "For very, very low frequencies it starts out being linear", - "because it's an omega relationship,", - "and then it goes up like this and then goes out there.", - "Let me go onto another example. Let me do another example here", - "which is something like -- I need to make sure I don't", - "make a mistake here. If I get R j omega C by R j", - "omega C, you know what, this ends up being a first", - "order system, and so is going to look like", - "this. I blew it there.", - "Back to this system here. If I have an L and an R and I", - "look at this equation to look at what happens across L,", - "you can plot that again. And for very low frequencies it", - "is going to be zero amplitude here and for very high", - "frequencies this is going to be an open circuit,", - "and so the response is going to look something like this.", - "That's going to end up being your high pass filter.", - "As another example, I would like to do a series RLC", - "circuit --", - "-- and try to get you some sense of what that output looks", - "like. Let's use our intuition and", - "first write down what this looks like and then go and do some", - "math and see if the math corresponds to what our", - "intuition tells us. I want to plot Vr with respect", - "to Vi. I want to plot it there.", - "For something like this, what happens at very low", - "frequencies? We are just looking to get", - "very, very crudely what this graph is going to look like.", - "Very, very crudely what this graph is going to look like.", - "Given that I am taking the voltage across VR,", - "what happens at very low frequencies?", - "At incredibly low frequencies, the inductor looks like a short", - "circuit, but the capacitor looks like open circuit.", - "An open circuit in series with a short circuit that ends up", - "looking like an open circuit. And so, therefore,", - "all my voltage falls across VR. Now, what happens at very high", - "frequencies? At very high frequencies the", - "capacitor looks like a short. But the inductor looks like an", - "open circuit now for very high frequencies, correct?", - "Just remember, capacitor is short for high", - "frequencies inductor open for high frequencies.", - "So, this ends up having a very high impedance.", - "At very high frequencies this guy has a very high impedance.", - "And, because of that, for a high value of frequency,", - "I end up going in that manner. This behavior has the effect of", - "the capacitor here. And for very high frequencies I", - "get the effect of the inductor. And so this means that I have", - "very low values for low frequencies, very low values for", - "high frequencies. And, as the frequency", - "increases, I do something like this.", - "I keep building up, then the inductor begins to", - "play a role, and then I taper off again.", - "This kind of a filter where I kill low and high frequencies", - "and pass intermediate frequencies is called a band", - "pass filter, BPF. This means that it passes", - "frequencies in some band. Let's get some more insight on", - "this by writing down the equations.", - "So, Vr divided by Vi is simply R.", - "Using the impedance relation it is R divided by j omega L plus", - "one divided by j omega C plus R. I am going to use this equation", - "later, so let me stash it away on my stack and put a little", - "notation there. I am going to multiply", - "throughout by j omega C. And what I end up getting is j", - "omega RC divided by one plus R j omega RC, and then here,", - "I get j times j is minus one, so I get minus omega squared.", - "Let me rewrite it this way. I get minus omega squared.", - "So, j j is minus one, omega times omega is omega", - "squared, and then I get an LC. That's what I end up getting.", - "And if I take the absolute value here, I end up getting,", - "back to your complex algebra, the square root of this real", - "value squared plus imaginary value squared.", - "So, one minus omega squared LC plus omega RC squared.", - "This is from, you can look it up in your", - "complex algebra appendix in the course notes.", - "It's simply omega RC here, then square of the real value", - "plus the square of the imaginary value, and take the square root", - "of that. By staring at this,", - "you can notice that you realize a really important property.", - "When omega equals LC. I'm sorry.", - "When omega equals one divided by LC, what happens?", - "Sorry, square root of LC. When omega is one divided by", - "square root of LC then omega squared times LC becomes one.", - "When this is true then this becomes one, and one and one", - "cancel out. And, not only that,", - "when these cancel out, these two cancel out at that", - "point, so I end up getting a one, which means that when omega", - "equals omega nought equals one by square root of LC and I end", - "up getting a value that is one. It's pretty amazing.", - "Which means that if I drive this at omega nought,", - "if my sinusoid has a frequency omega nought where omega nought", - "is one by square root of LC, if I'm sitting here and this is", - "a black box on the right-hand side, and I drive this at a", - "frequency omega nought equals one divided by square root of", - "LC, what does this entire circuit look like to me?", - "I'm sitting there, the black box here.", - "I'm driving it at omega nought equals one by square root of LC", - "at that frequency. What does that circuit look", - "like? Yes.", - "It looks like a resistor. It's pretty amazing.", - "It means that even though I have an L and a C here,", - "if I happen to drive this at omega nought then the circuit", - "looks purely resistive and it seems to give me the same input", - "appearing at the output. In other words,", - "the effect of these two cancels out.", - "And that aspect is called driving the circuit at its", - "resonance point. Resonance is when you're", - "driving the circuit at omega nought equals one by a square", - "root of LC.", - "I will very quickly sketch for you a couple of other ways of", - "looking at circuits. Supposing I looked at this", - "value here, Vlc, I looked at the value across", - "the inductor and the capacitor, what will the frequency", - "response look like? I am looking at the voltage", - "across the inductor and the capacitor in series.", - "Let's see. Let's go back to our usual", - "mantra. Think about Steve Umans when", - "you do this. What would he do?", - "He would say ah-ha, at very low frequencies the", - "capacitor is going to look like an open circuit.", - "In my voltage divider, I am measuring the voltage", - "across an open circuit, so the entire Vi must drop", - "across the inductor and capacitor.", - "Similarly, at very high frequencies the inductor looks", - "like an open circuit now, so it looks like this.", - "At very high frequencies inductor is an open circuit.", - "And, again, I'm looking at the voltage divider across the near", - "infinite resistance, impedance, so I get a high", - "value here as well. Well, in the middle the value", - "dips and I get something like this.", - "So, this thing is called a band stop filter.", - "Here I can nail any specific frequency, as long as the", - "frequency falls in roughly that regime.", - "Yet another example.", - "The reason I'm working on so many examples is that to", - "experts, a large part of what they do is look at a circuit and", - "boom, give a rough form of how it looks like.", - "That can get you half the way there in most of what you're", - "going to do. How did this look like?", - "If I take the voltage Vo versus Vi, let's take a look.", - "At very low frequencies, the inductor looks like a short", - "circuit, correct? I am talking the voltage across", - "a short circuit, so it looks like this.", - "At very high frequencies, I am taking a voltage across a", - "parallel combination, but the capacitor is now a", - "short circuit. So, that looks like a", - "capacitor. This looks like an inductor out", - "here and this is a capacitor holding sway here.", - "And so, somewhere in the middle it goes up and comes down like", - "that. So, it's a band pass filter.", - "What is amazing is that you can take fairly complicated", - "circuits, and just by doing a quick analysis of what happens", - "at very low frequencies, what happens at very high", - "frequencies, you can roughly sketch the response.", - "And then what you should do, in addition to that,", - "is if it's a second order circuit, just assume that it's", - "going to do something interesting at its resonance", - "frequency, at omega nought equals one by square root of LC.", - "Something interesting is going to happen.", - "Check it out. And for circuits that are first", - "order, RC or RL, the important number is the", - "time constant RC. Usually, when you're driving it", - "at one by RC, omega equals one by RC then", - "what happens is that you often times end up getting a value", - "that is one by square root two times the input value in the", - "circuits we looked at here. Next, what I am going to do is", - "talk about a major, major application of filters.", - "And that is an AM receiver. Let me do Radios 101 for 30", - "seconds. These guys have an antenna.", - "You take a ground here. You pick up a signal at your", - "antenna. There is an implied ground as", - "well. And what you do,", - "as a first step, is you begin processing the", - "signal now. What we place right there is a", - "little filter that looks like this.", - "It is a inductor and a capacitor in parallel.", - "And this capacitor is really your tuner that you can tune to", - "radio frequencies. And then what you have here is", - "a bunch of other processing and end up with your speaker.", - "And the processing that happens here is you have a demodulator,", - "you have an amplifier and a bunch of other things that let's", - "not worry about them for now. What we do here is the antenna", - "picks up a signal. So, in some sense,", - "this part of the circuit here is your source.", - "I could replace it with its Thevenin equivalent as follows.", - "So, the front end of your radio looks like a Vi,", - "R, L and a C. Where have you seen this", - "before? Right there.", - "That's the front end of radios. Let me tell you why I need a", - "band pass filter in a radio out here.", - "The way life works is as follows.", - "I have my frequency. Let me do this not in radians", - "but in kilohertz for now, and let me plot your radio", - "signal strength. In the Boston area,", - "the signals go between 540 kilohertz and they go all the", - "way to 1600 kilohertz. In some areas we have begun to", - "use the 1700 extra band as well for some new stations.", - "This is the frequency range of interest.", - "If you look at your radio tuner, you will see 540", - "kilohertz all the way up to 1600 and you can tune your AM radio.", - "The way it works is that each station is given 10 kilohertz of", - "spectrum here. And so, this is at 1000", - "kilohertz, 1010 kilohertz and so on.", - "And each station transmits its signal in plus or minus 5", - "kilohertz around that point. And this station transmits it", - "here and this station transmits it here and so on.", - "This is 1030. This guy is WBZ News Radio", - "1030, for those of you who listen to it.", - "What happens is that at 10 kilohertz, each station gets 10", - "kilohertz, and so WBZ transmits in the 10 kilohertz around 1030.", - "Notice that each of these signals transmitted by radio", - "stations happen within small bands.", - "Now, you will learn a lot more about modulation and how do you", - "get a signal to go in a small band and all that stuff.", - "You will learn about that in 6.003.", - "For now, don't worry about how I did all of this.", - "How do you listen to that station?", - "The way you listen to that station is you put a low pass", - "filter here. You put a low pass filter that", - "does the following. Let's say I want to hear WBZ", - "1030.", - "If I pass this entire signal through that filter.", - "And if I arrange to have the omega nought of my filter at", - "1030. If I can arrange to have the", - "omega nought at 1030 then this is the response of my filter.", - "And I am going to pick out this guy and cut out everything else.", - "I am just going to get this.", - "Let's listen to the station for some time.", - "So, you can see I can tune to the station WBUL." - ] -} \ No newline at end of file diff --git a/subs/XRVab8Q6dZ0.srt.sjson b/subs/XRVab8Q6dZ0.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/XRVab8Q6dZ0.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/XgSOO1sfsa4.srt.sjson b/subs/XgSOO1sfsa4.srt.sjson deleted file mode 100644 index 5043d89bcf..0000000000 --- a/subs/XgSOO1sfsa4.srt.sjson +++ /dev/null @@ -1,191 +0,0 @@ -{ - "start": [ - 0, - 3460, - 4680, - 6760, - 9350, - 12310, - 14480, - 18090, - 20390, - 22260, - 26930, - 30960, - 35530, - 38130, - 41330, - 44645, - 50050, - 51500, - 54070, - 57830, - 63480, - 67540, - 70730, - 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"circuit analysis.", - "This is actually a very simple method.", - "And oftentimes when you're applying some of the more", - "sophisticated methods, it is helpful to apply these methods", - "as some of the partial steps.", - "You can find more about this method and the KVL KCL method", - "in chapter two of the textbook.", - "So this method is very simple.", - "If you have a set of resistors in series, R1 through RN, then", - "you can write up an equivalent resistor whose resistance is", - "equal to the sum of the individual resistances.", - "Now you can also do a complimentary circuit.", - "You can make a set of conductances.", - "Notice that G is our nomenclature for conductance.", - "So G1, for example, is 1 divided by R1 and so on, so", - "G's a conductance.", - "So when I have a set of conductances in parallel, then", - "I can add them all up and replace them with a resulting", - "conductance given by G1 plus G2 plus G3 dot dot dot GN,", - "where G1 equals 1 by RI is a conductance.", - "Another simple thing to remember is when you have two", - "resistances in parallel, let's say R1 and R2, the equivalent", - "resistance is given by R1 R2 divide by R1 plus R2.", - "This is just a special case for two resistors.", - "Let's continue one with element combinations rules.", - "In case C is when I have two voltage sources in parallel.", - "Let's call them V1 and V2.", - "Then I can replace them with a single voltage source whose", - "voltage is given by V1 plus V2.", - "I can get the current based circuit in a similar manner.", - "So let's say I have two current sources in parallel,", - "I1 in parallel with I2.", - "Then I can replace them with a single current source whose", - "current is I1 plus I2.", - "In this example, I would like to use element combination", - "rules to solve for the following situation.", - "So I have a little circuit here with a voltage source of", - "three resistors.", - "And let's say I care about finding the current I through", - "that branch.", - "So how do I go about doing it?", - "So let's start applying element competition rules.", - "As a first step, let me combine these two resistances.", - "And so I get the same voltage source, my resistance R1 here.", - "But in place of R2 and R3, I get the combination of", - "resistors given by R2 R3 3 divide by R2 plus R3.", - "Now as soon as I get that, I now have two resistances in", - "series, so I can sum them up very quickly like so.", - "And I can get a single resistance here, R, which is", - "the sum of R1 plus R2 R3 divide by R2 plus R3.", - "So now notice that this was my current that I needed to find.", - "And I was the current I needed to find.", - "So I brought this down to a very simple pattern.", - "And so I can very quickly write I is simply given by V", - "divided by R.", - "Now the textbook in this particular section gives you a", - "lot more interesting examples of how you can use intuitive", - "analysis to analyze many, many circuits like this.", - "And I would encourage you to go and read that section", - 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So today, we are going to talk about what is both a basic device", - "in itself, the amplifier, and it also serves as a real key example of both nonlinear analysis", - "and small signal analysis.", - "So, today, dependent sources and amplifiers. So, let me first spend a few seconds just", - "pointing out to you some of the key points from our previous lectures. I also want to", - "point out that each chapter in the course notes has a summary at the end of it.", - "And if you take a quick scan of the summary at the end of each chapter, it highlights", - "the major takeaway points from each chapter. It stresses what's important, and if you have", - "to remember a few things, what are those things to remember? So, to quickly review, we talked", - "about a few primitive elements: resistors, voltage sources, and so on.", - "And by now, you should have the facility to play around with these device elements. And", - "then we talked about the Node method, and this is kind of the workhorse of 6.002. When", - "in doubt, use the Node method.", - "OK, and this will work both for linear circuits and nonlinear circuits. OK, so if you see", - "a problem, or if you see a situation in real life that requires analysis, then as a first", - "step, you should try to think of whether you could apply some of the key intuitive shortcut", - "methods, superposition.", - "One of my favorites, the Thevenin method, the Norton method, or the method that involves", - "composition, that is very quickly analyzing circuits that have resistors in series and", - "parallel. OK, so if you can apply one of these quick, intuitive, shortcut methods, go do", - "so.", - "If you can't, then usually you can resort to the Node method irrespective of whether", - "the circuit is linear or nonlinear. So the last week was focused on the nonlinear method", - "or nonlinear circuits, and we spent the first lecture talking about a straightforward application", - "of the Node method, which gave us a bunch of nonlinear equations that we had to solve.", - "In the last lecture, we talked about the small signal trick. What we said is if you look", - "at the whole space of nonlinear circuits, then within that space, if we focus on small", - "variations, small perturbations about an operating point, then even the behavior of nonlinear", - "circuits in that small regime would be linear.", - "So small signal method. And as an example, I showed you how I could take a highly nonlinear", - "device like the garage door opener LED, and using that, build a pretty nice transmitter", - "that would transmit music.", - "And as long as we kept the signal small, and operated the device in a region where its", - "transfer curve was relatively smooth, and I biased, or set the operating point appropriately,", - "I would get a linear, small signal response.", - "OK. So today, we're going to do a couple things. We're going to look at dependent sources.", - "And the reading for this is section 2.6 of your course notes. And, the dependent source", - "will be a new element in your tool chest.", - "We will also do amplifiers, and amplifiers are in section 7.1 and section 7.2 of your", - "course notes. So, before I begin with dependent sources, I'm just a huge believer in motivating", - "things with real world examples.", - "OK, so let me start by motivating: why we need an amplifier? Why do we need to do things", - "like this? Or why do we even bother? And, spend a few minutes really getting you to", - "appreciate that amplification is fundamental.", - "OK, it's as foundational to life as high fat potato chips and stuff like that. So, let's", - "do some basic examples here. So first, let me talk about, why do we need to amplify signals.", - "Why amplify? Why do we care about building an amplifier? So, an amplifier, think of a", - "little box, and apply some sort of small input.", - "And I get a larger output. In this example, this may be a voltage with a swing of 10 mV,", - "and in this case, the output might be another voltage with a swing of, say, 100 mV. And", - "commonly, the amplifier, in addition to an input and an output, input port and output", - "port, may also contain the power port, OK, so that I can apply a power supply to the", - "amplifier because commonly as an amplifier signal, I'm looking for a power gain as well,", - "an increase in the power provided by the output.", - "So, that's an abstract definition of an amplifier, and let's take a look at an example of why", - "we may need this. So let's say I have a small, useful signal, and let's say the signal has", - "1 mV peak to peak.", - "And, I'm looking to transmit the signal over a wire to some other point. But let's say", - "that in this environment, I get a bunch of noise that is in a noisy environment. And", - "in this environment, let's assume that some noise may get superimposed.", - "And if I have a 1 mV signal, and 10 mV of noise, then what I end up with at the output", - "is something that looks like this. And it's really hard to distinguish my 1 mV signal", - "from that large amount of noise.", - "On the other hand, if I do the following, if I took the signal and passed the signal", - "to an amplifier, and I amplified the signal to be a much larger version of the same signal,", - "let's say in this particular situation 100 mV peak to peak signal.", - "OK, so I magnified the signal by a factor of 100. OK, let's say it's a linear amplifier,", - "I linearly amplified signal to be 100 mV, then in that case, if I had a noise on top", - "of this, it's going to be less discernible.", - "The signal will look like this.", - "OK, my 10 mV noise would add on to it. But, this is still pretty decent. I can still recognize", - "the input. And so, this is one application of amplification. If I need to send something", - "from point A to point B as an analog signal, then an amplified signal is less prone to", - "noise attacks than a small signal.", - "Not surprisingly, a large number of devices that are used in everyday life have amplifiers", - "built into them. So, get a little cell phone, and virtually every single cell phone contains", - "an amplifier. By the way, this is an all digital cell phone.", - "It's a Kyocera, I forget the number now. It's completely digital. OK, although they say", - "it's completely digital, it turns out that a significant fraction of the circuitry is", - "analog, in particular, so digital is sort of a marketing term to say that there's something", - "special about this.", - "But remember, there's a bunch of analog stuff. So, here's my little antenna from the cell", - "phone. OK, and typically the first thing that happens to a signal as it comes out of the", - "antenna in your cell phone is, look at cell phone circuits, or cell phone systems would", - "be something that looks like this, OK, this, and may have a label LNA.", - "If someone were to take a guess at what LNA might stand for? What's that? Linear amplifier.", - "That's pretty good. So that's LNA. Close enough. A is correct. It's amplifier. What does L", - "and N stand for? Low noise.", - "OK, so this stands for low noise amplifier. So, I get a really rinky dinky small signal", - "here, and then the low noise amplifier amplifies a signal. And in real cell phones, and for", - "that matter, in your 802.11b, or 802.11a, or 802.11g wireless cards, same thing.", - "Antenna, low noise amplifier, and then you may have a bunch of processing. And commonly,", - "you have a bunch of analog processing. And then, you convert the analog to a digital", - "signal. OK, I recall last week I asked somebody in class here, how would we transmit the signal", - "from point A to point B without it being impacted way too much by noise, and he said, oh, go", - "digital.", - "Good point. OK, so if I go digital, I can transfer the signal without noise being a", - "real factor. But the analog to digital converters need the signal strengths to be a given value", - "before it can chop it up into digital levels.", - "OK, so an amplifier is very fundamental. OK, and so in this case, what may be a signal", - "of a few tens of microvolts to be amplified to some large enough value that it can be", - "further processed. So, that's application of amplification in the analog domain.", - "Let me talk about amplification in the digital domain. So, that's in the analog domain. This", - "amplification is in the domain that I have both analog and digital. OK, and now let me", - "talk about amplification in the digital domain, OK? I'm going to argue that amplification", - "is absolutely foundational to the digital domain.", - "OK, the digital abstraction would not occur if I did not have basic amplification. OK,", - "and the next minute and 37 seconds I will prove that to you, OK? So, let's do so. So,", - "let's suppose I have a very simple digital system, and the system simply contains a pair", - "of inverters.", - "So, if I send a one here, it's a zero here and a one here, which is a very simple, trivial,", - "digital system. And here's the input. Here's the output. And we said that for digital systems", - "of this sort to work, they have to follow a static discipline.", - "OK, our signals and our circuits must follow a discipline for them all to work together.", - "And, the discipline we described comprised of signals adhering to certain voltage thresholds", - "so that all the components in the system could agree on what comprised a zero, and what comprised", - "a one, OK? So the way we did that was we said that you would have a threshold called VIH,", - "V input high, and another threshold called VIL, V input low.", - "OK, and we said that this circuit must recognize signals that are higher than VIH, 3 V for", - "example as a one, and simultaneously, any signal that has a voltage level less than", - "VIL, say, two volts, should be recognized as a zero.", - "That was the input constraint. On the output, it had a similar set of constraints, where", - "we had tougher constraints on devices, where we said that the output had to satisfy a output", - "low constraint, output high constraint.", - "What this said is that for this circuit to be called a good digital circuit that satisfies", - "the static discipline, signals that were ones here should be recognized as such. And if", - "I am producing a one as an output, then the signal level should be higher than VOH.", - "Similarly, if the signal's a zero, then it should be less than VOL. So as an example,", - "this may be 2 V, this may be 3 V, and this may be 4 V, and this may be 1 V. OK, so input,", - "I should recognize 2 V and less as a zero, but at the output I have to produce a very,", - "very low value, 1 V.", - "So, I have some noise margin. So as an example, say if I made a plot of the input/output,", - "so I get my VIL here and VIH here. This is time. This would comprise a valid digital", - "signal: zero, one, zero, one, and so on.", - "OK, now, I had a tougher set of constraints at the output. I would have VOL, VOH. So,", - "at the output, OK, I'm required to stretch the ones and zeros to be further apart from", - "each other so that I get noise margin, and the corresponding signal for our little circuit", - "there would look like so.", - "Right, if this is a valid input, then this would be the corresponding, valid output.", - "OK, and need I say more? OK, you can see that, intuitively, look, there's amplification happening", - "here, and the reason is that VOL is chosen to be less than VIL, and VOH is higher than", - "VIH.", - "So therefore, the signal has to be stretched. The signal has to be amplified. OK, and what's", - "the minimum amplification needed for the system to work? The minimum amplification is if I", - "had a signal that looked like this.", - "OK, that barely skimmed the VIL, VIH level. OK, so if signal were this high peak to peak,", - "VIH minus VIL, and what's the absolute minimum signal at the output? It would look something", - "like this. OK, barely skimming VOL and VOH, OK, so the corresponding output level would", - "be VOH minus VOL.", - "OK, so this is the absolute minimum amplification that my digital circuit has to provide. OK,", - "and notice, VOH is larger than VIH. VOL is smaller than VIL. Therefore, this quantity", - "needs to be greater than one.", - "OK, so I've shown you both a simple, graphical, intuitive explanation, and this is a slightly", - "more formal proof that even the digital circuit really requires to have amplification built", - "into it, if it is to satisfy valid static disciplines.", - "Yes? Yes. The question is, is that the same as gain? Good question. Yes, the term amplification", - "has many, many variants. You could say gain. You could say amplification. You could say", - "increase in signal strength, and so on and so forth.", - "And in fact, when talking about low noise amplifiers, people sometimes talk about having", - "the low noise, high gain amplifier at the input stage. OK, so let me pause there in", - "terms of motivation. So, I believe I've motivated every which way: pure analog, analog/digital,", - "and digital.", - "OK, so I've covered every single base here. And so, we need amplification. OK, so let's", - "look at how to build a fundamental, primitive device called the amplifier. Before we do", - "that, however, let me take a quick detour.", - "It will be convenient for me, as I show you how to build an amplifier, to introduce a", - "new device, a new element, called the dependent source. OK, let me introduce a new device", - "for your arsenal of devices, along with resistors, You learned about a MOSFET, a switch, voltage", - "source, current source, and now a dependent source.", - "So, a dependent source looks like this, OK, has an output port, and has a control port.", - "So, a dependent source in its simplest form has two ports: an input port and an output", - "port. Remember, a port is a convenient pairing of terminals, and I apply signals to such", - "terminal pairs.", - "But this is a abstract diagram for a dependent source, and to get a little bit more specific,", - "let me show you an example of a dependent source. So, let's say, here's my input, and", - "I label the terminal variables for the input.", - "VC is the voltage applied to the input, and IC is the current into this terminal here.", - "And, here is the symbol for the dependent source. Much like a current source or a voltage", - "source has a circle around it, the corresponding symbol for a dependent source is like so.", - "So this example, for instance, is a dependent, current source. I can apply the corresponding", - "output variables, I0, OK, and I can say that the current, I, is some function. In this", - "example, I've designed the example that the current through the current source, I, is", - "some function of the input voltage or the control voltage, VC.", - "OK, so notice that the current through a current source, the current through this current source,", - "I, is some function of another variable. OK, in this example, it's the voltage across its", - "control port.", - "Not surprisingly, this device is called a voltage controlled current source -- -- or", - "a VCCS. So, in like manner I can also devise other forms of sources. You can think of this", - "is a device where a voltage controls an output current.", - "You can think of all other combinations, current controlling current, voltage controlling voltage,", - "current controlling voltage, and so on. So, another example, I give you another dependent", - "source, and in this situation, my output current is controlled by an input current, VC.", - "IC rather. And I claim that I for this one is some function of a current, IC. OK, it's", - "another dependent source where the output current for its output port is related to", - "the current, IC. And, this is a current controlled current source.", - "OK, it's a current controlled current source. And, if I had lots of time on my hands, and", - "I was wanting to kill time, I'd sit around drawing for you, other types of dependent", - "sources. I would draw for you a current controlled voltage sourced, and I could also draw for", - "you a voltage controlled voltage source.", - "OK, so that's an abstract diagram for such a source. And so, let's do a few examples", - "involving elements like this. To begin, just so you can build up your intuition, let me", - "start by doing a very simple circuit, involving an independent current source, OK, just so we can relate back to what we've", - "been doing so far.", - "So, let's say I have some resistor, and I have a standard current source with current", - "I nought. This is an independent current source. Remember the circle? And, some resistor, R,", - "and let's say I care about the voltage across the resistor.", - "OK, so I have a current I nought flowing through it. So, I can very quickly write down VR as,", - "simply, I0 R. OK, it's the drop across the resistor when a current I nought flows through", - "it. OK, so this is what you've been used to doing.", - "Correspondingly, I can do an example with a dependent current source. And, as an example,", - "I'll use a voltage controlled current source. OK, a voltage controlled current source is", - "a dependent current source whose output current depends on the voltage applied at the control", - "port of the current source.", - "So let me build a little circuit. OK, so here's my current. And let's say it's VC IC for the", - "control port, and similarly, let's say my current I here is some function of the control", - "port voltage. And let's say, to be specific, there is some K over VC, some function.", - "OK, there are a variety of dependent sources that can be built, and here's a hypothetical", - "device where the output current is mathematically related to the input in the following manner.", - "So, let me build a circuit of the following form.", - "So, let's add the resistor, R, and here's my circuit, OK? And, as before, let me look", - "to figuring out what VR is. So, notice that I have to supply some voltage at the input", - "so that the output can depend on the input because right now I don't know what the input", - "here.", - "So what I'll do is let me apply VR over here. OK, so let me make this connection. OK, let", - "me make the connection from here to here. What I've done is I've applied VR at the control", - "port of the dependent current source.", - "OK, and I often draw a circuit like this. This looks pretty messy. I will often draw", - "the circuit like so: R, VR. OK, short form circuit drawing would look like this. This", - "is a complete drawing that I show you the explicit connections of the control port,", - "but oftentimes, when the control port does not have any other impact in the circuit,", - "you can eliminate, don't explicitly show the control port.", - "Rather, you can simply show the dependence of the output current on whatever circuit", - "variable you have in mind. So, you can draw the diamond like this, and see its current", - "is some function of VR. VR in this is case is K divided by VR, OK? OK, so let's go ahead and analyze this little", - "circuit here, and look at what this might give us.", - "Our goal, as before, is to find out the value, VR. So, in this case, let's apply the Node", - "method to this node, and sum the currents into that node to be zero. OK, so sum the", - "currents going into that node to be zero.", - "The current going down is simply VR divided by R. OK, and that is equal to the current", - "that is going out of the node. And so that is equal to F of VR. And I know that F of", - "VR is given by K divided by VR.", - "OK, a simple application of the Node method. So then, I collect VR's on the left hand side,", - "and I get VR squared is K times R, OK, and VR is simply the square root of KR. There", - "you go: I'm done. OK, I've gone ahead an applied the Node method to this, and when have to", - "figure out the current here, I simply reflect the fact that it depends on VR like so, and", - "I just go ahead and solve the circuit.", - "Remember, the workhorse of the circuit industry, the Node method, when in doubt, apply it.", - "It simply works. And notice, this is a nonlinear circuit. OK, the dependence is nonlinear,", - "and I get the response like so.", - "So, to plug in some numbers, supposing K was 10 to the minus 3 amperes per volt, and R", - "was one kilo ohm, then I can plug the numbers in and the kilo here cancels with the 10 to", - "the minus 3, and I get VR equals 1 V.", - "OK, this simply says, if I build a circuit like this, then this voltage here will be", - "1 V. So, again, as long as you remember that the dependent source is simply another little", - "circuit element, OK, and you usually draw just the output port for dependent sources,", - "and reflect the way that the control affects the current, that'll suffice, and you get,", - "through the application of the Node method, the variable you're interested in.", - "Let's do another example,", - "OK, of another fun current source, a voltage controlled current source, and look at it", - "this way. So, let's say I have a resistor, and I have a current source, a resistor, RL,", - "and this goes to some, I apply a VS here.", - "Remember this short form notation; that's simply applying a supply VS between that node", - "and the ground. OK, and let us say the current IV through the device is some function of", - "the current at its control port.", - "OK, so I'm not going to show you that. But remember that the device already looks like", - "this, that there is a control port here. I'm not showing that to you. And let us say that", - "I apply some voltage, VI, to the input port.", - "The reason we often don't show the input port is for many practical dependent sources, the", - "input has no other effect on the circuit. So, for example, in this case, the input has", - "infinite resistance looking in.", - "So therefore, if I apply a VI here, it doesn't draw any current from VI. I simply apply the", - "voltage, VI. It doesn't affect the circuit in any other way except in terms of how it", - "controls the current ID.", - "So let's say the current ID is some function of VI because VI is applied at the control", - "port. OK, and as I pointed out before, I oftentimes, just for clarity, just to show this dependent", - "source explicitly.", - "OK, so let's work the example. So as I said, I'm going to choose ID to be F of VI, and", - "let's pick some specific parameters here. Let's say it's K by two VI minus one, both", - "squared. OK, and let's say this is true for VI less than equal to one volt.", - "And let us also say that ID equals zero for VI less than one volt. OK, it's a dependent", - "source, and it can have various forms of dependences on the input. And, I just picked an example", - "of some hypothetical, or as yet, hypothetical dependent source, the current through which", - "is related to the input using a square law relation, VI minus one all squared as long", - "as VI is greater than one.", - "And if VI is less than one, then the current is simply zero, it shuts off. So, I can go", - "ahead and apply. So, let's say I want to find out V0 versus VI. So, I care about finding", - "out V0. V0 is the voltage of this node with respect to ground.", - "OK, so it's a slightly more complicated circuit than you saw up here, than you saw up there.", - "So, let's go ahead and do this example. Start by applying the workhorse of the circuits", - "business, the Node method, and let's start with doing this for VI.", - "Let's first do it for VI greater than one, notice the behavior of this is different for", - "different ranges of VI. So let's first do it for VI greater than or equal to one and", - "apply the Node method. Node method says sum the currents going into this node; we know", - "the voltage at this node.", - "It's VI. We know the voltage at this node. It's VS. OK, the only unknown is V nought.", - "And so, let's go ahead and write the node equations for that node. So, the current going", - "up, let me simply equate the current going up to the current that has been supplied by", - "this particular node here.", - "And, that should equate that the two of them should sum to zero, the current going up plus", - "the current going down should sum to zero. So, I get V0 minus VS divided by R. That's", - "the current going up.", - "Plus, the current going down must sum to zero, plus ID must sum to zero. And ID is going", - "to be K divided by two VI minus one all squared. That must equal zero. Straightforward application", - "of Node method, current going up plus the current going down at this node should equal", - "zero because the total current leaving the node must be zero, OK? So I can go ahead and", - "simplify this, multiply it throughout by, I call this RL here.", - "So, multiply it throughout by RL, and move all of this to the other side, so I get VS", - "divided by RL, multiply it throughout by RL. I get VS at this side. I take this term to", - "the other side. This becomes a minus.", - "RL multiplies here, so I get KRL. That's the expression I get. V nought is VS minus KRL", - "divided by two times VI minus one all squared. Let me put a box around this because I will", - "be referring to this more times in 6.002 for a variety of reasons than probably any other", - "equation on Earth.", - "OK, this is the first time you saw it. You saw it here. OK, mark it down. You'll smile", - "every other time you look at it in quizzes, and you will find out why this comes up very", - "often in 6.002. So, I'll just give you a few seconds to savor this big moment in your 6.002", - "life.", - "All right, OK, so it's pretty simple actually. I mean, there's really not much. A lot of", - "this stuff is just a plain old, simple application of the Node method, and things just fall out.", - "It's just so simple.", - "So, the V nought, I apply the Node method, I get V nought for this nonlinear circuit.", - "I can also it for VI less than one. For VI less than one, when VI is less than one, what", - "happens? ID is zero. OK, since ID is zero, think of this as an open circuit.", - "OK, so there's no voltage drop across RL. And, this voltage V nought is equal to VS.", - "So, I like to see things in pictures. I'm not an equations kind of person. I'm much", - "more of a graphical person.", - "So, let me draw a little graph to show how V nought, to see the form of V nought, and", - "then let's study that little system a little bit more carefully. So, this is page seven,", - "and we plot V nought versus VI for you.", - "And let's take a look at how this really simple circuit looks. This has got nothing. It's", - "got an RL resistor connected to a supply, and a dependent current source, and I apply", - "some voltage VI at the input.", - "It's a very, very simple circuit. So, let's see. So as long as VI is less than one, the output stays at VS. OK, that makes intuitive", - "sense, right? As long as the current here is zero, this is like an open circuit here.", - "If this is an open circuit, then effectively, V nought is simply the voltage VS. V nought", - "simply appears here. If you want to grunge through KVL and KCL, go ahead. VS minus RL", - "times the current is V nought, and the current is zero so it's, yes.", - "So, this is simply VS. When VI goes above one volt, fun stuff begins to happen. OK,", - "when V nought goes above one volt, then this equation applies because VI is greater than", - "one. This equation applies.", - "And, when VI is a one, one minus one is zero. This term cancels out, so this is VS. OK,", - "phew! So, I start off here. As VI increases, what happens now? As VI increases, this term", - "here becomes increasingly negative, OK, subtracting from VS.", - "OK, so I get some behavior like this. V nought begins to drop. And it makes intuitive sense,", - "right? As ID begins to increase, the voltage here will begin to drop because I'm drawing", - "more and more current through RL.", - "I'm dropping more and more across RL. So more and more drops across RL, so V nought begins", - "to drop too. So, it looks something like this. I'll show you a little demo, but my claim", - "is that you have just seen an amplifier.", - "Whoa. You just saw an amplifier. So, I snuck an amplifier by you, OK? So, I just snuck an amplifier past you. I'll show", - "you why in a second. So, let's take a look at this waveform here. Let's not worry about", - "what happens way down here.", - "We'll talk about that a little later. But, look at this curve here. I claim there is", - "amplification in the following sense. Focus on some change in the input voltage, delta", - "VI, OK, and for that change in input voltage, I get some change in the output voltage.", - "OK, for some change in the input voltage, delta VI, I get some change in the output", - "voltage. And guess what? In this, at least the way I have drawn it, delta V nought divided", - "by delta VI, if I can find regions of the curve where this is greater than one, then", - "I have amplification.", - "OK, so what's that saying? What that's saying is that if I apply some voltage here, OK,", - "and I change that voltage by a small amount from, let's say, 2 V to 2.1. OK, I am going", - "to find the output voltage.", - "Let's say I go from 2 V to 2.1 here. OK, abstractly out there, I might have an output that goes", - "from three to, let's say, two V perhaps. OK, so for a 0.1 change here, I'm going to get", - "a bigger drop here, so from 3 V to 2 V, giving me an amplification in this little circuit.", - "OK, so we'll see this again and again, and you'll really understand it. So, I have a", - "small change in the input, and I have a corresponding larger change in the output. So, I've shown", - "you an amplifier.", - "I haven't shown you a linear amplifier. There's an extra charge for that. OK, that'll happen", - "later. OK, all I've shown you so far is an amplifier, and this happens to be a crummy", - "amplifier. It's a nonlinear amplifier because, notice, this is not linear.", - "It's a nice little curve, and so it's not linear. But, I promised you an amplifier,", - "and I'm cheap, and that's all you get for now. OK, we'll see linear stuff later, but", - "for now, I have a little amplifier.", - "So, let's do some real numbers, and plot some numbers down, and also look at a demo. So,", - "let's do an example. Let's say VS is 10 V, that the K is two milliamps per V squared,", - "and let's say RL is five kilo-ohms, OK? So, let me substitute these values into that equation,", - "and I get V nought is, VS is ten.", - "So, it's ten minus, KRL divided by two. So, K is two milliamps. Two milliamps times five", - "kilo-ohms is ten divided by two gives me five, and VI minus one squared. That's what I have.", - "I just plug in a bunch of numbers, and that's what I get.", - "So, what I'll do is let me just do a little table for you, and plot using real numbers,", - "simply plot those values for you.", - "So when VI is zero, my current is zero, and I get - oh, that equation doesn't apply, by", - "the way; that applies when VI is greater than one. Ok. So as long as VI is less than one,", - "my output is simply VS, the output is simply ten volts.", - "Ok, so all the way up to one, my output V is - all the units are all volts - that's", - "what I get.", - "I come down to 2, I plug in two for VI, 2 minus 1 is a 1. So it's 1 squared. 5 times", - "1 squared is five. And 10 minus 5 is 5. I get 5 out here.", - "Ok? And then, I can go and do the math. If it's 2.1, I get 4 volts here. And 2.2, I get", - "2.8. And so on. Ok, notice that the .1 volt change here resulted in a - go up a .1 change", - "here results in a minus 1 volt change there. So input went up by .1 volts, my output...", - "kerplunked down by one whole volt.", - "Ok, so a small change here resulted in a bigger change there. And that's the amplification", - "that I am claiming here.", - "Ok? So. Let me show you a small demo of a small device that I built involving such a", - "dependent source.", - "Let's do it here.", - "Ok. So on my s axis, here is VI. And VO is on my y axis. And focus on this little point", - "here.", - "Ok? Right now my VI is zero. And so therefore that's my output. I will gradually increase", - "VI, we're going to watch the output and see how it behaves. Pretty much like the little", - "graph I drew for you.", - "So I'm increasing VI. Ok, notice that invitially the current source is off, the dependent source", - "is off, so I move straight down. Ok, nothing happens. Until I hit a value at which the", - "the current source begins to come on. And then I begin to see a drop in the output as", - "the current source begins to conduct current.", - "So you see that as I increase the voltage VI, boom! You see the huge drop.", - "Ok, notice that for a small change, I'm now getting a big drop in the output. Ok?", - "So let's pause here for a second, and in the last couple of minutes, I want to cover one", - "last point.", - "Notice that the curve I've shown you up there looks like the curve up here: it goes kaboom!", - "and drops according to come kind of formulation that I've shown you here.", - "In the last couple of minutes, let me discuss a small point that's a practical issue.", - "In the curve that I showed you, in the mathematics that I gave you, if you just go by the math.", - "So what I'm about to show you will differentiate a mathematician from an electrical engineer.", - "Mathematicians would have taken the curve, and reported it like this. This is zero. Mathematically, that equation says that starting", - "here, this current simply goes down. But if I told you this device that I have here, this", - "dependent source is a practical dependent source, a device that I have physically built,", - "and I also say that it's a passive device. In other words, it cannot produce power. It's", - "like a little resistor. It doesn't produce power. It's a passive device.", - "So if it's a passive device, if I tell you that, then you'll say, Something doesn't make", - "sense here. Mathematically, it says it should look like this. But what's special about a", - "point down here? The point down here says the output has gone negative. This is zero", - "here. The output has gone negative. And my current source is still supplying a current.", - "Ok, so up here, the voltage across the device is positive, and it's supplying a current,", - "so it's consuming power like a resistor. Like all bad little resistors do, they burn power.", - "So here, on the other hand, my output is going to be negative, but it's still sitting there", - "sinking current. Ok, because VO is negative, but my current is still in the same direction,", - "what has now happened is the device has begun to supply power.", - "So mathematically, this curve says the device has begun to supply power.", - "It turns out it's not a practical device, it's a passive device. So it cannot go here.", - "So what happens is that somewhere along here, our model breaks down. The equation I've shown", - "you for the current source, where is it?", - "This model breaks down.", - "When V0 becomes very small, the model breaks down and it no longer behaves like a current", - "source.", - "It begins to behave more and more like a resistor. And what happens realistically, is that the", - "output goes down and then kind of becomes a zero-hugging line. I'll show you that in", - "a second.", - "And it doesn't - for this particular device it doesn't really go down here.", - "Let me just show you that part. So notice for that device, mathematically, just by that", - "model, it should have just gone through the floor and it points through to the corridor", - "below, but this is a prcatical device.", - "So notice that the model breaks down. And that's what begins to happen.", - "Ok, the device stops behaving like a dependent current source, rather it behaves like some", - "corny old resistor or something like that and saturates out. Ok." - ] -} \ No newline at end of file diff --git a/subs/bH1ytKNX_Fg.srt.sjson b/subs/bH1ytKNX_Fg.srt.sjson deleted file mode 100644 index bc505bb0d1..0000000000 --- a/subs/bH1ytKNX_Fg.srt.sjson +++ /dev/null @@ -1,5 +0,0 @@ -{ - "start": [], - "end": [], - "text": [] -} \ No newline at end of file diff --git a/subs/bX8i2yECWaU.srt.sjson b/subs/bX8i2yECWaU.srt.sjson deleted file mode 100644 index 5c71cd7308..0000000000 --- a/subs/bX8i2yECWaU.srt.sjson +++ /dev/null @@ -1,1469 +0,0 @@ -{ - "start": [ - 5000, - 11368, - 14894, - 20466, - 27403, - 34000, - 41431, - 47137, - 54170, - 62000, - 70235, - 76411, - 84509, - 90000, - 97721, - 104430, - 110759, - 116455, - 123828, - 130033, - 136897, - 143498, - 148382, - 154455, - 160000, - 165145, - 171025, - 177430, - 184417, - 191960, - 198207, - 202685, - 209167, - 217731, - 225323, - 232529, - 239477, - 246683, - 252214, - 259357, - 266500, - 270785, - 275785, - 284000, - 288117, - 292529, - 296573, - 304109, - 314668, - 319947, - 330506, - 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I am one of the recitation", - "instructors for those of you who have not seen me.", - "We will talk today about a neat application of RC networks and", - "expand those to application in MOS memory systems.", - "To connect with everything, we will get back to the basic", - "circuit that we have been discussing so far.", - "And you recall the circuit that we have been studying,", - "the canonical RC with an input voltage function of t.", - "And we had specified that we solved this problem for the case", - "of a step input or a condition in which a t=0.", - "At t greater or equal to zero vI is equal to some capital VI", - "value that for now on is constant.", - "And the other condition that we discussed was the value of the", - "voltage on the capacitor that would exist at time t=0.", - "Let's call that vc(0). And in general there is some", - "finite value here. It can be zero or it can be", - "different from zero. Given that, we learned how to", - "write down directly, without messing around with", - "differential equations, the answer for the voltage on", - "the capacitor vc(t), let me define also my vc right", - "here, is equal to VI, the final value,", - "plus vc(0), the initial value on the capacitor,", - "minus the final value, e^-t/RC.", - "This is our standard equation to which we plug in,", - "and it's either a rising exponential if VI is larger than", - "VC or a decaying exponential if VI is a smaller value than VC.", - "This should all be familiar. And, again, as pointed out in", - "the notes, the reading for today is 10.3 and for the new material", - "you should look at Chapter 11 where we discuss memory.", - "This is where we stood as of last time.", - "Now, I would like to discuss a little bit more about the", - "storage of charge in capacitors. And how we can take advantage", - "of that for storing logic state. One of the things that I am", - "sure you must be aware of is that one of the perhaps most", - "massively produced chips is actually the so-called DRAM", - "which you find in every PC and every computer that exists", - "anywhere. This DRAM is dynamic random", - "access memory in which we can store a state and come back and", - "look at it at any time later, provided we don't power off our", - "machine. The logic state in the basic", - "memory elements, of which instead there are", - "close to 1 giga elements per chip, are stored on capacitors.", - "And so we will play a little bit with that concept today.", - "And, although we're not going to discuss the specific example", - "of the DRAM, the basic elements of the DRAM you will see", - "actually in a demo shortly. So that's the general response", - "of this network that I have here to an input VI that happens at", - "t=0. Now, the one thing that you", - "recognize immediately is that it really doesn't matter what the", - "value of VI was for t less than zero.", - "What really counts is the value of VI at t=0.", - "And that's the value that we're interested in.", - "Now, there is an implicit statement in that.", - "And that statement is that somehow that network appears", - "like this at t=0. So, there has to be some switch", - "there, and you will see that, that basically starts my", - "condition to that at t=0. And so the history of VI really", - "doesn't matter. The response following that", - "equation that we have there will depend on the initial value", - "which is vc(0) here. Now that is the voltage on the", - "capacitor at that time. And then assuming that VI is a", - "value that is larger than vc(0) will have a rising exponential", - "that will come to this value. And this is the time constant", - "RC and this is time. So, the capacitor starts with", - "some voltage here and goes to a new voltage that is imposed by", - "the input for time greater than zero.", - "We can define at any one time, say this time,", - "this time, this time, this time the state of the", - "capacitor. The state.", - "What is the state of the capacitor?", - "The state is the summary of all inputs that are relevant to", - "predicting the future. If I know the state of the", - "capacitor this time, I can predict what it is going", - "to go given a response VI here in the future.", - "So, predicts the future. Now, what is the state variable", - "on the capacitor? What is actually stored on the", - "capacitor? You can say,", - "well, what is stored is voltage.", - "The real physical quantity that is stored is the charge q which", - "is for linear capacitors related to the voltage,", - "let me actually write it correctly, vc like this.", - "So, the real state variable is this.", - "But for a linear capacitor, since there is one-to-one", - "relationship between the two, v is also a state variable.", - "OK, so let's then go back to our original circuit.", - "What we have is --", - "-- vc(t), so that's the future value of the voltage on the", - "capacitor, is a function of vc(0), the initial value and the", - "variable input now in the future time.", - "And for the case of vI(t) being constant VI for t greater or", - "equal than zero we have the equation that we just described.", - "Nothing new.", - "All the past inputs to the capacitor for time t less or", - "equal to zero is summarized in this value.", - "And vi being constant the future is predicted from that.", - "So, that's the concept of the state.", - "There is an initial state on the capacitor.", - "And then there is a final state that will be reached when", - "equilibrium actually is achieved.", - "There is a fair amount of discussion in the text,", - "and we don't go in great detail here, but it is both convenient", - "for analysis and also it's interesting in many cases to", - "look at the response of a linear network for two different", - "conditions. So, we're interested in two", - "cases. One is the so-called zero state", - "response. Now, what is the zero state", - "response? It's the response to a", - "condition in which we impose an input and impose also the", - "condition that the initial value, initial state of the", - "capacitor is zero. So then we ask how does it", - "respond to vi(t)? So, starting with a capacitor", - "at zero state what is the response?", - "It allows us to decouple the initial conditions from the", - "response to the input. Now, you will see that this is", - "actually very useful. The second condition to which", - "we're also very interested is the so-called zero input", - "response. What is that?", - "That is vi(t)=0. Now, it's the condition under", - "which there is no input. vi(t)=0.", - "The question here is how does it relax?", - "We're starting with an initial state.", - "So, how this state relaxes out in the circuit.", - "Now, the zero state response, this one here is Z so called SR", - "for our case, which I will write like this,", - "vC, ZSR is simply a rising exponential.", - "We start from zero and we go to VI.", - "So, it's VI-VI e^-t/RC. So, that's the ZSR.", - "The ZIR, the zero input response is like this.", - "It's the decay of the initial voltage on the capacitor to zero", - "or to equilibrium. Starting from vC(0) we're", - "decaying like this. Now, do you see something", - "that's rather obvious from what's on the board in terms of", - "ZIR and ZSR and the final complete answer which is there?", - "They are specific cases, but how do they relate to the", - "full answer? It's the sum.", - "It's the superposition of the two.", - "What basically we see here -- And that's actually a general", - "statement, is that vC = vC,ZSR + vC,ZIR.", - "Now, you may say this is trivial because we started from", - "that, ended back in that from some very simple observations.", - "However, we are not always solving networks for responses", - "that are steps. The input voltage may be a", - "ramp. We did that in recitation.", - "Or, it could be an impulse. Or, it can be a more", - "complicated function. Having this observation in", - "place actually allows us to solve the problem rather neatly.", - "If I have time at the end, I might come back to this.", - "So, this is the same equation as I started with,", - "arrived at from a principle of superposition of two different", - "solutions. One application of state which", - "can be, since we have energy storage element here,", - "the capacitor, which can be stored on the", - "capacitor is in memory. And you may ask,", - "so why do we need a memory node to perform logic?", - "Well, there are cases in which a result depends on previous", - "results. So, a computation proceeds in", - "time. In order to do that,", - "we need to store intermediate results and proceed forward.", - "One good example is if you're doing a continuous summation,", - "say, on your calculator, you keep putting things in the", - "memory. The M+ button,", - "right? And you keep adding a series of", - "numbers. Every time we store the sum of", - "the previous operation we add another number and so on.", - "Clearly we need some way of storing state.", - "For a complete computing system, we need combinational", - "logic and we need memory. In fact, these are the two", - "basic elements that are essential for any kind of", - "computing system. We need to remember", - "intermediate results. We need to remember transient", - "inputs. And that's the role that all", - "these enormous amount of memory that comes to play in computers", - "is doing. The basic memory abstraction is", - "as follows.", - "Imagine a block which needs to be populated by transistor,", - "resistor, capacitor, whatever elements.", - "And it has a control input, which we will call the store.", - "It has a state input that we will call dIN and has an output", - "dOUT. When we're telling this", - "element, OK, now it's time to store, it looks at the input dIN", - "and stores it for, in principle,", - "an infinite amount of time. If we were to make a drawing of", - "this, of what this looks like, let's suppose,", - "let me do all this in one axis. So, time moves this way.", - "Let's suppose that we have an input dIN that looks like this,", - "and the store command comes in the form of a logic.", - "Let's actually suggest here this is logic one,", - "this is logic zero. And, although this is not", - "absolutely necessary, let's also define that the", - "store command comes in the form of a logic one at this store", - "input. Store, let's say,", - "looks like this.", - "What does the output look like then in this particular case?", - "Assuming that the output was dOUT, the stored element was", - "zero prior to the store, then the output would look like", - "this. This is dOUT.", - "As you can see, it would remember the one that", - "it saw at this point. In fact, it would do that", - "irrespective of what was stored in this memory cell.", - "For example, suppose it was storing one and", - "the output didn't change, it's still one.", - "If it was storing a zero, it would flip to a one.", - "If we had another store, let's say here,", - "then what happens? Then it would go back down to", - "zero because now we sampled an input that is zero and we", - "flipped the state. That's what a memory --", - "-- element or cell would do for us.", - "It would remember the output state.", - "And, not only that, but in principle it should be", - "undisturbable. In other words,", - "I may do something to this dOUT but it should not flip the", - "state. And that comes about quite a", - "bit. Because in actual integrated", - "circuit memory there is lots and lots and lots of nearest", - "neighbors to this cell which, when they're flipped,", - "have a cross-coupling to the cell.", - "The cell must be designed robust enough that it doesn't", - "flip, that no coupling actually occurs.", - "All right. Now we're going to try to apply", - "what we've learned so far to invent a basic memory element.", - "And, believe it or not, this is the key to the DRAM.", - "Let's implement this in a circuit.", - "Suppose I have a switch here like this.", - "And I will put a capacitor. I take my dOUT here.", - "This is dIN. And the switch is operated by a", - "command here that we will call store.", - "When store is one it goes up. When store is zero it is down", - "here. That's capacitor C.", - "This is the storage node.", - "What are we actually storing in this case?", - "Let's suppose that this voltage here is 5 volts.", - "I flip the switch up to one and I flip it back down to zero.", - "What's the voltage in this capacitor here?", - "5 volts. Now the capacitor is at 5", - "volts, I put dIN to ground, flip the switch back up and", - "then back down to its known storing condition.", - "What's the voltage in the capacitor?", - "It's zero, exactly. So, it does store the value of", - "the voltage that it saw, five or zero,", - "high and low. It stores it because it stores", - "charge. That's actually the physical", - "quantity that's stored. It's manifested as a voltage,", - "which we see. All right.", - "Now, is this, oh, before I move from here.", - "What is the basic cell in a DRAM, one that you go out and", - "buy by the billions of cells? It's actually this.", - "The only difference is that this switch here is replaced", - "with a MOSFET.", - "And that's all it is. So, a MOSFET plays the role of", - "the switch. When the gate is high this is a", - "resistor and connects the input to the capacitor.", - "And when the gate voltage is below the threshold voltage this", - "is an open, as we've seen, and it isolates the transistor", - "from the output. So, that's the basic memory", - "element.", - "And, as I said, it's the key to a DRAM.", - "OK. Now let's consider a little bit", - "the conditions of operation of this thing.", - "Let me draw the circuit in two conditions.", - "One in which it is storing, one in which it is sampling and", - "one in which it is storing. Not to redraw this thing.", - "Assuming that I have a MOSFET there, I would have the on", - "resistance in place here when store=1.", - "Now, in principle, the output is connected to --", - "-- some load resistance. We'll talk a little bit more", - "about this load resistance in a minute.", - "This is the situation when we are at store=1 situation.", - "For example, let's suppose that dIN is 5", - "volts. Now, what is the situation for", - "store=0? It's very simple.", - "We have the capacitor C and dOUT and here we have a", - "resistance. The switch is open.", - "This is store=0 condition. What we have in this case is we", - "have a problem similar to what I was discussing earlier.", - "It is a ZIR, if you like,", - "situation. And this you can think of as a", - "ZSR if we're starting with zero charge on the capacitor,", - "but I'm interested in this part.", - "In this case, I am starting with a vC(0)=5", - "volts. And I'm asking myself how long", - "will this cell hold the value? And, in fact,", - "that is actually what happens in a dynamic RAM.", - "The value on the capacitor is not stored forever.", - "In fact, that's why we call it dynamic because we have to come", - "back and restore it every once in a while.", - "For how long are we going to store the charge?", - "What's the response of vc for t greater than zero after the", - "switch flicked? It's very simple.", - "It's vc is equal to 5 volts e to the minus t over RC,", - "right? That's the response.", - "We have a decay. And applying to the things we", - "know. We start from 5 volts,", - "let's say here, I have a decay going down", - "towards zero, at some point we are going to", - "cross the threshold for high. The only period in which I have", - "a valid output, if the capacitor was storing a", - "one, is this period here. This is the only period in", - "which I have valid stored one because, once I go beyond", - "capital T here, I have crossed the legal limit,", - "threshold for discriminating a high output.", - "And from then on the output is no longer valid.", - "So, this memory is good provided time is less than", - "capital T. It's not a case in which the", - "capacitor can hold charge forever.", - "In fact, we can calculate, that is we can solve for T in", - "this particular case. It's in your notes.", - "Nothing really profound. T is equal to minus RC log VOH", - "over 5 volts. So, this is basically what the", - "response is going to be. Now, there is an implicit", - "assumption here, which is that the store pulse", - "width is much, much larger than RON C.", - "In other words, when we want to store a one", - "here starting from zero, we better charge it all the way", - "up to 5 volts in the time that our switch is connected here.", - "And what is the relevant time constant?", - "It's going to be the RON C. In fact, it's actually the RON", - "parallel RL with C. But typically RON is much,", - "much less than RL so we don't have to worry about that.", - "Dominant time constant is RON C.", - "So, provided these things are happening, we have a memory.", - "Now, we can try to improve things a little bit.", - "We see here that we will have a decay to an invalid state in", - "time T. How can we improve things?", - "One way to improve things are the buffer.", - "Here is our memory element again.", - "Here is the capacitor. This is the storing node.", - "Now I am going to put the buffering effect.", - "I am going to put two buffers here.", - "Two invertors, I should say,", - "because if I am storing a one here I want to be able to see a", - "one here as well. And, in this case,", - "what I am looking at is the RIN of the buffer.", - "And, in principle, I have out here the RL.", - "Now, this is better because if RIN is much larger than RL then", - "the time T, in this case, is much larger than the case", - "without buffer. So, we buffer the effect of VL.", - "This could be one of these neat circuits we saw in recitation", - "like a source faller, for example,", - "or it can be just an inverter in which case you just see the", - "input of a transistor. So, now this condition can be", - "satisfied. Let me give you some cases", - "which are some numbers that are typical for a dynamic RAM.", - "Typical times we're talking about is RIN on order of 1", - "gigaohm and storage node capacitor on order of 1", - "femtofarad to one picofarad. Now, if you can do the math in", - "your head, which is just multiplication,", - "you will see that the time constant, the RC is between 1", - "millisecond to 1 microsecond. And for DRAMs,", - "actually, we try to be in the order of milliseconds.", - "These are the times we're talking about.", - "If I have this kind of circuit, somehow there has got to be", - "additional circuitry that comes back, samples the voltage here", - "and restores it. And that is actually what is", - "happening in a DRAM. And my laptop is working there", - "and its DRAM keeps getting refreshed every,", - "say, millisecond or whatever the condition is.", - "But, in our case, we are going to do a slightly", - "different case in which we will create a static memory.", - "Let's actually look at, first of all,", - "the case of the discharge. Pay attention to,", - "let me actually break the loop here.", - "This is my capacitor. This is a resistor that is in", - "series with a capacitor like you see here.", - "Actually, I am going to keep that resistor in series with the", - "capacitor, even in this case, because I have it for my second", - "part of my example. I charge the capacitor to 5", - "volts. And you can see here this", - "lights up, I hope everybody can see it, proportional to the", - "voltage that I have here. From here on it's all logic", - "levels. So, the intensity of light here", - "will always be the same. It's either lit or it's not", - "lit. Right now I am charging the", - "capacitor. In fact, let's see.", - "Maybe I can discharge the capacitor first.", - "Here the capacitor is discharged.", - "As you can see, the input is zero,", - "the output is a one, and then the output of this", - "inverter here is a one. I have two inverters in series.", - "And I am going to charge the capacitor.", - "I charged it to 5 volts and this lit up, this is off of", - "course, that's an inverter, this is a valid zero,", - "produce a valid one. And now I am going to take the", - "input out. As you can see it's stored.", - "In fact, we have to wait for a very long time.", - "We don't have enough time to wait for this to discharge,", - "so instead what I am going to do now is I am going to add also", - "the resistor. Now I am going to flip the", - "resistor in parallel with the capacitor to imitate what", - "happens when we have an input resistance.", - "You saw that there was a discharge of the capacitor.", - "This input level went down. Voltage here flipped over to a", - "one. Let me do it again now with a", - "resistor in place. Storing charge on the", - "capacitor. That's the store command.", - "Now, don't store. I have less,", - "about a second. The element here is 20,000", - "microfarads and 100 ohms which gives me a time constant of two", - "seconds. Assuming a VOC of the order of,", - "let's say, I don't know what it is for this case,", - "2.5, the log would be about 0.5, so it cuts basically the", - "time to about one. So, it lasts about one second,", - "if my math is all correct. It's actually a little longer", - "than a second, excuse me, but the point is", - "that the charge is gone. Now, notice,", - "however, that there is something I can do here,", - "which is that suppose I take the switch or a switch and bring", - "it back and provide a path from the output to the input here.", - "And this switch is open when this is closed and closed when", - "this is open. So, this basically is the", - "compliment of store. What I am doing now is I put a", - "charge here, it produces a valid one at this point,", - "and then I am feeding this valid one back to the input.", - "As you can see, this will now allow me,", - "even though I have a high resistance, to store the value", - "for a long time. In this case,", - "what I am going to do is I am going to connect the output,", - "as you can see here. And I have my resistor in.", - "And I am storing zero here, storing 5 volts.", - "Now I am going to flip the switch.", - "Basically, I mean the don't store, don't look case.", - "You notice this dims a little bit.", - "Sorry. No, I want the resistor in.", - "There. Yes.", - "OK, so the output remain value. This dimmed a little bit but", - "the output has remained OK. All right.", - "So, we've provided a feedback. Now we've created a static", - "memory. This will hold charge for as", - "long as the circuit is powered up.", - "Now, there is still one little problem that I have with this", - "kind of configuration. And that is if I disturb this", - "output the charge may, the state may change.", - "So, for example, let's say that I have --", - "I disturbed it by coming close to it, so let's charge it again.", - "OK. I flipped the switch.", - "I flipped the state from the output.", - "That is an invalid condition. I shouldn't be able to do that.", - "How do I avoid that? How can I avoid this problem", - "that you just saw?", - "Well, I need yet another buffer.", - "The answer is in your notes. If I don't take the output here", - "but rather take the output here, or if I don't want an inverted", - "output, if I don't want an inverted output,", - "I could put yet another element there.", - "Then the situation would be fine.", - "In this case, let me do it again.", - "Charge.", - "Why isn't this lit?", - "A bad one?", - "Now, of course we disturbed the input.", - "Now, of course I can do anything I want here.", - "Nothing happens, but you may say this is a", - "trivial case because this is already zero.", - "So, I am going to change the state.", - "Here's is the changed state. See.", - "I can show this. Nothing happens up there.", - "So, this is an interesting situation in which I am", - "buffering the output so that the output does not feed back to the", - "input. And, by and large,", - "in designing circuits this is something that we do.", - "Now, in the remaining three minutes there is an example that", - "we have. Can we put the laptop here?", - "OK, so here is an example of how memory can be put together", - "now to create something a little bit more complicated.", - "And you can see the memory cells that we were discussing", - "here. There's four of them,", - "so this is a four bit memory. There is a decoder at the", - "beginning here which decodes the address of each cell,", - "so the input here will tell me which cell I need to address.", - "Let's look at the truth table. This is the truth table for the", - "decoder. As you can see,", - "depending on the address that I have here, this is zero,", - "one, two and three in a binary system, only A,", - "B, C or D is up, is high.", - "Which means that this end operation here only allows the", - "input that is presented to all of the cells,", - "what is going through the AND gate here to appear at the", - "output. If, for example,", - "we have a one, zero, the only end input that", - "is going to be high is going to be this one.", - "And that means the only cell that will look at the input when", - "the store comes up is going to be this one here.", - "At that point it will store whatever is on the input cell", - "because that's an AND operation. That is a simple example of a", - "memory. And following that simple", - "arrangement you can build incredibly large memory systems.", - "So, that's all I had for today. And I will see you on Tuesday." - ] -} \ No newline at end of file diff --git a/subs/bmys8aKCjCo.srt.sjson b/subs/bmys8aKCjCo.srt.sjson deleted file mode 100644 index af25915a53..0000000000 --- a/subs/bmys8aKCjCo.srt.sjson +++ /dev/null @@ -1,113 +0,0 @@ -{ - "start": [ - 530, - 1580, - 4780, - 6870, - 9220, - 12320, - 13820, - 19230, - 22940, - 26010, - 30210, - 32480, - 34580, - 36875, - 39590, - 41220, - 45150, - 46710, - 50570, - 53550, - 59710, - 64280, - 67170, - 69750, - 70590, - 73250, - 77710, - 81300, - 84390, - 92215, - 93420, - 100620, - 101650, - 104740, - 107970 - ], - "end": [ - 1580, - 4780, - 6870, - 9220, - 12320, - 13820, - 19230, - 22940, - 26010, - 30210, - 32480, - 34580, - 36875, - 39590, - 41220, - 45150, - 46710, - 50570, - 53550, - 59710, - 64280, - 67170, - 69750, - 70590, - 73250, - 77710, - 81300, - 84390, - 92215, - 93420, - 100620, - 101650, - 104740, - 107970, - 470140 - ], - "text": [ - "OK, let's go ahead.", - "So to turn off this voltage source, all I have to do is", - "replace it with a short circuit like so.", - "So notice that I have replaced the voltage source with a", - "short circuit, and I've left the current source in place.", - "I have my ground node here.", - "And notice that my goal is to find the partial voltage eI", - "that is a result of the current source acting alone.", - "So notice that I have a second pattern here.", - "And in this case, this is a current divider pattern.", - "Actually, this is a even simpler pattern.", - "I simply have a current that is flowing", - "into a pair of resistors.", - "OK, so I have a current, I, that is flowing into a pair of", - "resistors, R1 and R2.", - "And so I can compute the voltage across the pair of", - "resistors very straightforwardly.", - "So eI is simply the resistance times the current.", - "And the resistance of a paralel pair of resistors is", - "simply R1 R2 divide by R1 plus R2 times the current I.", - "OK, so now I have computed both ev and eI, the two", - "partial voltages with each of the voltages acting alone.", - "And now I am ready for step two of the", - "superposition method.", - "And the step two of the superposition method simply", - "says that you sum the two partial voltages, ev and eI.", - "So my resulting voltage e is simply the sum of the two", - "partial voltages ev and eI.", - "And I have those as R2 divide by R1 plus R2 times v. And I", - "sum that to eI.", - "And eI is R1 R2 divide by R1 plus R2 times I. And", - "there you have it.", - "Not surprisingly, this expression here is identical", - "to the expression that you obtained by using the node", - "method in the previous lecture." - ] -} \ No newline at end of file diff --git a/subs/dyxcCoUgETU.srt.sjson b/subs/dyxcCoUgETU.srt.sjson deleted file mode 100644 index bd71bbc994..0000000000 --- a/subs/dyxcCoUgETU.srt.sjson +++ /dev/null @@ -1,2054 +0,0 @@ -{ - "start": [ - 0, - 2925, - 8395, - 13738, - 19844, - 23915, - 31420, - 38435, - 42250, - 46228, - 49476, - 54022, - 58000, - 77000, - 79282, - 82602, - 86682, - 89933, - 93599, - 96919, - 101000, - 104492, - 107920, - 109634, - 113317, - 116174, - 119539, - 123021, - 126995, - 130229, - 133328, - 137101, - 140536, - 143433, - 147273, - 151450, - 156355, - 165165, - 170898, - 178728, - 186000, - 191400, - 197942, - 202823, - 208119, - 213000, - 219875, - 225125, - 229375, - 236500, - 242000, - 245788, - 251173, - 255560, - 260146, - 264035, - 269419, - 276000, - 284494, - 289500, - 297387, - 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Good morning.", - "Good morning. So, we have some fun stuff for", - "today's lecture, and as far as the final is", - "concerned and so on, I'd like you to forget about", - "anything we do today, absolutely.", - "So, get your mind to become a blank, and forget anything you", - "hear in today's lecture. So, what I'm going to show you", - "today will hopefully completely blow your minds.", - "And I'm not talking about controlled substances or", - "anything. So what I'm going to do is show", - "you a few things that behave completely and spectacularly", - "differently than how you expect them to.", - "And, today's lecture is appropriately called --", - "OK. So, we're going to violate the", - "abstraction barrier here, and do some fun things.", - "And, the important thing to realize is that in all of 6.002,", - "we have, after all, based on some assumptions we", - "made at the beginning of the course like lumped matter", - "discipline and so on, we have landed ourselves in", - "this playground called the playground of 6.002.", - "And, within that playground, certain ground rules apply.", - "OK, and our entire course depended on those assumptions", - "being true. So, for example,", - "the first assumption we made that brought us from Maxwell's", - "equations to the lumped matter discipline was,", - "or rather the circuit abstraction, was a lumped matter", - "discipline. And there were three tenets of", - "the lumped matter discipline. One is that the rate of change", - "of flux was going to be zero within our circuits,", - "not inside elements, but in the circuit itself,", - "and second, the dq by dt was going to be zero outside the", - "elements, and third, something we did not dwell upon", - "in the course, but it's certainly present in", - "the course notes is that the speeds of signals that we are", - "going to consider are going to be much slower than the speed of", - "light. OK, so we're going to be", - "working in a realm where we are going to be well slower than the", - "speed of light. OK, so starting with that,", - "let me walk you through some examples and some fun stuff.", - "So, the first case is called the Double Take.", - "So, let me sketch out a small little circuit for you,", - "and take a look at the expected behavior, and then show you what", - "really happens in real life. So, the first case,", - "I have a voltage source, and what I'm going to do is", - "make a transition from a zero to a one.", - "Think of it as a step input, and through a Thevenin like", - "resistance, I want to feed it to a circuit.", - "The circuit will go to an inverter.", - "This node goes to an inverter, and goes through some other", - "circuits within our own design here.", - "So, again, remember, a step input here,", - "and this input goes through a Thevenin like resistance,", - "or is applied to some other circuit elements.", - "So, if I apply a step here, what do you expect?", - "You expect that, so let me call that VI,", - "and let me call that Vo. So, if I plot VI as a function", - "of time, and let's say this step input happens at t=0.", - "So let's say this is t=0 here, and let's say this is a 5V", - "step. So, I expect that this input", - "here is going to go to, VI here, is going to go to 5V", - "at t=0. What do I expect at Vo?", - "At Vo, based on our circuit abstraction, I get a step input", - "here. I should get a step of some", - "magnitude here, depending on what's connected", - "in this direction. And let's simply say that", - "what's connected here is an inverter, and maybe other", - "inverters at the other side. So essentially,", - "as far as this node is concerned, it's got some wires", - "connected to it. And at the end of the wires,", - "it has an open circuit, an open circuit,", - "for example, like the gate input of this", - "inverter. So what do you expect at V", - "nought? A step input here,", - "and at V nought I see an open circuit.", - "OK, so I expect the same step at V nought: 5V.", - "So, that's what we've prepared you for, OK?", - "But, the fun thing that we're going to see,", - "so this is what you expect, and I'll show you a little demo", - "that is going to show you something very different.", - "What you're going to see is not this.", - "OK, you're not going to be seeing that.", - "Rather, I'm going to show you something that looks like this.", - "So, at t=0, I do see Vo looking like a step, and approximately", - "halfway through, decides, ah,", - "well never mind, and flattens out,", - "OK, then says, oh, OK, and zoom,", - "it goes back up to 5V. So, it sort of does a bit of a", - "double take up there saying, hey, what's going on here?", - "And zoom, jumps up to 5V, and then it's five as you", - "expect. OK, so this is some finite", - "amount of time that looks like that.", - "OK, so try to understand what's going on.", - "So let me show you a quick little demo.", - "So that's the input VI. OK, so that's the input VI that", - "you expect, and I won't do anything to my circuit at this", - "point. And, go ahead.", - "So, let's see what happens now. There you go.", - "So now, I'm showing you the output here at Vo.", - "So at VI, there's a nice little step, and at Vo,", - "notice that I get something that behaves like this.", - "OK, and I promise you, nothing we've taught you in", - "6.002 prepares you for this. OK, and as I mentioned at the", - "beginning of this lecture, it would behoove you to forget", - "about everything you learn in today's lecture for the next two", - "weeks at least. So what's going on here?", - "Any ideas? Anybody?", - "Any thoughts? So what's up with my circuit", - "here? It says, oh,", - "OK, a step. It starts off and says,", - "oh, never mind, and then meanders along at 2.5V", - "and then says oh, step, yes, I remember,", - "and then boom, it jumps up to 5V.", - "So, any theories? Any guesses?", - "Any wild guesses? OK, so let me draw you a little", - "bit more of a detailed circuit, and see if you can explain", - "what's going on here. So, the circuit that I've drawn", - "there is not quite the circuit I have at least in terms of my", - "wires. So, what I have is something", - "that looks like this, VI, and this is going to step", - "to 5V. I do have a resistance,", - "R. This is Vo, this does go to an", - "inverter. But what is also happening is", - "that I have a long wire. OK, you see this guy here?", - "We had one of our union folks stretch out along the floor", - "here. We have a really long wire that", - "connects to the Vo node, and there's also a long", - "corresponding ground. So, this wire is a coaxial", - "cable that is used for Ethernet and such like.", - "It's got a core that carries a signal, and around the core is", - "shielding that is the ground. OK, so that goes a long way,", - "and at the end, it is open.", - "OK, it's an open circuit at the end.", - "I haven't connected anything out there: open circuit.", - "So, you know, something's happening here", - "that's making the circuit behave like this.", - "So, this is VI. At Vo --", - "So at Vo I'm getting this funny behavior.", - "OK, so does anybody want to take the next piece of clues", - "here, does anybody want to take a stab at guessing what might be", - "going on here? Yes?", - "Ah, we have a shill in the audience here.", - "So, the theory is that the step here, think of it as an", - "electromagnetic pulse that goes from zero to five,", - "and things in real life don't travel instantaneously.", - "So, there's something with a wave that flies down,", - "and the wave goes to the end, flips, and then comes back,", - "and then establishes the full voltage here.", - "So that is indeed at the root of what's going on.", - "And let me put it in layman's terms and then describe the", - "details of what's going on here. OK, so the way to view what's", - "going on is that I have this long wire.", - "OK, in the very first lecture, I started off by saying wires", - "are ideal. OK, ideal wires are such that I", - "can transmit signals on them. Wires are small so that the", - "propagation time of signals is inconsequential compared to the", - "rise times and fall times of the signals of interest.", - "By having this really long cable here, I have clearly", - "violated that assumption, which is the wires are really,", - "really long here. OK, and so I somehow need to", - "model what the wire is doing to my circuit when I don't have a", - "small wire. So what actually happens,", - "the way to view it is the following.", - "So, although this is a wire, to understand the mechanics of", - "what's going on, I really have to model it much", - "more accurately, OK?", - "And, the way to model a wire like this is that notice that", - "every small element of a wire has associated with it some", - "inductance. OK, so let's take a small", - "segment of the coax cable here. The coax cable is a small core", - "surrounded by a metallic shield. OK, that's a ground.", - "And so, when I have a wire surrounded by a metallic shield,", - "that also has the capacitance, OK, inductance and capacitance.", - "So this small segment can be modeled as a really small", - "inductance, and a really tiny capacitance.", - "Similarly, the next segment can be modeled as a tiny inductance", - "and a capacitance. There is also a resistance", - "here, but let's assume that the resistance is zero for our", - "model, and also the parallel resistance is also infinity.", - "OK, so it's an inductor, capacitor, and really the", - "situation that I have is not a pair of ideal wires,", - "but really a really, really small inductance,", - "and a small capacitance in parallel.", - "So, it's more of a set of distributed elements that I have", - "here. Notice that in my lump circuit", - "abstraction, when we talked about the RLC model for the wire", - "between two inverters, we lumped it.", - "We lumped this thing into a model that looked like this.", - "OK, we lumped the resistance into a source resistance.", - "We lumped all the inductors into a lumped inductor.", - "We lumped all the capacitances into a lumped capacitance.", - "OK, but in this situation, I can do this when the signal", - "speeds of interest are much, much, much slower than the", - "speed of light than the propagation speeds of", - "electromagnetic signals. In this case,", - "that is not quite true. And so, therefore,", - "we have to model it much more exactly.", - "We need to see what's going on. So, what's happening here is", - "that at t=0, I get this step. So, think of that as a pulse of", - "energy, and the instant it comes here, and instantaneously this", - "guy looks like a voltage divider, OK?", - "I've chosen my resistance, R, here to match the", - "instantaneous impedance looking in, which is also R.", - "I've arranged it to be that way.", - "So, instantaneously, the point at which the pulse", - "appears at this point, looking down here looks like", - "another resistor to this pulse. OK, therefore,", - "when I start out, I start out going up and", - "pausing at 2.5 because instantaneously,", - "this looks like a resistance, R.", - "So instantaneously, it's a voltage divider,", - "R, and so it's 2.5 here, instantaneously.", - "OK, then what happens? Then those little pulse", - "propagates down. What does it mean for a pulse", - "of energy to propagate down? Well, it begins sending a", - "current through the inductor, begins charging up the", - "capacitor, current here, so that's what I mean by saying", - "that the pulse of energy goes down.", - "OK, it's a step that sends current to the inductor and", - "charges of the capacitors, and that wave front moves out", - "here and comes all the way here. What happens there?", - "Well, think about it. Supposing you stand here,", - "and you hold a long string in your hand somehow,", - "and just do this Gedanken experiment.", - "It's not easy to do. And so, let's say you somehow", - "have the long string that you're holding onto,", - "and the string on the other side is not connected to", - "anything. OK, just imagine this", - "experiment. OK, and what you do is you", - "suddenly raise the string up at your end by about a foot.", - "What are you going to see happen?", - "So instantaneously, the string is up here,", - "but the rest of the string is down a foot below.", - "And then you see this wave propagate down the string,", - "right? So here's a string.", - "I lift this thing, and you see this wave propagate", - "all the way down, the one foot wave propagate all", - "the way down until you come here.", - "What happens here? So, out here,", - "the string is down here, the wave propagates out here", - "and pulls it up to one. And then what?", - "There's nothing connected there, so the string is zipped", - "up, but it's got the energy. OK, where does energy go?", - "Well, it continues going up, and sends a wave back.", - "OK, so just think of a string that you pull up like this and", - "propagates down, boom, hits the other end,", - "reverses, and comes back at me. OK, you can look at a", - "complementary situation, not the same as this,", - "but complementary by taking a string, tying it to a door,", - "and lifting it up. It's not the same situation.", - "It's a complementary situation where it's tied down.", - "Tying down a string is tantamount to shorting the ends", - "here. OK, in that case what you'll", - "see happen: as the wave goes down, at the end the string", - "can't move, so the wave goes and flips around and comes back.", - "Try it out at home. Take a long piece of string,", - "tie it up there, do this, OK?", - "And you'll see the wave go out, flip, and then come back at", - "you. So, if your friends see you", - "tying a long piece of string doing this, hopefully they won't", - "think you're nuts or something. OK, so the same way here:", - "this thing flies down, OK, there's no way to dissipate", - "the energy here, so this thing continues up.", - "And then, what I'm going to see happen is the wave move back.", - "OK, the wave begins to move back, and that's another 2.5V,", - "resulting in a net 5V at this terminal.", - "That wave begins to blast back, OK, and then when it comes back", - "here, after some amount of time, it raises this to 5V,", - "and that's what you see happen here.", - "So, this is a wave going down, and then after a time,", - "2t, it goes back up to 5V. That's a return wave.", - "It's 2t because to get down here is t seconds,", - "and then t seconds to come back, which is why we have 2t.", - "OK, that is why you see that pulse at 2.5.", - "OK, so I'd like to show you a few more things here.", - "Clearly we don't want that in our circuits.", - "Could someone tell me what problem would happen if my", - "signals looked like this in my digital circuits?", - "Instead of being nice little steps, if there was a little", - "thing in the middle and then a step, what's the problem with", - "signals like this? In digital circuits,", - "what did it violate? Yeah?", - "Exactly. This little sucker here is", - "meandering out in the forbidden region for all of 2T.", - "Can't do that. OK, can't have that.", - "Well, so we need to fix the problem because this is real", - "life. OK, but what if you and your", - "buddy were signaling each other but using digital signals from", - "one dorm room to another maybe a few hundred feet down?", - "Your circuit isn't going to work because the signal's going", - "to meander around in the forbidden region for some time.", - "So, any ideas what might you do?", - "Yeah? Put a resistor on the end.", - "OK, trick the circuit. So, what you can do,", - "and I'm going to show you a little demo here,", - "what you can do is the reason I got this wave propagating back,", - "was that there was nothing to absorb the energy.", - "So instead, what if I put another resistor here,", - "R? So, as far as a burst of energy", - "is concerned, it says, oh,", - "yeah, it just looks the same. It's R, and goes and dissipates", - "in this resistor, R, and guess what?", - "I don't have any wave going back, and I'm done.", - "So, what I'm going to find, then, is that out here,", - "this goes up to 5V, but out here,", - "I will have a signal that starts out and goes up to 2.5,", - "and that's it. OK, I lift it up,", - "it goes down, it goes to 2.5 because in the", - "lumped model that you've been dealing with,", - "it's a resistor R, a resistor R to ground,", - "and you're taking the connection here or here.", - "So, it's your standard lumped model, your voltage resistive", - "divider, and it just simply works.", - "Yeah, that's it. So, this is the end of the", - "cable. OK, if somehow you could watch", - "this and that at the same time, so what I'm going to do,", - "and this is a resistor, R, I'm just going to plug it", - "in. OK, if the fates are smiling at", - "me, what should you see there? What should happen is that the", - "second jump from 2.5 to 5 should simply go away.", - "It should just go to 2.5. Let's try that.", - "There you go. I take it out,", - "it jumps back up. OK, so all I've done here is", - "put in a resistor at the end, and I'm still measuring the", - "voltage here. So, that's one solution.", - "One solution is to put a resistor here.", - "So, I absorb the energy, and the resistance has to be", - "equal to the instantaneous impedance looking in.", - "And the instantaneous impedance, for many of these", - "cables is 50 ohms. It's called a characteristic", - "impedance. OK, you'll learn a lot more", - "about it if you take 6.014. That course starts out with", - "assuming that things are distributed in that matter.", - "OK, so if you want to design multi-gigahertz chips,", - "it turns out that if you have signals that are traveling", - "around at edge speeds in the 0.1-1 nanosecond range,", - "remember, light travels roughly one nanosecond a foot.", - "And if the signals are roughly of interest are 0.1 nanoseconds,", - "then if the chips are one inch in size, right there,", - "the propagation speed of a signal across a chip is 0.1", - "nanoseconds. OK, so today,", - "we have to deal with these issues and try to figure out", - "what to do about them. OK, so that's one solution that", - "somebody pointed out. There is a second solution.", - "Anybody else have a second solution for me?", - "And then there's a third solution, too.", - "So it's OK. You can give me either the", - "second or the third solution. It doesn't matter.", - "Anybody? You have two to choose from,", - "come on. Yeah?", - "You can do that, yeah.", - "So we could define the problem away by saying this transition", - "is such that my high is below 2.5.", - "So, once it goes above 2.5, who cares what it does?", - "That's a good point. That's solution number four,", - "and that works. OK, so I still need two and", - "three. Put a diode in there?", - "Yeah, I guess you could. If the diode had the same kind", - "of impedance looking in, it kind of may work.", - "That's solution 4.2. I'm still waiting for solution", - "two and three. Pardon?", - "Cut off the cable? Exactly.", - "So, the solution says, work on a different problem.", - "And that is solution number two.", - "OK, so the idea is, the root of all evil,", - "this long wire, which is why I had this thing", - "here. So instead, if I had short", - "wires, then what will happen is if it's a very small wire,", - "it'll look like this. And the wire's small enough.", - "I will see an itty-bitty thingamajig out there,", - "but not a whole lot. By the way, the fun thing is", - "that you can actually calculate the speed of light,", - "the experiment I just showed you.", - "Can we put that up again? No, the big one.", - "So, in the experiment that I showed you, this distance was", - "about 500 nanoseconds, OK?", - "This distance was 500 nanoseconds this time interval.", - "The length of this cable is about 500 feet,", - "somewhere around 500 feet. So you can figure out the speed", - "of light. What's the speed of light?", - "So, this is about 500 nanoseconds, and this cable is", - "roughly 500 feet. What's the speed of light?", - "Roughly a foot per nanosecond. So, would you believe that in", - "6.002 we've figured out the speed of light from a simple", - "experiment? All right, so let's do the next", - "experiment now. Let's take out the long cable,", - "and connect a short cable instead.", - "So, what I'm going to do is disconnect the long cable,", - "and instead, connect a small cable.", - "It's still relatively long, but much shorter than the 500", - "foot cable. So what you should see happen", - "now is that the little step should not be this big,", - "but much, much smaller. So, take a look up there.", - "There you go. OK, so with this thingamajig,", - "the little blip there is very small.", - "And of course, if I make it even smaller,", - "then that can virtually vanish. OK, so that is solution number", - "two. So, we've done one,", - "two, four, 4.2. So, what's solution number", - "three? One more solution.", - "Pardon? So, another solution we", - "mentioned is we change this resistance.", - "and that will work, if I make this very,", - "very low, then I'll get much closer to 5V here.", - "Yeah, that's a possibility. That's solution six I guess.", - "So what was solution number three?", - "And you all should be able to solve this.", - "You guys know the answer. OK, you folks should be able to", - "solve this. Yes?", - "Ah, clock. So, what I can do is just as", - "was pointed out, that I leveraged my abstraction", - "by changing my VOH and VIH thresholds.", - "So that'll work. The alternative thing is to use", - "a clock. A clock is a distinguished", - "signal that I send around in my digital circuit,", - "OK? So all I do is if I arrange it", - "such that my clock doesn't happen in this vicinity,", - "but rather, my clock happens late enough, then I'm going to", - "sample and look at my signals only on the rising and falling", - "edges of the clock, in which case I won't be", - "looking at the signal, but the signal is doing weird", - "things. OK, so a decent clock would", - "also solve the problem. OK, any last minute questions", - "before we go onto the next one? OK, the next problem that we're", - "going to look at is titled the Double Dip.", - "OK, so what I'm going to do here is our Vs power supply,", - "and what I'm going to do is feed the power supply to an", - "inverter. OK, so we've been doing this", - "all along; Vs, I feed the supply to an", - "inverter. And what I'm also going to do", - "is, so this is ground, and I'm going to feed it to,", - "so feed the power supply connection to a couple of", - "inverters. OK, and what I'm going to do is", - "apply some sort of a signal to this inverter,", - "and I'm going to observe, and I'm going to look at this", - "signal here. So, the abstraction should tell", - "you that here's a power supply. This is 5V, or whatever the", - "supply voltage is to these two inverters.", - "That should be fine, and feed some sort of input to", - "this inverter, OK, and the output here should", - "be simply determined by this input.", - "This signal can have absolutely no bearing on this output.", - "OK, and let's look at that and actually confirm it.", - "So, I build a circuit like this, and we look at this", - "output, and initially there should not be any,", - "it should simply work fine. OK, so it should work now,", - "right? OK.", - "So what you have here, this input here is the input", - "that I'm feeding to this inverter.", - "That is a straight line. Is that the power supply?", - "It doesn't matter? OK, so I believe this is the,", - "we'll check in a few minutes, but I suspect this is the power", - "supply, and this guy here is the output looking here.", - "So, the green one is the look here part.", - "So, there must have been a one-to-zero transition here,", - "and that's all fine. So, so far, so good.", - "OK, no problem so far. Now what I'm going to do is I'm", - "going to do something to the circuit that as far as", - "abstraction is concerned, it doesn't show up on the", - "circuit. OK, it's below the abstraction", - "layer. OK, I'm going to do something,", - "and suddenly, some things are going to", - "happen. Look up there.", - "The circuit hasn't changed. It's the same circuit.", - "I've done nothing to the circuit.", - "OK, look at the green output. I've done nothing to the", - "circuit that is visible here. OK, it's below the radar screen", - "here. It's below the abstraction", - "barrier. But, look at the disaster here.", - "OK, in particular, the spikes going up are not so", - "much of a problem. Because of the static", - "discipline, if I am at five or six or seven,", - "it doesn't matter as long as I am higher than VOH.", - "So as long as I'm higher than VOH I don't have a problem.", - "But the problems are these repeated dips.", - "OK, the dips are a problem here, which is why I labeled", - "this experiment the Double Dip. OK, the dips are bad because if", - "they are large enough, they can then group the output", - "down into the forbidden region, or worse yet,", - "make it look like a zero. OK, so you're not prepared for", - "this. So what I'm going to do is tell", - "you what I did to the circuit, and then ask you to help me", - "figure it out. So all I did was applied a load", - "resistance to this, I think of 50 ohms or some RL.", - "I just applied a load resistor. And this inverter here,", - "I believe, is a CMOS inverter that looks, OK?", - "So I have this input applied to this inverter,", - "and all I did is I applied an RL load here.", - "And notice that the load here should not really change what's", - "happening if this is an ideal inverter, OK,", - "the load here should simply draw some current but really", - "should not change any other property.", - "OK, so just remember, what's the signal doing?", - "The signal is high. This guy turns on,", - "and current flows like this. So, let's say I had some sort", - "of a capacitor here. This charges like this,", - "and when it's slow, the PFET is on,", - "and current flows through here down here.", - "And then when this goes high, this guy goes off,", - "and this guy turns on. OK, so the current flows out", - "this way and this charges through this guy.", - "When I turn it off, the P fret turns on and draws", - "current from the top. OK, so do we have any theories", - "as to why I'm getting that messy stuff, the dips and the spikes,", - "on the output of this inverter? So why does this inverter care", - "what the load of this inverter is?", - "I mean, who cares? So, put your thinking caps on.", - "Any theories? You guys did pretty well with", - "the previous one. And this is much easier,", - "actually. Need a better power supply;", - "OK, so what I'm going to do is I'm going to replace the power", - "supply, and instead, use a much bigger power supply", - "at 5V. A big, mongo power supply that", - "can supply 100 amps, and guess what,", - "I've made the changes, but guess what,", - "I still see the spikes. Good try, but it didn't work", - "out. Good try, good try.", - "What next? Any other solutions?", - "Yes? So dips are because of the", - "resistance, and the spikes are because of the inductance?", - "You're half correct. So, which one is it?", - "So, dips are because of resistances, and spikes are", - "because of inductances. You're half correct.", - "It turns out that both the dips and the spikes are because of", - "inductances. OK, but be that as it may,", - "let me give you the next clue here, and then see if you can", - "come closer to the answer. So, what I've done here is I've", - "made this wire really, really long.", - "OK, it's a really long wire, OK, but it's a thick wire,", - "so it's a long, long, thick wire.", - "So it's not the resistance. It's really,", - "really thick and mongo, and it's a long wire,", - "so a signal wire above a ground plane behaves like an inductor.", - "And so here, it has the capacitance to,", - "but in this case it's inductance.", - "It's inductance here. So, I'll give you another ten", - "seconds to think about it and then tell you the answer.", - "But despite the inductance here, it turns out if I take out", - "this resistor, the problem goes away.", - "Look, I take out the resistor, the problem goes away.", - "Yes, there is an inductor here. OK, I take out this resistor,", - "problem goes away. I put the resistor back in,", - "boom. Yes?", - "OK, pretty good. That's 86 points.", - "So here's what's going on. There's an inductor here,", - "and when I put a 50 ohm resistor here,", - "I put this resistor. When the PFET turns on,", - "it draws a current. OK, it's going to draw a", - "current. It draws a current;", - "remember that across an inductor, I have a drop.", - "And the drop relates to the di/dt.", - "Remember, for a capacitor, the current is Cdv/dt.", - "For the inductor, the voltage across the inductor", - "is Ldi/dt. So, if di/dt,", - "from switching a large current through the inductor every", - "cycle, OK, big di/dt, di/dt is large.", - "I've made it large by having a very small RL,", - "so, you know, pulling a big current through", - "every few, whatever, every cycle,", - "and then stopping it. And so therefore,", - "I'm getting these big drops across this inductor that relate", - "to Ldi/dt. In other words,", - "the power supply here is fine. While you guys were watching,", - "I switched to the huge, mongo power supply,", - "and so this voltage is fine. But then this voltage after the", - "wire is the problem. So, this voltage here doesn't", - "look like this anymore. Rather, it has spikes that go", - "down, for example, and when I switch the other", - "way, they go up. OK, so therefore,", - "what I end up having here is big spikes on this power supply.", - "And when this guy's power supply goes wacko,", - "then I see the spikes on its output as well.", - "OK, so what are the solutions for that?", - "Any solutions here? What can I do to fix the", - "problem? Pardon?", - "Stop using the, exactly.", - "When in doubt, do something else.", - "Build a different design. So what I could do is this is", - "pretty dumb, using a long wire. And so, no, but trust me,", - "oftentimes you go to the store room and they give you a big", - "roll of wire, and you're too lazy to cut a", - "piece out. Use the whole roll,", - "and use the two ends, and connect it in,", - "OK? So, if I had a much shorter", - "piece of wire, then that can solve my problem.", - "But again, remember, what's small to you may not be", - "small to the circuit. OK, so let's say,", - "for example, I'm Intel, and I'm building a", - "10 GHz Pentium 6 processor. OK, it's 0.1 nanosecond is my", - "cycle time. There, even a small,", - "itty bitty wire can be a real problem.", - "OK, and so therefore, distributing power throughout a", - "one inch chip that's clocking at 10 GHz is a really,", - "really hard problem. And our own David Perreault,", - "who is doing one of our sections, is one of the world's", - "experts in this field. Distributing power,", - "something as simple as, how do I get 1V in a stable", - "manner to every single device on my chip?", - "It's a hard problem. OK, so now, you have to begin", - "feeding your power supply connections much like RC", - "circuits, OK, and you have to solve some hard", - "problems to be able to simply distribute power decently", - "throughout your circuit. So, what else can I do?", - "Yeah? Say it again?", - "Ah, I can do that. I could use different wires to", - "connect each of the inverters. That's a good point.", - "So here, the coupling happens because I connect the two", - "inverters way out here. So instead, I use a different", - "cable. I hadn't thought of that.", - "That's a creative solution. OK, so in fact,", - "if you build a chip, so we built this chip called", - "RAW in our group, and it has on the order of 10", - "million gates. And this chip we built with", - "IBM's technology, and it turns out that you don't", - "send power supply in through a pin and then connect that 1.5V", - "supply to all your gates. What you do is from that pin,", - "you then build special power supply buffering trees.", - "And each tree, each leaf of the tree drives a", - "subcircuit. In other words,", - "if this is a chip, you have lots and lots of gates", - "throughout your chip. What you do not do is bring in", - "a power supply like this, and then connect.", - "You don't do that. That's the worst possible thing", - "you can do. It's an absolute disaster for", - "the reason just brought up. OK, so instead what you do is", - "divide up the chip into, say, four quadrants.", - "OK, in our case, we have 16 quadrants.", - "And then what you do is from this point, you take one wire", - "that goes to this quadrant, one wire that comes here,", - "one here, and one here, so that you're getting the", - "power supply very close to the source, and you have different", - "connections going to each quadrant so that switching in", - "this quadrant will not affect this guy because of the", - "inductance of this lead here. OK, and if you hadn't taken", - "6.002, you'd have been arguing with IBM, I don't want 16 wires.", - "I want just one wire. OK, so there are other", - "solutions, of course. There's a couple more solution.", - "One is that what you can do is part of the problem here is that", - "all my transitions are really, really sharp.", - "OK, so di/dt is very, very large.", - "So, there's a whole new technique in design of digital", - "and analog circuits, which talks about,", - "maybe I should call it waveform engineering, OK,", - "or edge engineering. OK, it's also called edge", - "smoothing. The idea is that rather than", - "have very sharp edges in your circuit, you try to have", - "smoother edges. And when you have smoother", - "edges, OK, then your di/dt is now going to be less.", - "It's not going to be very, very high.", - "Rather, your delta I is spread out over a longer period of", - "time. Of course, that means the", - "circuits may have to run a little slower,", - "but that can also solve the problem.", - "And in fact, that same smoothing of the", - "waveforms was also the solution you saw in the capacitive", - "coupling we saw a month and a half ago.", - "And let me show you the demo, and then close up.", - "Not working? OK, that's OK.", - "It doesn't matter. So if you remember the demo", - "from the lecture about a month and a half ago in capacitors,", - "I talked about a chip with two pins, and there was this", - "capacitive coupling between the pins.", - "And because of this, if this waveform is switching,", - "then because of this coupling, you will end up getting,", - "if this is the signal here, you will end up getting spikes", - "on this pin because of the signaling of the other pin.", - "And that's good old capacitive coupling.", - "OK, and to eliminate this, what you can do is much like", - "with the inductance system, if you, rather than having", - "sharp transitions on this pin, if you have smooth transitions", - "that look like this, then what you can do is you'll", - "now spread delta V from here to here over a longer delta T.", - "OK, delta T has become longer, and because of that,", - "you end up getting much better behavior, and you don't end up", - "getting these spikes. So therefore,", - "if you want to build really, really fast circuits,", - "you have to be really careful. You can build fast circuits,", - "but watch out for them fast edges.", - "OK, fast edges are nasty. They kill you.", - "That's something to remember as you build the next generation of", - "circuits. Well, thank you all.", - "I had a blast, and I hope you guys had fun", - "too. Thank you." - ] -} \ No newline at end of file diff --git a/subs/eLAyO33baQ8.srt.sjson b/subs/eLAyO33baQ8.srt.sjson deleted file mode 100644 index 4d2f5069ab..0000000000 --- a/subs/eLAyO33baQ8.srt.sjson +++ /dev/null @@ -1,326 +0,0 @@ -{ - "start": [ - 430, - 3070, - 5680, - 9120, - 12590, - 13280, - 17280, - 20200, - 23630, - 26720, - 29450, - 32700, - 35920, - 39280, - 43310, - 44850, - 46400, - 48270, - 52110, - 54140, - 57570, - 61600, - 63040, - 64410, - 66980, - 69920, - 72490, - 75110, - 77540, - 80680, - 84430, - 87190, - 91790, - 94420, - 97830, - 101030, - 104180, - 106960, - 108320, - 110885, - 113180, - 115630, - 119930, - 122740, - 129590, - 131000, - 134200, - 138470, - 142200, - 145410, - 150500, - 153590, - 158000, - 160290, - 164600, - 167370, - 169272, - 173420, - 176650, - 180460, - 183390, - 185200, - 188940, - 190750, - 194040, - 196510, - 198060, - 202670, - 206860, - 209980, - 213620, - 219130, - 221760, - 222700, - 227050, - 230340, - 234810, - 236930, - 239030, - 241390, - 246630, - 248200, - 252220, - 255370, - 257160, - 258709, - 263370, - 264280, - 266840, - 270190, - 275640, - 277790, - 280880, - 282680, - 285990, - 287870, - 290740, - 294140, - 299760, - 305270, - 308230, - 310160, - 311540, - 314150, - 316160, - 316440 - ], - "end": [ - 3070, - 5680, - 9120, - 12590, - 13280, - 17280, - 20200, - 23630, - 26720, - 29450, - 32700, - 35920, - 39280, - 43310, - 44850, - 46400, - 48270, - 52110, - 54140, - 57570, - 61600, - 63040, - 64410, - 66980, - 69920, - 72490, - 75110, - 77540, - 80680, - 84430, - 87190, - 91790, - 94420, - 97830, - 101030, - 104180, - 106960, - 108320, - 110885, - 113180, - 115630, - 119930, - 122740, - 129590, - 131000, - 134200, - 138470, - 142200, - 145410, - 150500, - 153590, - 158000, - 160290, - 164600, - 167370, - 169272, - 173420, - 176650, - 180460, - 183390, - 185200, - 188940, - 190750, - 194040, - 196510, - 198060, - 202670, - 206860, - 209980, - 213620, - 219130, - 221760, - 222700, - 227050, - 230340, - 234810, - 236930, - 239030, - 241390, - 246630, - 248200, - 252220, - 255370, - 257160, - 258709, - 263370, - 264280, - 266840, - 270190, - 275640, - 277790, - 280880, - 282680, - 283930, - 287870, - 290740, - 294140, - 299760, - 305270, - 308230, - 310160, - 311540, - 314150, - 316160, - 316440, - 318500 - ], - "text": [ - "SPEAKER 1: In this sequence, are going to look at a whole", - "bunch of techniques for analyzing circuits.", - "Think of these as your tool chest. So you are embarking on", - "6.002 and going on to build lots of useful electronic", - "systems.", - "But before we go and build these systems, much like a", - "carpenter who needs to go build a house, much like a", - "carpenter has to go and buy a set of tools from the local", - "store, we need to go and make sure that you have the tools", - "in your tool chest to analyze these circuits.", - "This tool chest will include things like the KVL KCL", - "method, the Node method and so on.", - "But before I begin talking about these techniques for", - "your tool chest, I'd like to do a extremely quick review--", - "as is my usual practice--", - "of what you've covered so far.", - "So remember our EECS playground.", - "We've gotten into this place by promising that we are going", - "to observe the lumped matter discipline.", - "By observing the discipline recall that the complexities", - "of Maxwell's equations and the differential equations that", - "you have to solve-- the partial differential", - "equations-- goes away.", - "And you're left with very simple linear equations.", - "And you will see a lot of that today.", - "As you make the lumped matter discipline, you end up with", - "these lumped elements, like resistors and voltage", - "sources and so on.", - "And what you do with these lumped elements is we can", - "label what are called the branch variables or the", - "terminal variables for these lumped elements, OK?", - "So for example, v is the voltage across the element.", - "And i is the current through the element.", - "The power consumed by the element is given by vi.", - "Continuing with our review, the lumped matter discipline", - "enables us to create the lumped circuit abstraction.", - "So you take these lumped elements and you connect them", - "with ideal wires.", - "So in this case, I have a resistor which is a lumped", - "element, a voltage source.", - "And I connect them with these ideal wires.", - "And what you end up with is called a lumped circuit.", - "But this is your lumped circuit abstraction.", - "Well as we made the transition from physics to EECS by", - "adhering to the lumped matter discipline.", - "I had discussed in the last sequence that Maxwell's", - "equations turn into very simple algebraic equations.", - "And these are captured by Kirchoff's voltage and current", - "laws, called KVL and KCL.", - "So KVL says that for all loops in your circuit, the sum of", - "the voltages around the loops add up to zero.", - "Similarly for all the nodes in the circuit, the currents that", - "enter into a node add up to zero.", - "And in the same matter, if I just summed the currents", - "leaving a node, they also add up to zero.", - "So whether you sum the currents entering the node or", - "currents leaving a node, they would add up to zero by KCL.", - "And the beauty of this was by adhering to lump matter", - "discipline, recall the complexities Maxwell's", - "equations whether an integral form or", - "differential form went away.", - "And we were now left with extremely simple algebraic", - "expressions of the sort.", - "And you will see shortly that you will end up solving", - "extremely simple linear equations", - "as we analyze circuits.", - "So as one example here is a linear circuit.", - "It has one, two, three, four, five, six elements.", - "It's got a voltage source of a voltage v zero.", - "It's got a resistor, r one and so on and so forth.", - "So for this circuit according to our abstraction and the", - "laws of KVL and KCL, the following", - "are going to be true.", - "So for instance if I look at node a, then according to KCL,", - "the currents entering the node must be zero.", - "So in other words, the current here is ica.", - "And I can sum to that the current", - "entering from the d direction.", - "So that would be plus ida.", - "And then there is a current from the ba direction and iba.", - "Those are going to sum to zero.", - "Now I can multiply the whole thing by minus 1.", - "And that would give me the sum of the currents leaving the", - "node are also going to be zero.", - "So that is KCL.", - "Now I can also write KVL in this case for this loop, for", - "instance, here.", - "For this loop I can add up the voltages around the loop.", - "And by KVL they must add up to zero.", - "So for example if I look at the voltage vca, I can add", - "that to the next voltage here.", - "That is to vab and then add that to the", - "final voltage, vbc.", - "And by KCL--", - "so all of those must add up to be zero.", - "Now if you go back to our circuit here that you see on", - "the left hand side, I am going to show you a little demo that", - "will look at these currents, ica, ida, and iba, and also", - "look at the voltages, vcabab and bbc and actually go and", - "look at the circuit, make the measurements, and show that", - "they indeed sum up to zero.", - "Not surprising.", - "KVL and KCL really work.", - "And so the demo should also work.", - "OK.", - "So let's go and do our demo." - ] -} \ No newline at end of file diff --git a/subs/fDtrSZ69xII.srt.sjson b/subs/fDtrSZ69xII.srt.sjson deleted file mode 100644 index c5eb8f6458..0000000000 --- a/subs/fDtrSZ69xII.srt.sjson +++ /dev/null @@ -1,455 +0,0 @@ -{ - "start": [ - 760, - 5550, - 7730, - 15040, - 22780, - 26410, - 31490, - 35630, - 39890, - 47340, - 49390, - 53330, - 59924, - 65640, - 72340, - 75120, - 80660, - 83550, - 88110, - 92500, - 99170, - 103910, - 113990, - 118090, - 121540, - 125630, - 131510, - 135680, - 139700, - 145380, - 149430, - 154330, - 159440, - 164260, - 166990, - 170886, - 174520, - 179664, - 190760, - 196600, - 201060, - 207444, - 211940, - 217210, - 220450, - 223430, - 224640, - 226290, - 228162, - 233830, - 238620, - 239640, - 242880, - 249490, - 257300, - 260600, - 262290, - 265810, - 269740, - 275500, - 278270, - 281910, - 284090, - 286260, - 289730, - 293659, - 298570, - 309794, - 315430, - 318030, - 322270, - 326892, - 331472, - 340490, - 347140, - 349891, - 355780, - 363420, - 366200, - 370890, - 375180, - 378400, - 379900, - 383420, - 384510, - 390320, - 393190, - 397940, - 401926, - 407770, - 414400, - 422680, - 427140, - 429670, - 432810, - 436560, - 442370, - 445760, - 449640, - 453620, - 458010, - 464530, - 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260600, - 262290, - 265810, - 269740, - 275500, - 278270, - 281910, - 284090, - 286260, - 289730, - 293659, - 296010, - 309794, - 315430, - 318030, - 322270, - 324090, - 331472, - 340490, - 347140, - 349891, - 355780, - 363420, - 366200, - 367450, - 372140, - 378400, - 379900, - 383420, - 384510, - 390320, - 393190, - 397940, - 401926, - 407770, - 411120, - 417430, - 427140, - 429670, - 430920, - 436560, - 442370, - 445760, - 447010, - 453620, - 454870, - 464530, - 465986, - 470180, - 472500, - 476240, - 478710, - 480150, - 482916, - 489880, - 491110, - 493680, - 495670, - 500440, - 501690, - 513270, - 516730, - 522400, - 523650, - 536980, - 540980, - 544230, - 555060, - 557980, - 562700, - 571034, - 576200, - 584250, - 588640, - 596830, - 601340, - 609590, - 614220, - 617850, - 623470, - 628620, - 633760, - 638190, - 642230, - 646780, - 652090, - 653476, - 663470, - 667910, - 675020, - 676490, - 681835, - 687310, - 692610, - 695330 - ], - "text": [ - "SPEAKER 1: OK, in the previous segment, we", - "looked at a linear circuit.", - "And you saw that the equations that governed the behavior of", - "such a circuit were linear in the inputs, because the", - "components of the circuit were linear.", - "Next, let's take a look at some of the", - "properties of linearity.", - "What does linearity bias?", - "In particular, linearity will bias homogeneity and", - "superposition.", - "Let's take a look at each of these in turn, and see what", - "homogeneity and superposition really means.", - "So let's start with homogeneity.", - "So suppose I have a system in a little box, and let's assume", - "it's a linear system.", - "I apply a set of inputs, x1, x2, and so on, to", - "produce an output y.", - "So in my facetious example here, think of", - "the inputs as apples.", - "And the processing produces a ripe apple.", - "Now, what homogeneity says is this.", - "In the same system, if I feed it with fraction of apples,", - "then I will get fraction of ripe apples at the output.", - "In other words, if each of my inputs is multiplied by some", - "constant, alpha, then my outputs will also be", - "multiplied by the same fraction, alpha.", - "This simply says that if I reduce my inputs by some", - "proportion, then my outputs will also reduce by the same", - "proportion So that's homogeneity.", - "Next, let us look at superposition.", - "This is some really fun stuff.", - "So suppose I have a linear system as before.", - "And in this case, I give it one set of inputs,", - "x1a, x2a, and so on.", - "And for fun, let the a's stand for apples.", - "So if you have a set of apples, and let's say I get", - "applesauce at the output.", - "Now, if I take the same circuit, and if I feed the", - "main same circuit a different set of inputs-- x1b, x2b, and", - "so on, in this case, b stands for blueberries--", - "let's say I get blueberry jam as an output.", - "So what supervision says is this.", - "If I take the same circuit, the same system, and if at", - "each input where I had previously fed", - "an apple or a blueberry.", - "The [UNINTELLIGIBLE]", - "at each of the inputs, I want to feed", - "an apple and a blueberry.", - "That's x1a + x1b, x2a + x2b, and so on.", - "Then the outputs will simply be the sum of the", - "two original outputs.", - "So they could be ya plus yb.", - "You facetiously think of it as mixed fruit jam.", - "So superposition simply says that if I find the output by", - "feeding the system apples, find the output by feeding the", - "system blueberries.", - "If I fed the same system the sum of apples and blueberries,", - "then I could compute the output simply by looking at", - "the outputs of the system in which I fed just apples or", - "blueberries.", - "Let's look at a specific superposition example and get", - "a sense of what this means.", - "So here's the same system.", - "And in this case, I want to feed two voltages, v1 and v2,", - "and I want to find out the output.", - "What superposition says is this.", - "I can take the same system, and set one output to zero,", - "and feed it just v1, and measure an output.", - "Similarly, I take the same system.", - "And this time around, set v1 to v0, and feed it v2, and I", - "obtain a net output.", - "By the method of superposition, what it says is", - "that for the same system, if I feed it the sum of the two", - "inputs, then I can get my output simply by summing up", - "the two individual outputs.", - "In other words, I can obtain the effect of v1 and v2 acting", - "as inputs simply by taking the same circuit and applying one", - "input, setting the others to zero.", - "Measuring the output.", - "Setting the second input.", - "And then having all the other inputs be zero.", - "And measure the output.", - "And then take the individual outputs, y1 and y2, and simply", - "add them up.", - "And that would be the result of v1 and v2 acting together.", - "So that is a specific superposition example.", - "What it does is it allows us to solve two", - "problems, p1 and p2.", - "But each of them is a simpler problem, and simply sum the", - "two outputs of the simple problem to obtain the result.", - "So method of superposition can be summarized as follows.", - "You first find the response of the circuit to each source", - "acting alone.", - "And then second.", - "If you want to find the response of the sources acting", - "together, then you simply sum the individual responses.", - "It is important to point out that this works only for", - "independent sources.", - "You will see later how superposition works with", - "dependent sources.", - "Now, in circuit position, we talked about each source", - "acting alone.", - "And for each source to act alone, I had to set all the", - "other sources to zero.", - "So what does it mean to set a source to zero?", - "So let's say, for example, I have a voltage source, as", - "shown here.", - "What does it mean to set that this voltage source to zero?", - "Well, it simply means that we will short the voltage source", - "as shown here.", - "That sets a voltage source to zero.", - "Similarly, for a current source.", - "The way you set the current source to zero is you open", - "circuit the third course.", - "OK, now let's get back to our original example that we had", - "previously solved using the known method.", - "So let's go ahead and solve the same circuit using the", - "superposition method.", - "OK, using the superposition method for the goal, I have to", - "find the output for each source acting alone.", - "And then I sum the outputs.", - "So let me start by finding the output with v acting alone.", - "So we'll start by setting the current source to zero.", - "And I can do that by open circuiting the current source.", - "Now, as I do this, I can compute the", - "output, ev, as follows.", - "ev is simply this voltage appearing at the output", - "through a voltage divider, r1 and r2.", - "So I get r2 divided by r1 plus r2 times v. So that is a", - "component of the output as a function of v alone.", - "OK, next, let me work on i acting alone.", - "So this case with i acting alone, I want to set the", - "voltage source to zero by shorting it.", - "Now, I can write ei, the component of the output that", - "relates to just a current source, as follows.", - "So I have the current flowing through here, and that current", - "flows through a parallel resistor pair.", - "And so the voltage is simply the current times the", - "effective resistance, which is simply r1 parallel r2, which", - "is given by r1, r2 divide by r1 plus r2.", - "So that gives me ei.", - "So the superposition method simply says that you get the", - "effect of both sources acting simultaneously if I simply add", - "up the two components, ev and ei, like so.", - "There you go.", - "So this is due to the voltage source acting alone.", - "And this is due to the current source acting alone.", - "Notice that this equation is the same as the one you got", - "with the application of the load method." - ] -} \ No newline at end of file diff --git a/subs/hIea8V5vXh8.srt.sjson b/subs/hIea8V5vXh8.srt.sjson deleted file mode 100644 index ac2e9d7c04..0000000000 --- a/subs/hIea8V5vXh8.srt.sjson +++ /dev/null @@ -1,647 +0,0 @@ -{ - "start": [ - 0, - 760, - 2910, - 6520, - 7950, - 8340, - 10500, - 14200, - 16890, - 18510, - 21020, - 22420, - 25140, - 29980, - 30750, - 32060, - 33450, - 35250, - 36560, - 39400, - 40340, - 40750, - 42210, - 43350, - 44910, - 47570, - 50500, - 52290, - 54420, - 55470, - 57990, - 60250, - 61350, - 65319, - 68980, - 71430, - 75290, - 76190, - 79300, - 82570, - 86130, - 86890, - 87430, - 91570, - 94910, - 96820, - 98310, - 101500, - 104280, - 106650, - 109770, - 111300, - 113640, - 114540, - 117080, - 120310, - 124650, - 128080, - 129550, - 132060, - 134630, - 137400, - 139660, - 143690, - 146290, - 150370, - 151400, - 153410, - 156130, - 158440, - 160620, - 166130, - 168950, - 172340, - 175830, - 178170, - 181150, - 181950, - 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436520, - 439350, - 443020, - 445870, - 446230, - 447120, - 450480, - 453070, - 454000, - 455360, - 456950, - 459270, - 461700, - 463260, - 467300, - 470040, - 474100, - 476440, - 480230, - 481120, - 485080, - 488220, - 492190, - 493990, - 498610, - 499800, - 503120, - 505790, - 508200, - 512080, - 515650, - 516400, - 521789, - 523909, - 528407, - 532040, - 534260, - 536670, - 539100, - 542160, - 545800, - 548170, - 550390, - 552610 - ], - "text": [ - "SPEAKER 1: OK.", - "So let me proceed here.", - "I've applied a force, F. And I have asked you the question,", - "what is the acceleration?", - "OK?", - "Now, the answer here is pretty simple.", - "What you would do, given that you've taken physics,", - "mechanics, and so on, you would very quickly ask me what", - "is the mass of the object, m.", - "And I would very quickly tell you the mass of", - "the object is m.", - "And then, you would very quickly respond that the", - "acceleration is given by the force divided by the mass of", - "the object.", - "Gives you the acceleration.", - "So that was pretty simple.", - "So you asked me for m.", - "I tell you what m is.", - "You respond a equals F divided by m.", - "And you are done.", - "OK?", - "That was pretty simple.", - "It wasn't hard at all.", - "Now, why wasn't that hard?", - "It wasn't hard because, in trying to figure out the", - "acceleration of the object, you just asked me for the", - "mass, m, of the object.", - "You ignored a whole bunch of other", - "properties of the object.", - "You ignore its shape, its temperature, its color, where", - "did I apply the force, how it smelled, and", - "so on and so forth.", - "This kind of simplification where you took an object and", - "you assumed that the object had a mass acting at that", - "point and the force was applied at that point is", - "called point-mass discretization or point-mass", - "simplification.", - "And by making the point-mass simplification, you were able", - "to tremendously simplify how you solved the problem.", - "And in doing so, you were able to get the acceleration very,", - "very quickly.", - "OK.", - "So with this little piece of insight, let us go back to our", - "light bulb example and see how we can find the current", - "through the light bulb through the filament and by an", - "application of a [? voltage read ?]", - "and somehow take inspiration from the point-mass", - "discretization that we did in physics.", - "So let's data the bulb for a second here.", - "In this bulb, we really don't care about exactly how the", - "current flows inside the filament.", - "We don't care about its temperature, its shape, its", - "orientation.", - "We just don't get about a lot of things.", - "All I care about is what is the current through the bulb.", - "So to do so, much like we did the point-mass discretization,", - "what we're going to do is replace the bulb with a", - "discrete resistor.", - "We will replace the bulb with a discrete resistor for the", - "simple purpose of calculating the current.", - "And using this very simple model, this very simple", - "simplification, I'm not going to be able to tell you what", - "its temperature is or what its shape is and so on, but I will", - "be able to tell you what its current is.", - "So let's proceed with this simplification and continue", - "down the easy path.", - "So as I said, we'll replace the bulb with a discrete", - "resistor for the purpose of computing the current.", - "And so, let me draw a little picture.", - "So here's my representation for the battery.", - "And what I'm going to do is here are my two points, A and", - "B, representing the two terminals of the bulb.", - "And I'm going to replace the bulb and model it as a", - "resistor with resistance, R. There's going to be some", - "voltage, V, across the resistor.", - "And my goal, as I said earlier, was to figure out the", - "current, I.", - "So what I've done is I've replaced the bulb here with a", - "resistor, where the resistor is serving as a", - "model for the bulb.", - "It's a discrete element called the resistor.", - "And by doing so, now I can very quickly compute the", - "current through the bulb using Ohm's Law, as the current, I,", - "is simply V divided by R. Now, wasn't that simple?", - "OK?", - "Show me where the differential equations are.", - "They're all gone.", - "By making an extremely simple model, by making the", - "simplification and replacing all of the properties of the", - "bulb with the simple resistor with resistance, R, I was able", - "to compute the current, I.", - "Let me continue.", - "And in EE what we are going to be doing is we're going to be", - "doing things the simple way.", - "And in this particular situation, to find the", - "current, I, through the bulb, I replace the bulb with a", - "resistor with resistance, R. And I very quickly was able to", - "find the current.", - "So this is going to be a constant, constant point that", - "we make in 6002X, which is that, in EECS, as engineers,", - "we do things the easy way.", - "In fact, this is true of all engineering.", - "Here in engineering, our goal is to build useful systems", - "that help humanity.", - "And our goal will be to try to do it in the simplest manner", - "possible, unlike like science where, in science, you have to", - "learn what is.", - "But in engineering, we're going to take the easiest path", - "possible in order to build useful systems and possibly", - "make as many simplifications as we want, as long as we get", - "to our goal", - "So in this particular situation with our resistance,", - "R, represents the only property of interest for us,", - "in terms of computing the current, I, for the filament", - "of the bulb.", - "So this is very much like the point-mass simplification", - "where we replaced placed objects with their mass, m, in", - "order to find the acceleration, a equals F", - "divided by m.", - "So I really hope that you see this relationship between the", - "simplifications we made in physics to the simplifications", - "we make in EECS.", - "And as we go on, I'm going to show you some really, really", - "extraordinary results that we get by making some of these", - "some simplifications.", - "So as I said, the R represents the key property of interest", - "for the bulb and enables us to compute the current.", - "What R has done is that it relates the voltage across the", - "resistor to its current.", - "So R relates the voltage and current", - "related to the element.", - "R relates the V and I of the element to each other by the", - "expression I is given by V divided by R.", - "So this relation, I equals V divided by R, is called the", - "element v-i relationship.", - "So obey these elements, and we will define a v-i relationship", - "for those elements that's going to capture the voltage", - "and current relationships for each element that you will see", - "in this course.", - "So this lumped element, R, that we've created to replace", - "the bulb for the purpose of computing the current through", - "the bulb is a lumped element abstraction for the bulb.", - "You've abstracted out all the properties of the bulb into", - "this element, R, for the purpose of computing the", - "current through the bulb.", - "It's important for me to point out this word that you see", - "here, abstraction.", - "This is probably the single most common word that you will", - "hear in an EECS curriculum.", - "A large part of what we do in engineering is we build", - "abstractions.", - "We make things simple and represent them with some", - "abstract properties.", - "OK?", - "Many of you have probably done computer programming.", - "And in computer programming, you are very used to writing", - "programs with a set of lines of code.", - "And what you might do is if you have a function, f, with", - "some arguments, then you might replace the properties and the", - "actions of a bunch of lines of code with this abstract", - "function, f.", - "So that's another example of abstraction where f replaces a", - "set of lines of code that will perform the same function.", - "So it's so much easier to use f.", - "f can replace a set of lines of code.", - "The same manner, our element, R, will replace a large set of", - "differential equations and properties that would", - "characterize the bulb.", - "So you will see this concept of abstraction again and again", - "and again in all of electrical engineering and computer", - "science as you do more and more courses in this area.", - "And if there's one word that describes our entire field of", - "EECS, it is this word abstraction.", - "OK.", - "Enough on abstraction.", - "As you can see, I love the concept of abstraction.", - "And let's pretty quickly summarize what", - "we've seen so far.", - "We build lumped elements.", - "And lumped elements are", - "characterized by their vi relation.", - "So for example, I could have a lumped element", - "that looks like this.", - "And I can define a voltage across a lumped element.", - "And I can define a current through the lumped element.", - "And in this case, when I define the voltage and the", - "current going in through the positive terminal of the", - "element, the power consumed by the element is given by the i.", - "So remember this.", - "You will see this again and again as well that I take an", - "element, and I define a voltage, v, across the", - "element, and I define a current going in to the", - "positive terminal of the element.", - "And in that case, the power consumed by the element is", - "going to be vi.", - "I want you to be careful whenever you define power as", - "whether the power was consumed by the element or power is", - "supplied by the element OK?", - "In this case, the power consumed by the element is vi.", - "So to continue with the resistor, my resistor is a", - "lumped element.", - "And I can describe it with a voltage, v, and a current, i.", - "And I can also plot the values.", - "So for the resistor, the vi relation is given by i equals", - "V divided by R, where R is the resistance", - "property of this resistor.", - "So this element is characterized by its iv", - "relation. i equals V divided R.", - "One interesting computation you can make is, how do you", - "plot this element relationship on an iv curve?", - "Then I show you a pair of axes here.", - "So let me pause for a couple of seconds while you think", - "about what this relationship might look like." - ] -} \ No newline at end of file diff --git a/subs/j-6AcHqrZZc.srt.sjson b/subs/j-6AcHqrZZc.srt.sjson deleted file mode 100644 index ed5b705e35..0000000000 --- a/subs/j-6AcHqrZZc.srt.sjson +++ /dev/null @@ -1,212 +0,0 @@ -{ - "start": [ - 285, - 1900, - 6410, - 8374, - 11530, - 14560, - 15550, - 19060, - 21260, - 25200, - 28230, - 29540, - 31390, - 34100, - 38650, - 42200, - 46420, - 48230, - 50740, - 51600, - 55200, - 58110, - 59380, - 59840, - 61800, - 63350, - 67790, - 69120, - 72160, - 73420, - 76810, - 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170700 - ], - "text": [ - "SPEAKER 1: OK, we are ready to begin.", - "So, as I said earlier, 6.002x will represent a big jump from", - "physics to EECS.", - "And let's just dive right into it and take a look at an", - "example of the kind of problems that we", - "might want to solve.", - "So, suppose I have a battery here that supplies the", - "voltage, v. And I connect that to a light bulb.", - "And let's say that I wish to find out the current, I, that", - "will flow through the bulb as a result of connecting the", - "light bulb to the battery.", - "Now, I don't want to find out anything else.", - "All I want to know is, what is the current through the bulb?", - "Oh, I want to remind you that as I go through various parts", - "of the course, I will point to readings in the textbook.", - "And for this material in this set of segments, you will skim", - "chapter one of your textbook.", - "The readings are also indicated in your course at a", - "glance handout.", - "So with the kind of problem we want to solve, with a battery", - "connected to a light bulb, I want to find out what is the", - "current, I, through the bulb.", - "OK.", - "So, here's my problem.", - "Now, I could do it the hard way.", - "As I've said before, we have captured the way nature is", - "through sets of equations.", - "In particular, those that relate to 6002", - "are Maxwell's equations.", - "So I'll parade a bunch of equations in front of you, and", - "don't get scared here.", - "This is the hard way.", - "This is not how we're going to do it in 6.002x.", - "I just want to show you how exciting and fun 6002 is, and", - "how simple things are.", - "But let me start by showing you how we could do it if we", - "were crazy.", - "OK, so I showed you Maxwell's equations in differential form", - "or in integral form.", - "So for example, this is Faraday's equation--", - "del cross E is minus del B by del t.", - "In integral form, it is integral E dot dl is minus del", - "phi B by del t, and so on and so forth.", - "Now I could take Maxwell's equations, and of course, you", - "can go and solve all of them somehow.", - "It would be horrendously hard.", - "But normally this is not what we do in 6002, and not what we", - "do as EECS engineers.", - "Instead, there is a much, much easier way.", - "We are going to make our life extraordinarily simple.", - "So before I show you what that method is, let me help us", - "build some insight.", - "So let's do it by analogy.", - "So supposing I have an object, and suppose I apply some", - "force, F, to the object.", - "And my question to you is, what is the acceleration of", - "the object?", - "OK, so if I ask you this simple question--", - "I have an object, and I apply a force, F, to the object, and", - "I ask you, what is the acceleration of the object?", - "I don't tell you anything else.", - "All right?", - "No more data.", - "I want you to think about how you might solve this problem.", - "What sort of questions would you ask me?", - "How would you answer this problem?", - "Let me pause here for a couple of seconds, and give you some", - "time to think about the answer before I proceed." - ] -} \ No newline at end of file diff --git a/subs/kZj5cQ4SQrE.srt.sjson b/subs/kZj5cQ4SQrE.srt.sjson deleted file mode 100644 index 7e36e20308..0000000000 --- a/subs/kZj5cQ4SQrE.srt.sjson +++ /dev/null @@ -1,326 +0,0 @@ -{ - "start": [ - 370, - 3130, - 5940, - 10140, - 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269450, - 270700 - ], - "text": [ - "SPEAKER 1: At this point, I'd like to do a quick summary of", - "all that we have covered in 6.002 so far.", - "We began life in 6.002 by discretizing matter into", - "lumped elements.", - "And we agreed to observe the lumped matter discipline.", - "What this did was it turned real life elements, as our", - "little pickle on which we performed the fun experiment a", - "little while ago.", - "And we were able to turn that into lumped elements, such as", - "a resistor, which we could use in circuits to obtain", - "properties such as voltages and currents.", - "And when we took these lumped elements and put them together", - "into circuits, we got the lumped circuit abstraction.", - "All right.", - "So once we built these circuits containing these", - "lumped elements, we then went on to develop an arsenal of", - "tools that we could use to analyze circuits.", - "So notice that the fun part of 6.002 doubled", - "has really not begun.", - "We just made some assumptions that allowed us to make the", - "transition from physics and the complications of Maxwell's", - "equations into some very simple territories where", - "algebraic equations rule.", - "And then, we sat down and developed some analysis", - "techniques for the circuits that we built.", - "Notice we really haven't built anything useful or", - "done any fun stuff.", - "We are still developing our tools for the", - "circuits that we created.", - "So we developed a bunch of circuit analysis methods.", - "We started off with the KVL, KCL method.", - "And in this method, you took a circuit.", - "And you wrote the KVL, KCL equations and also the I-V", - "relations for each of the elements.", - "And then you got a whole series of linear equations.", - "And we went and solved them.", - "The second technique we learned was applying", - "simplification rules, where you combine resistances in", - "series and so on and so forth, a resistance in parallel or a", - "voltage in series, and then used those to", - "simplify the circuit.", - "The third method that we developed was the node method.", - "The node method is really the workhorse of our industry.", - "When in doubt, use the node method.", - "The node method applies to all circuits and, in fact, is used", - "for linear or nonlinear circuits.", - "And by and large, when in doubt, we just", - "apply the node method.", - "So if you look at these techniques here, they apply to", - "any network.", - "And then, we looked at another class of techniques, the", - "superposition, Thevenin, and Norton.", - "In the superposition method, we simplified a circuit into", - "subcircuits by shutting off all sources save for one.", - "And then we found the subcircuit result.", - "And then we added up all the results.", - "That was the superposition method.", - "And then we learned about the Thevenin and Norton methods.", - "The Thevenin method, it determined a Thevenin pattern", - "circuit to replace an arbitrary network, while the", - "Norton method replaced an arbitrary circuit with the", - "Norton pattern.", - "Now, don't forget that the superposition, Thevenin, and", - "Norton methods apply only to linear circuits.", - "So these techniques, superposition, Thevenin and", - "Norton, are extremely powerful.", - "And they will work with linear networks.", - "And we will see a lot of situations where we have", - "linear networks.", - "And so these are very important techniques.", - "And then, of course, for nonlinear networks, or for", - "networks that contain nonlinear elements, we will", - "largely use the node method, where the node method is", - "really the workhorse of our industry.", - "Now people often ask me, when do I use which technique?", - "You've taught us the KVL, KCL method, the node method, the", - "Norton method.", - "Where do I apply these techniques?", - "The way to think about it is just imagine if you are a", - "carpenter, and you have a tool chest full of tools.", - "You know, you have a chisel.", - "You have a screwdriver.", - "And you have my favorite tool, a chainsaw.", - "So you have all of these tools.", - "And if you asked a carpenter, well, where do you use which", - "tool, what do you expect the carpenter would respond?", - "The carpenter would say, well, that's why you pay a carpenter", - "the big bucks.", - "They know what tool to use where, and they're practiced", - "in using it.", - "Similarly, as engineers, as you get more practice, you", - "will begin using these tools and beginning to figure out", - "where to use what tool.", - "But fundamentally, the superposition, Thevenin, and", - "Norton methods apply to linear networks.", - "And the node method applies anywhere.", - "So when in doubt, just use the node method.", - "And much like a carpenter would use a chainsaw to chop", - "down a tree, you can use your superposition method to", - "analyze circuits that contain a number of sources, where you", - "can break it down into very simple subcircuits.", - "But of course, the circuit has to be linear to begin with.", - "So really, you will develop experience in terms of where", - "to apply which method.", - "But again, don't forget that the node method will apply in", - "any situation." - ] -} \ No newline at end of file diff --git a/subs/ke3SL_R92ys.srt.sjson b/subs/ke3SL_R92ys.srt.sjson deleted file mode 100644 index 9bc5ffd3b6..0000000000 --- a/subs/ke3SL_R92ys.srt.sjson +++ /dev/null @@ -1,2036 +0,0 @@ -{ - "start": [ - 0, - 1586, - 9000, - 14852, - 19711, - 27000, - 31810, - 36300, - 39507, - 44398, - 49369, - 52095, - 56505, - 59873, - 65311, - 68614, - 72412, - 76458, - 78110, - 81990, - 84633, - 90000, - 94142, - 98598, - 102741, - 107274, - 110557, - 115247, - 119000, - 123008, - 126943, - 131248, - 134812, - 148000, - 151976, - 157248, - 161410, - 176000, - 183000, - 187153, - 191397, - 195822, - 200608, - 205484, - 210000, - 214132, - 217144, - 221137, - 224640, - 228632, - 232415, - 234586, - 239000, - 243636, - 248636, - 264000, - 267692, - 272538, - 275812, - 278875, - 282812, - 286375, - 289437, - 292937, - 295250, - 298750, - 301441, - 303913, - 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Good morning,", - "all.", - "You have two handouts, lecture notes and an article on", - "mixed signal chips. A mixed signal stands for", - "circuits that have both analog and digital components to them.", - "The reason I am giving you the handout is that Lab 4 and also", - "your last homework involve designing and building a mixed", - "signal circuit. It's a real fun exercise.", - "And I just wanted to tell you that from past experience people", - "who have taken 6.002 often view the last lab as the single most", - "fun thing they did in all of 6.002.", - "So, as you go into Lab 4, you should be telling yourself", - "I should be having fun, I should be having,", - "I should be having fun. You have to positively psych", - "yourself. Otherwise, it's going to go by.", - "And then you're going to say boy, that was fun,", - "I wish I had savored the moment as I was doing it.", - "All right. Let's see.", - "What do we do today? Today's lecture is actually", - "going to be a fair amount of fun.", - "We are going to blast through a bunch of fun things.", - "And some things that you will be quite unprepared for.", - "Until now, in the last two lectures with op amps we talked", - "about negative feedback. That is applying some portion", - "of the output voltage to the negative input so that I could", - "control this high strung device, my op amp.", - "Today, what we are going to do is try to get a handle on what", - "happens if we use positive feedback.", - "It's the usual curious child. You tell them to do this,", - "and of course they're going to try to do this as well.", - "And we are going to try to do that and see what happens and", - "look to see if we can build some useful circuits.", - "Today --", - "As motivation, let me do a quick review of a", - "circuit that should now become affixed in your brains in a", - "standard pattern. This is a circuit that gives", - "you negative feedback.", - "R1 and R2.", - "And I apply a vIN. By now you should be able to", - "look at this pattern. And this is your inverting", - "amplifier pattern. So, you should be able to write", - "down by inspection this is simply vIN or the minus vIN", - "times R2 divided by R1. This is an amplifier whose gain", - "is controlled by the ratio of R2 and R1.", - "This is a negative feedback circuit because it is always fun", - "to do the intuition thing and say that look,", - "if this voltage tends to go more positive than I care then", - "this negative input goes more positive than I care.", - "If that goes more positive then the negative input v minus", - "becomes more positive in the plus input which yanks the", - "output down. So, there is a nice", - "counteracting force that keeps the output stable.", - "Let's look at this circuit. Being curious engineers,", - "let's look at the opposite here where I give myself some", - "positive feedback in this op amp.", - "And it is going to be interesting to analyze this", - "because what we find out on the face of it is not quite actually", - "how it behaves. We are going to spend most of", - "the lecture today on understanding the dynamics of", - "circuits that look like this and to see if we can build some fun", - "and interesting circuits and systems based on this kind of", - "positive feedback. It is positive feedback because", - "I am feeding back a portion of the output to the positive", - "input. And you should be able to stare", - "at this and already begin to intuit what should happen to", - "this. Let's think about it.", - "This is zero. Remember, with positive", - "feedback, the famous v plus is equal to v minus method doesn't", - "apply anymore. Let's apply very simple", - "analyses. If this is zero,", - "let's say for example that this output tends to go a little bit", - "more positive. This output,", - "due to some noise or perturbation,", - "tends to go up a little bit. If that goes up a little bit", - "then because of feedback this node tends to go up a little", - "bit. If this node tends to go up a", - "little bit this exacerbates the positive input here and this one", - "goes cachunk, whacks into the positive rail.", - "Let's take the other point of view and look at it intuitively.", - "What if this one tries to droop a little bit?", - "If it droops a little bit then the input at the plus terminal", - "droops a little bit. If that tends to go down a", - "little bit, that makes the output droop further and it goes", - "and hits into the negative rail. I can see that this circuit", - "wants to hammer into the positive rail or hammer into the", - "negative rail because of the positive feedback.", - "It is like if you give incredibly positive feedback all", - "the time, and by positive feedback I mean feedback", - "encouraging the child to do whatever the child is doing.", - "It could be if he does bad stuff you give a lot of positive", - "feedback or good stuff you give a lot of positive feedback then", - "you are guaranteed to have a very good child or a very bad", - "child. You are not going to have", - "anybody in the middle. Same way here.", - "By giving positive feedback you're going to drive this into", - "the positive rail or drive this into the negative rail.", - "Now, I am going to analyze this in two steps.", - "First I am going to analyze this using a method you've seen", - "before which is replace the op amp with its equivalent circuit", - "and analyze it statically. And by analyzing it statically", - "we are going to show that the simple static analysis will", - "yield the following expression. I put this in quotes,", - "well, for a reason you will see shortly.", - "When I apply a plain and simple static analysis here is what I", - "find. Let's go ahead with the", - "analysis and see what is basically different about these", - "two. And, first of all,", - "I will confirm for you that our naive analysis we have seen so", - "far will give rise to that expression.", - "So, let's go ahead and analyze that circuit.", - "And to analyze that circuit what I will do is replace the op", - "amp with its equivalent circuit. If you remember the op amp is", - "characterized by the following circuit, A times v+ minus v-,", - "vOUT. This is the equivalent circuit", - "of my op amp. And let me just impose that", - "external circuit on this op amp. I have grounded my v- terminal.", - "My v+ terminal goes through a resistor and a supply,", - "the v into ground, it's the resistance R1.", - "This terminal goes to the output through a resistor R2.", - "So, this is the equivalent circuit.", - "And I can apply the same good-old techniques I have", - "learned about all through this course to this circuit and see", - "what vOUT looks like. Very simply,", - "vOUT is this expression here A times v+ minus v-.", - "And because of my ground connection v- is zero.", - "Then let me go ahead and replace v+ with the voltage that", - "relates vOUT and vIN. What is v+?", - "v+ is simply the current through this part of the", - "circuit, the current flowing here times the resistance R1.", - "That gives me the drop across R1.", - "And to that I add vIN and that will give me V+.", - "And then of course I multiply this by the gain here.", - "So, let me write down that expression.", - "The current through this is simply vOUT minus vIN.", - "That is the voltage drop between these two points.", - "I divide that by the resistance R1 plus R2.", - "That gives me the current flowing through here.", - "That times R1 is the drop across resistor R1.", - "And to that I add vIN and that gives me the voltage v+.", - "So, this is v+. That is simply vIN plus the", - "drop across the resistance R1. Let me shuffle things around", - "and put all the vOUT terms on this side here.", - "I get a 1+ for that vOUT and let me move AR1 divided by R1", - "plus R2 to the left-hand side. And I pick up a minus sign.", - "So, I get AR1 divide by R1 plus R2.", - "I pick up that. And on the left-hand sign I end", - "up with vIN, and my vIN here is a function of the vIN that I", - "have here. I have an A multiplying both", - "the vINs. And then I get a one for this", - "vIN here and there is a minus sign, so I get a minus R1", - "divided by R1+R2. That is the expression that I", - "have. Let me go ahead and simplify", - "that a little further and move this whole thing down here.", - "That gives me my expression as a function of vIN.", - "What I will do is, let me continue here.", - "vOUT=vIN A(1-R1/(R1+R2)). By the way, you may be", - "wondering why I am going through so laboriously what is seemingly", - "a very simple exercise. The reason I want to do is it I", - "want to very carefully show you that the result produced by this", - "exercise is exactly that. No magic here.", - "No cheating. We are going to get exactly", - "that. And then stare at it and say", - "huh, how did that happen? And then we are going to try to", - "figure out how it actually behaves following that.", - "I divide this by 1-AR1/(R1+R2). And by now you should be", - "familiar with the technique of ignoring small numbers when I", - "have a big number next to it. So, AR1/(R1+R2) can be very", - "much larger than one because A is very large.", - "So, I can ignore my one there. And then what I am going to do", - "is multiply the numerator and denominator by R1+R2.", - "Oh, this A and this A is going to cancel out.", - "This A and this A will then cancel out.", - "And then I multiply the numerator and denominator by", - "R1+R2, so this R1+R2 vanishes. I get R1+R2 here.", - "R1+R2 minus R1 is simply R2. And then down here I get a R1", - "and then I have a minus sign out there.", - "Notice that vOUT we have found to be equal to vIN R2 divided by", - "R1. That is not wrong.", - "That is correct. Technically that is correct.", - "But you will see in a few seconds that in practice that", - "that's rarely what you are going to see happen.", - "And we will try to understand why that is so.", - "What we have done so far, if you stare at these two", - "panels here, first of all, we know that the inverting", - "amplifier has the expression for vOUT up there.", - "And through this laborious exercise we have also shown that", - "even with positive feedback, if I take a static view of the", - "circuit -- If I take a snapshot of the", - "circuit and simply analyze it as a static circuit,", - "I get the same expression vOUT. But what we are going to do is", - "when I explain to you that look, a small perturbation in vOUT is", - "going to drive the op amp to the positive and negative rail,", - "that is where the insight begins to show.", - "That if everything were magical and I could somehow exactly keep", - "things just so that will be true.", - "I will be able to build that positive feedback circuit where", - "the output is equal to R2/R1 vIN.", - "But remember even the slightly amount of perturbation is going", - "to send the op amp scurrying off to the positive rail or the", - "negative rail. How do we analyze that?", - "How do we analyze the behavior of a circuit that based on a", - "small perturbation begins to move one place or another?", - "We want to analyze the dynamics of the op amp.", - "And to analyze the dynamics what I need to do is give you a", - "slightly more detailed view of the operational amplifier.", - "If the operational amplifier is not moving instantaneously", - "between the plus and minus rail, I need to give you a more", - "detailed model that encapsulates the behavior of the op amp.", - "And so let me do that. If you want to study the", - "dynamics of an op amp -- By dynamics I mean how an op", - "amp moves as I perturb the input or the output and so on.", - "To capture the dynamics of the op amp we build a slightly more", - "involved circuit, so v+ and v-.", - "This is what we've seen before, two terminals and dependent", - "source that amplifies the difference input here by a large", - "amount. Instead what we are going to do", - "here is something slightly different and interpose the", - "following circuit in the middle here.", - "This is a model of the dynamics of an op amp.", - "We are going to impose a small RC circuit in here.", - "This is R. This is C.", - "And I am going to call the voltage across the capacitor v*.", - "Notice what I have done is rather than say this is Av+", - "minus v- I am breaking it apart in two dependent sources,", - "the first dependent source, which is simply v+ minus v-,", - "and there is a RC time constant surrounding it and then here I", - "simply add on my gain Av*. Notice that if it turned out", - "that the resistance here, for example,", - "was zero then v+ minus v- would appear across v* and this would", - "be A(v+ - v-), what you have seen before.", - "It is always good to take a look at circuits and look at", - "what happens when some component goes to an extreme value.", - "This would give you your basic op amp circuit.", - "What I would like to do next is analyze the following circuit to", - "understand how positive and negative feedback work together.", - "And by understanding that then be able to explain how a", - "positive feedback circuit works or a negative feedback circuit", - "works. Here is what I will do.", - "This part simply corresponds to my positive feedback circuit,", - "R2, R1. So, that is my positive", - "feedback circuit. And I will do the same thing on", - "this side.", - "All I am doing is applying both a positive feedback through R2", - "and R1 and negative feedback through R4 and R3 and", - "representing the dynamics of the op amp and then standing back", - "and ee, all right, let's see what happens to you.", - "So, I am sticking positive feedback, negative feedback,", - "the dynamics of the op amp here and let's see what happens.", - "What I would like to do is impose this circuit on top of", - "this op amp model. To save myself some effort,", - "let me just go ahead and modify this circuit directly.", - "I get an R2 here, an R1 here, and then up here I", - "get an R4, R3 here. The math is going to be just a", - "little bit grubby but the result is actually pretty spectacular.", - "So, all I have done is replace the op amp with its internal", - "circuit out here. And now we are going to take a", - "look at what happens to op amp dynamics when there is a small", - "perturbation. Let's develop an equation of", - "this circuit containing a capacitor using techniques that", - "we already know. Just to give you some insight", - "into what you're going to see, notice that if I make a small", - "perturbation in the voltage across the capacitor,", - "let's say I make a small perturbation to the capacitor", - "voltage let's say by applying some initial condition kind of", - "thing onto the capacitor. Then let's say that the output", - "changes to some value K. So, the change on the capacitor", - "must have been K divided by A. And what you are going to see", - "is what happens to the op amp when the initial condition on", - "the capacitor is such that this output gets perturbed to the", - "value K. Let's write an equation for", - "this little circuit and see what happens.", - "Recall our goal was to understand what happens when I", - "perturbed the output a little bit.", - "Here I perturbed the output such that its value goes to K.", - "And I can perturb the output by changing what happens at the", - "capacitor. Let me write the equation for", - "this circuit now and then to understand what happens to this", - "capacitor circuit if I let go after giving it a small", - "perturbation. What I am going to do is let me", - "start by writing the good old equation for this little circuit", - "here. And that equation is simply the", - "voltage here v+ minus v- equals the voltage across the RC.", - "So, v+ minus v- will be equal to the voltage drop across the", - "resistor plus that across the capacitor.", - "The voltage across the capacitor is v*.", - "The voltage across the resistor is the current through the", - "capacitor C dv*/dt times R. So, v* plus RC dv/dt is equal", - "to v+ minus v-. RC dv*/dt plus v* is v+ minus", - "v-. You have done this millions of", - "times before, but yet again.", - "This voltage here is equal to the drop across these two,", - "and the drop across these two is v*, the drop across C,", - "plus the current through the capacitor C dv/dt times the", - "resistance R. Or you can apply the node", - "method as well and get the same expression.", - "Now, we also know here that vO divided by A is v*.", - "I can go ahead and replace this guy here, v* by vO divided by A.", - "RC/A dvO/dt. Recall, I want the dynamics of", - "vO so let me just get an expression in vO.", - "So, I get vO divided by A plus v+ minus v- equals.", - "Now, I want an expression in vO, an equation in vO,", - "so I need to express v+ and v- in terms of vO.", - "What are these expressions? The expression for v- is vO and", - "this voltage divider, so it's vOR3/(R3+R4).", - "And just for simplicity, let me call this some constant", - "gamma minus. This is some fraction", - "R3/(R3+R4). And let me call that fraction", - "gamma minus. Similarly, v+ is vO R1/(R1+R2).", - "And let me call that gamma plus.", - "All I am doing is replacing v+ and v- in terms of vO.", - "So, effectively, what I have here is v+ is some", - "fraction of vO. That's the best intuitive way", - "of thinking about it, some fraction of vO.", - "And v- is some fraction of vO as well.", - "And I just stick these. I now have an expression in vO.", - "Don't get psyched by gamma plus and gamma minus.", - "Simply read this as if it is an F1 and F2 if you would like.", - "So, vO times some fraction minus vO times some other", - "fraction. I am feeding back some fraction", - "of the output to the positive and to the negative terminals.", - "Then, just moving things around a little bit,", - "dividing throughout by A divided by RC.", - "So, I divided by A divided by RC.", - "Plus vO divided by RC. And what I am going to do here", - "in a second, vO gamma plus minus gamma minus.", - "And I have multiplied by A divided by RC throughout.", - "Finally, collecting all the vO terms I get vO times one divided", - "by RC plus A divided by RC. I got a plus sign here so I", - "will just reverse these two guys in there, gamma minus minus", - "gamma plus equals zero. All I have done here is simply", - "grunged through some math to express this equation in terms", - "of vO. And just to make it even", - "simpler, I will just replace this thing by one divided by T,", - "much as we did for first order equations.", - "What I end up with is dvO/dt+vO/T=0.", - "Despite all the grubbiness, I end up with something that is", - "very, very familiar to all of us.", - "I went through a bunch of gyrations to substitute for v+,", - "v- and v*, but at the end of the day I got the simple", - "expression which was dvO/dt+vO/T=0.", - "Where capital T is the time constant of the circuit,", - "and the time constant of the circuit relates to the", - "expression in there 1/RC+A/RC(gamma minus - gamma", - "plus). The gamma minus and gamma plus", - "are the respective portions of the output fed back to the", - "negative input and the positive input.", - "Now, as we all know, based on very simple intuition", - "that we can completely predict the behavior of a first order of", - "an RC circuit once we know what the initial condition of the", - "capacitor is and once you know the time constant.", - "That's it. We know, we are masters at the", - "fact that the capacitor is going to behave like this.", - "It is going to be exponential. And I do know that the time", - "constant capital T. What's here?", - "It is simply the initial condition.", - "There is no drive input. I am not driving this with any", - "input here. There is no input drive", - "anywhere here. This is simply the natural", - "dynamics of the system. And, recall,", - "I start off with bumping the capacitor voltage such that the", - "output starts off being K. That is it.", - "You should be able to write down this expression and the", - "form of the response simply based on this.", - "So, this is what I bumped up the output to be by perturbing", - "the capacitor voltage. My output response based on", - "this equation is going to look like that.", - "Let's try to understand what that means.", - "It is actually quite a lot of fun.", - "How do we plot that response? You all learned that the way to", - "plot the response is plot the initial value,", - "plot the final value, and go cachoock,", - "right? It's pretty simple.", - "I am going to start at K. I know that.", - "I am going to start at K and I am going to go and find out what", - "the steady state value is. Here is where the interesting", - "stuff comes in. The final value on the", - "capacitor depends a lot on whether T is positive or", - "negative. In my RC circuits that I looked", - "at what was T? In the very simple RC circuit", - "we looked at what was capital T? What was the time constant?", - "RC. This was RC.", - "This was a positive quantity. When capital T is positive my", - "output is going to look like this.", - "When T is positive. And T is positive when this", - "expression is positive. And if A is so large that I can", - "ignore the 1/RC term, if A is very,", - "very large and I can ignore the left-hand term here then T is", - "positive when gamma minus is greater than gamma plus.", - "So, when gamma minus is greater than gamma plus,", - "I have a stable circuit, this is the good-old stuff we", - "have seen before. Now things begin to make sense.", - "Intuitively, what am I saying here?", - "All the gammas and other pieces of crapola aside,", - "what am I really saying here in English?", - "What I am saying here is that if the portion of the output fed", - "to the negative input is greater than that fed to the positive", - "input then I have net negative feedback.", - "I have net negative feedback. I am feeding the output back to", - "both the positive and negative inputs.", - "And if my negative input has a stronger effect then I am going", - "to see the op amp output decay down to a value that I expect", - "which is going to be zero. Notice that since I am not", - "applying any input here, I expect the stable point for", - "this to be output going to zero. I don't have any input there.", - "Let's take a look at another situation.", - "What happens when the opposite is true?", - "What happens when gamma minus is less than gamma plus?", - "When I feedback more, what happens when I do this,", - "when gamma plus is greater than gamma minus?", - "The opposite is true. This means that I am feeding", - "back more to the positive input. A bigger proportion goes to the", - "positive than the negative. What happens then?", - "Then what happens is capital T becomes negative.", - "We cannot see this happening on the RC circuit because capital T", - "is equal to RC, but here we have a more", - "complicated circuit and capital T can go negative.", - "If capital T goes negative then this whole thing in the exponent", - "there goes positive. If that goes positive what", - "should the output look like? It should take off into", - "never-never land. There we go.", - "I start off at zero and a make a small perturbation,", - "and the output should go as t divided by capital T.", - "The dynamics of this it goes berserk, so it is net positive", - "feedback. This is called a stable", - "situation. This is unstable.", - "What happens when capital T goes to infinity?", - "When capital T goes to infinity, spend five seconds", - "thinking about what it means physically.", - "What does it mean for the time constant of an RC circuit to go", - "to infinity? That means that your R and C", - "are very, very, very large.", - "That means that circuit is going to be very,", - "very sluggish. Think elephant.", - "A big time constant. I want to move a leg.", - "It takes a while to do that. Think big.", - "Big time constant. So, everything is going to", - "happen really slowly. It's like moving in molasses.", - "Big time constant. Everything is going to happen", - "really, really slowly. If gamma minus is greater than", - "gamma plus with a huge time constant it is going to look", - "like this. And the output is going to look", - "like this. I make T even larger.", - "All right. It is going to like this.", - "I make these so large that T tends to zero,", - "T tends to infinity in which case I get this situation.", - "The output goes dah. OK?", - "Very slow. Very lethargic.", - "Big time constant. T tends to infinity.", - "And so if this is stable, this is unstable,", - "this is called corresponding neutral.", - "And there is a mechanical analog to all of this.", - "You can show that this situation is akin to let's say I", - "had a physical well of the sort and I had a ball in there.", - "I let the ball go. Then the ball will come down", - "here and settle down in a stable state.", - "Any small perturbation of the ball will get it to come down", - "and settle down here. The unstable situation is this", - "situation where I have a ball sitting up here where any small", - "perturbation will get it to zip down to a positive rail or to a", - "negative rail. So, this is an unstable", - "equilibrium situation. And exactly the reason we got", - "this analysis in the static situation is that this can", - "happen. If I do this circuit here and", - "don't perturb it then I could get the output sitting at zero,", - "but the slightest perturbation, boom, it is going to fall down", - "or go up. What about the neutral", - "equilibrium state? That can be modeled like a", - "table top and the ball is here. It doesn't matter where you go.", - "There you are. How many people saw the", - "Buckaroo Bonzi thing? Possibly well before your time.", - "OK. I have this table here.", - "No matter what I do to it, it just goes and settles down", - "where it is, and that is neutral equilibrium.", - "But what this gives you is a fun view of the dynamics of the", - "operational amplifier as I make small perturbations to it.", - "And the even more interesting thing here is you have the tools", - "based on your first order RC analysis to analyze the dynamics", - "of a simple op amp circuit. OK, so much for theory.", - "Now let's get to some action here.", - "All right. Fine.", - "That is really pretty, good and so on,", - "but what can you do for me? What good does this property do", - "for me? What can I build?", - "What we will do is look at the op amp circuit and focus on the", - "situation where I have net positive feedback.", - "In particular just look at this circuit with R1 and R2 and send", - "both to infinity. So, I have no negative feedback", - "and I ground this terminal here and take a look at what happens", - "to a circuit with positive feedback and see if I can build", - "some interesting circuits. What you are going to do is", - "build on a circuit called the basic comparator.", - "What is that? If I have an op amp that looks", - "like this, and remember a VS rail and minus VS supply there,", - "this is v+, this is v-, I can build a very basic", - "comparator by doing the following.", - "All the circuits I am going to show you are going to build on", - "this basic little circuit. What I am going to do is", - "consider applying an input to the v- terminal,", - "applying some sort of an input and taking a look at how the", - "output behaves. So, I apply some input vIN.", - "And if I just do that, if this is v+ minus v- here", - "then I am going to get something that goes like this.", - "That is when this is positive here then this guy is going to", - "go to the VS rail and this guy is going to go to the minus VS", - "rail. In terms of the,", - "if I plot the same thing, in terms of vIN,", - "and this is vOUT, if I plot the thing in terms of", - "vIN then notice that as vIN increases this guy should go to", - "a negative rail. So, in terms of vIN it looks", - "like this. What this says is that as the", - "input becomes more and more positive applied to v- then the", - "output goes to minus VS, and if the input becomes more", - "and more negative then the output goes to VS.", - "This is what is called a very basic comparator circuit.", - "It compares the two inputs and goes up if the input is in one", - "direction and goes to the other rail if the input is in the", - "opposite direction. So supposing I feed this- I can", - "plot this is a function of time. Let's say I plot vIN.", - "Let's say I feed some vIN here. Let me just call this.", - "I feed some vIN to this circuit here, then what do you expect", - "the output to look like, the output wave form?", - "For all positive vINs the output is negative.", - "So, my output vO is going to be negative as long as vIN is", - "positive. And when vIN becomes negative", - "this one shoots up and behaves like this.", - "This is minus VS. That is plus VS.", - "This is my input vIN. Then this guy is going to be my", - "output. As vIN is positive output slams", - "to the negative rail. When vIN becomes negative the", - "output slams to the positive rail.", - "So, that is quite nice. And so such a circuit is pretty", - "useful to me. Let's say, for example,", - "I want to build a little digital circuit that is fed ones", - "and zeros. I can use a comparator to turn", - "my vIN voltage into a sequence of ones and zeros.", - "When vIN is positive I produce a zero and when vIN is negative", - "I produce a one. I can get this one,", - "zero, one, zero sequence coming out corresponding to the values", - "of vIN being greater or less than zero.", - "Now, one problem with something like this is that this circuit", - "can be quite messy in the following situation.", - "Suppose I superimpose a small amount of noise in vIN.", - "In particular, let's say that I have some", - "amount of noise on vIN. I get a bunch of noise sitting", - "around here. What happens is that at this", - "point where the value goes negative, I do bump up.", - "But when for a second I have my input going above zero again --", - "-- this output comes down again and out here it goes up again.", - "I get this nasty behavior at the point where the input is", - "around zero. When the input is around zero,", - "the input is meandering around zero because of noise,", - "I get a huge amount of up and down glitches on the output.", - "That's not very nice. And we will do a little circuit", - "that attempts to fix that little problem.", - "What we are going to do is use positive feedback.", - "And I am going to build you a circuit that shows that we can", - "eliminate this for small noise on the input.", - "So, let's build the following circuit.", - "So I still feed vi to the negative input,", - "but this time around I give it some positive feedback.", - "So, I give it some positive feedback.", - "And what I am going to do is feedback a portion of vO to the", - "positive input. This is positive feedback.", - "And, in particular, let's assume that VS equals 12", - "volts. And to the negative one I", - "connect -VS. This guy is going to go between", - "12 and -12. And correspondingly because", - "these two are equal this one is going to go between 6 and -6.", - "This is going to be a 12 or -12.", - "Remember, the top rail and the bottom rail.", - "And this one is going to be a +6 or -6.", - "And let's understand how this circuit works when I apply an", - "input vIN. Let's start by saying that", - "assume my input is zero for a moment.", - "And let's say my output starts off being 12 volts.", - "The output is 12 volts then the input here is going to be 6", - "volts. In this case v+ is going to be", - "6 volts. The output is 12,", - "v+ is going to be 6 volts. And my circuit is sitting out", - "there doing nothing. Now, this started off being", - "zero. Let's say vIN increases.", - "As vIN begins to increase what happens?", - "Well, nothing until vIN reaches 6 volts.", - "Since this is 6, vIN has to go up to 6 volts,", - "has to equal this voltage before I can flip the circuit.", - "What happens when vIN is greater than 6 volts,", - "if vIN goes above 6 then I have more voltage on a negative", - "terminal than the positive so the op amp flips its state.", - "And vO gets to -12 volts. When vi goes above 6,", - "vO gets to 12 volts. And what does v+ go to?", - "In this state v+ goes to half of -12 which is -6 volts.", - "Now, this guy is sitting at -6 and this guy is sitting at -12.", - "If this one keeps rising nothing happens,", - "so output can stay at -12. So I am pretty safe.", - "Then let's say v begins to come down.", - "As v begins to come down, does anything happen when v", - "gets to 6 again? If v is equal to 6 what", - "happens? Nothing because this is at -6", - "now. So, there is still a huge net", - "negative voltage here from v+ to v-.", - "And so therefore I sit at -12. Oh, well, I keep coming down", - "until I reach -6. When I reach -6 here these two", - "become equal. And what happens when this", - "becomes less than -6? v- becomes less than -6.", - "If this one goes below this voltage, this is -6 and this is", - "-7. There is a net positive voltage", - "between v+ and v-, so this output swings to the", - "positive rail like so. We will spend a lot more time", - "on this in the next few minutes to really hammer the point home.", - "What is interesting about this is that even though the moment", - "vi became more than 6, I swung to the positive rail,", - "and then I had to go all the way back down to -6 before I", - "could change state. I had to go way down before it", - "could flip again. How can we make use of that?", - "Well, let me draw you a little vi versus vO diagram and then", - "talk about how that can be useful to us.", - "This is vi, this is vO, this is zero.", - "Let's say this is 12, -12, -6, +6.", - "Let's plot that on the screen and see what it looks like.", - "As I told you, the output was at 12 volts to", - "begin with and my input was at zero.", - "So, my input kept increasing. When the input hit +6 what", - "happened to my output? My output swung down to -12.", - "As the input kept increasing nothing happened.", - "This was step one, this was step two,", - "step three. My input kept increasing and", - "output stayed at -12 volts. Then what I said was well,", - "let's bring the input down. So, my input began to go down,", - "step four, became more and more negative.", - "Nothing happened until I reached -6.", - "When I reached -6 I swung positive, step five.", - "Again, one, two, three, four,", - "five. I am going up here.", - "It came up here. And nothing happens until I", - "reach -6, but at -6 boom, I switch to the positive rail.", - "And as I get more and more negative I stay there.", - "Then again, as I start increasing again,", - "nothing happens until I reach +6.", - "Think of that as your seventh step.", - "What is spectacular about this is that I seem to have a circuit", - "that now has some knowledge of where it came.", - "If it is coming from here it switches at +6,", - "but if it is coming from here it switches at -6.", - "So, there seems to be sort of a lag in the behavior of the", - "circuit or some memory property in the circuit.", - "This kind of behavior is called hysteresis.", - "The word comes from magnetic circuits where,", - "or rather elements that you're trying to magnetize.", - "Where if you take a magnet and move it over a piece of metal it", - "may leave some residual magnetism in it.", - "And, in the same way, that is called hysteresis.", - "Same way here. As the voltage increases it", - "seems to leave some residual in the circuit so that it effects", - "when it shifts. The good news with this is that", - "now, if I take the same kind of noisy wave form that I had", - "before and do this -- If this is vi then what is", - "going to happen is for vO I am going to be negative at this", - "point. Nothing happens here because I", - "have to get to -6 or +6 before something happens.", - "Out here I get to -6 and I switch state and go up to +12.", - "And then this one comes up above -6 very slightly out", - "there. Nothing happens because the", - "next change will happen only when the input goes to +6.", - "So, if eventually the input gets to +6 and then I am going", - "to change state again. It is actually a really cool", - "property and something that is completely non-obvious.", - "In the last 30 seconds let me show you a quick demo.", - "And, based on this property of hysteresis, I have actually", - "built a little circuit. Let me do that first.", - "Notice here that I am showing you the input on the X axis vi", - "and vO on the Y axis. Notice how the output switches", - "at +6 volts and switches at a -6 volts to +12 or -12.", - "That's the hysteresis property. And we can actually use this", - "property to build a clock circuit, which is on page 9,", - "build an oscillator that sits there and oscillates by itself.", - "And you will see details of that in recitation tomorrow." - ] -} \ No newline at end of file diff --git a/subs/pnHDLuxmXHo.srt.sjson b/subs/pnHDLuxmXHo.srt.sjson deleted file mode 100644 index 6a6f2be8d6..0000000000 --- a/subs/pnHDLuxmXHo.srt.sjson +++ /dev/null @@ -1,251 +0,0 @@ -{ - "start": [ - 200, - 960, - 4620, - 8960, - 11150, - 12420, - 15490, - 16430, - 21270, - 23350, - 26680, - 27640, - 30660, - 33870, - 35400, - 38440, - 42690, - 45660, - 48420, - 52700, - 54000, - 56210, - 58070, - 60140, - 63270, - 65420, - 67780, - 69250, - 72920, - 78070, - 80770, - 82250, - 82640, - 84470, - 88630, - 92050, - 95180, - 97790, - 101090, - 103030, - 106090, - 107230, - 109350, - 111210, - 112595, - 116310, - 118410, - 121680, - 124690, - 129570, - 132520, - 137390, - 140520, - 142440, - 144980, - 146010, - 147590, - 152290, - 155730, - 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], - "text": [ - "SPEAKER 1: OK.", - "I'm now going to show you a demo of superposition in", - "action with something you see every day in real life.", - "So in this demo, I am going to have an empty", - "vat to begin with.", - "And then what I'm going to do is I'm going to pour some salt", - "water into it.", - "OK, some salt water poured into it will behave like a", - "distributed resistance.", - "And so each small volume of water can be modeled as a", - "lumped resistor.", - "And so you end up with this three-dimensional connected", - "network of resistors.", - "Now, this is a linear circuit.", - "And we will see superposition in action with this circuit.", - "So what do is I'll connect one input to it, which will be a", - "high-frequency triangular wave, like so.", - "OK, that'll be input at one part of the water.", - "And then I will input a low-frequency sinusoid at a", - "different location.", - "So those are my two inputs.", - "And as we've seen before, you can think of", - "these as V1 and V2.", - "And what I'm going to do is I'm going to observe the", - "output at a third port.", - "And my goal will be to take a look at what", - "this input looks like.", - "If superposition truly holds true, then this output should", - "really show both a component that relates to V1 and another", - "component that clearly relates to V2, if", - "superposition really worked.", - "OK?", - "So let's go on to the demo.", - "And as I said before, in the demo, you will see a vat, an", - "empty vat to begin with, into which I will add salt water.", - "And then we will take a look at what happens at the output", - "as I apply two input voltages to it.", - "This is a vat of nothing, right, and it's all empty.", - "So this is a screen of the oscilloscope now.", - "So notice that I have a sinusoid, and I have a", - "triangular wave.", - "And the output is zero.", - "And the reason is there's nothing in this vat.", - "It's empty.", - "Previously when I taught this course, I would get salt water", - "and pour salt water.", - "Then we discovered a much better source of water that", - "conducted electricity, like one real mean", - "fluid, Cambridge water.", - "It just works very pleasantly.", - "It just conducts electricity like nothing at all.", - "And I've been thinking of using Charles River water next", - "time and see what happens.", - "Although there, we'd probably get some biological organisms", - "doing strange things at you.", - "But go ahead.", - "OK, so our friendly demonstration expert, Lorenzo,", - "will pour some water into the vat.", - "And you should begin seeing the output begin superposition", - "now of the two.", - "You see that?", - "So you do see the sinusoidal articulation", - "and the jagged waveform.", - "And just to have some more fun, what I can do is increase", - "one of the voltages.", - "And you'll see.", - "[LAUGHTER]", - "SPEAKER 1: Now you know what would have happened if I'd", - "used Charles River water.", - "OK.", - "So my output keeps increasing as I increase the", - "corresponding waveform.", - "OK?", - "I could do this.", - "This is fun.", - "OK.", - "So let me pause there and go on to the next topic.", - "So that little demonstration showed you that even something", - "as simple as this physical entity, a vat of water,", - "behaves like a linear system.", - "And we can model that linear system as a set of resistors." - ] -} \ No newline at end of file diff --git a/subs/rysqcHqcuBw.srt.sjson b/subs/rysqcHqcuBw.srt.sjson deleted file mode 100644 index 92b5ee3afb..0000000000 --- a/subs/rysqcHqcuBw.srt.sjson +++ /dev/null @@ -1,266 +0,0 @@ -{ - "start": [ - 430, - 2360, - 5150, - 7530, - 8800, - 10650, - 12550, - 15580, - 20230, - 21470, - 24710, - 28570, - 33080, - 36910, - 37760, - 41340, - 43580, - 46300, - 49210, - 50790, - 54340, - 55560, - 58730, - 61340, - 63680, - 66160, - 67470, - 71970, - 75080, - 76780, - 80630, - 82170, - 84340, - 87600, - 89220, - 92530, - 93690, - 97000, - 99880, - 103900, - 105270, - 107520, - 111150, - 113850, - 117880, - 120410, - 124200, - 126160, - 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180260, - 183360, - 186880, - 187670, - 191830, - 193640, - 196620, - 198110, - 201380, - 204390, - 205390, - 208400, - 212220, - 213750, - 217710, - 221690, - 225630, - 227170, - 229870, - 232430, - 235170 - ], - "text": [ - "INSTRUCTOR: Based on the previous method or the", - "previous property that you saw for linear circuits, we are", - "now ready to define the superposition method for", - "circuit analysis.", - "Note that the superposition method", - "applies to linear circuits.", - "And again, to refresh your memory, remember, we are in", - "the EECS playground that we got into by adhering to the", - "lumped matter discipline.", - "And within that, we looked at the node method and the KVL", - "KCL method that applies all over the EECS playground.", - "And then what we'll now do is look at some methods that will", - "apply to only a region of this playground where linear", - "circuits reside.", - "So the first of these methods is the superposition method.", - "And again, it applies to linear circuits.", - "So the method is very simple and inspired by the", - "superposition property that we studied for linear circuits.", - "So the method simply says this.", - "You first find the responses of the circuit to each source", - "acting alone.", - "Think of this as a divide and conquer method where you take", - "your entire circuit, and you find the responses of the", - "circuit to each source acting alone.", - "You turn off all the sources, and you find the response to", - "each source acting alone.", - "Then what you do is simply sum those individual responses.", - "Note that this technique applies to", - "independent sources only.", - "So if I have a linear circuit, then this technique applies to", - "independent sources only.", - "Now we will look at what happens when you have", - "dependent sources and so on in later lectures.", - "OK, let's move ahead.", - "The first step was find the response of the circuit to", - "each source acting alone.", - "But what does it mean for each source to act alone?", - "What it means is that you turn off all the other sources.", - "So for example, suppose we are focused on a", - "voltage source here.", - "What does it mean to turn off this voltage source?", - "In other words, if I want to set this voltage to 0, what", - "does it mean in terms of my circuit?", - "So in terms of my circuit, what this means is that I am", - "going to short the source.", - "So what you do is you short the source, and you end up", - "with a short circuit here.", - "And that is my voltage source having been set to 0.", - "And so I take all my voltage sources in the circuit and", - "simply short them out.", - "And this would be making each of the sources to act alone.", - "OK, next let's look at a current source and see what it", - "means to set a current source to 0.", - "So in this case, what you do is much as you set a voltage", - "source to 0 by shorting it out, you set the current", - "source to 0 by open-circuiting it like so.", - "So you create an open circuit in place of the current", - "source, and that's what it means to set a", - "current source to zero.", - "OK, so now we are ready to go try out an example using the", - "method of superposition.", - "And again, remember the method of superposition has", - "two parts to it.", - "In the first part, you find the responses of the circuit", - "to each source acting alone.", - "And then second, you sum up the partial responses.", - "So let's go back to our old faithful example.", - "In this example, we have two sources, a voltage source and", - "a current source.", - "And let's say our goal is to find the node voltage e taken", - "with respect to this ground.", - "And we are going to use the superposition", - "method to do the circuit.", - "So I showed the circuit on the right-hand corner here.", - "And notice that e is the node voltage that I", - "need to figure out.", - "So by the superposition method, I have two steps.", - "My first step is find the responses of the circuit to", - "each source acting alone.", - "So what I'm going to do is let me start with finding the", - "response of the circuit to the voltage source acting alone.", - "So what do I do to get a subcircuit in which the", - "voltage source is acting alone?", - "So I want you to think about this and try to figure out", - "what the resulting subcircuit is going to look like.", - "I'll give you a few seconds to do that before I do it myself." - ] -} \ No newline at end of file diff --git a/subs/t24YP3JIKI8.srt.sjson b/subs/t24YP3JIKI8.srt.sjson deleted file mode 100644 index ed29622137..0000000000 --- a/subs/t24YP3JIKI8.srt.sjson +++ /dev/null @@ -1,86 +0,0 @@ -{ - "start": [ - 290, - 830, - 4140, - 6550, - 7710, - 10620, - 11890, - 16340, - 19580, - 23230, - 25530, - 27800, - 28160, - 28780, - 32250, - 35850, - 39250, - 40590, - 44190, - 48230, - 50950, - 53700, - 54240, - 58410, - 61390, - 63910 - ], - "end": [ - 830, - 4140, - 6550, - 7710, - 10620, - 11890, - 16340, - 19580, - 23230, - 25530, - 27800, - 28160, - 28780, - 32250, - 35850, - 39250, - 40590, - 44190, - 48230, - 50950, - 53700, - 54240, - 58410, - 61390, - 63910, - 66290 - ], - "text": [ - "SPEAKER 1: All right.", - "So I can apply the KVL rule.", - "The KVL rule simply says that I can take the difference in", - "the node voltages.", - "And then applying the element rule, I can divide by R1 to", - "get the current going up.", - "So the current going up is simply E1 minus V0, which is", - "the voltage difference between these two points.", - "And I can divide that by R1 to get the current going up.", - "And dividing by R1 is the same as multiplying by the", - "conductance, G1.", - "OK.", - "Next.", - "What is the current going in this direction?", - "The current going in that direction is simply E1 minus", - "E3 divided by R3, or multiplied by the", - "conductance, G3.", - "And finally, I can figure out the current going down, which", - "is simply E1 minus 0, which is the ground", - "potential, times G2.", - "And that sums to 0 by KCL.", - "OK.", - "Next let me write down KCL at the node two.", - "So let me give you some practice, and let me pause", - "while you think about doing it yourself.", - "And then I'll go ahead and do it." - ] -} \ No newline at end of file diff --git a/subs/v6vqWasIHaw.srt.sjson b/subs/v6vqWasIHaw.srt.sjson deleted file mode 100644 index 149cc1602f..0000000000 --- a/subs/v6vqWasIHaw.srt.sjson +++ /dev/null @@ -1,1982 +0,0 @@ -{ - "start": [ - 25000, - 30000, - 35108, - 40869, - 46739, - 66000, - 71349, - 74559, - 79588, - 85901, - 90395, - 95077, - 99110, - 103885, - 109085, - 113967, - 119692, - 123078, - 126394, - 130697, - 134929, - 138315, - 142406, - 146286, - 149248, - 158000, - 164495, - 170152, - 175390, - 180000, - 185963, - 190734, - 196590, - 202228, - 208409, - 216000, - 220943, - 226161, - 231105, - 235591, - 242000, - 246222, - 250524, - 255464, - 260085, - 263112, - 267494, - 273589, - 277565, - 281541, - 286996, - 291434, - 298000, - 302655, - 308156, - 313976, - 318525, - 322757, - 326354, - 331761, - 337476, - 340714, - 345380, - 348523, - 351476, - 355857, - 360689, - 365673, - 368460, - 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Good morning.", - "Let's get started. So the last lecture we showed", - "you how to go digital. The fact that going digital had", - "some key benefits for us. And what we'll do today is go", - "inside the digital gate.", - "Let's do a quick review. We began life by observing", - "nature. We said those Maxwell's", - "equations are tough. Let's simplify our lives by", - "discretizing or lumping matter. So we got the lumped circuit", - "abstraction. Then we had this noise problem", - "here. In order to be able to handle", - "that let's do some more discretization,", - "some more lumping. So we said let's discretize", - "values and deal with two levels, a high and a low.", - "That's where the binary voltage levels come up,", - "a high level and a low level. And then we said that in", - "discretizing it we have to make some assumptions.", - "We have to impose some constraints on ourselves.", - "Just as with the lumped matter discipline, we imposed a couple", - "of constraints in going from the continuous matter world to a", - "lumped matter world. Similarly, we have to impose", - "some discipline on ourselves, some constraints on ourselves", - "in going from the continuous value regime to the digital", - "value regime. And that discipline is called", - "the static discipline.", - "And what the static discipline says is that if you have senders", - "and receivers in a digital system then they all need to", - "adhere to some standard. If I was a sender I had to", - "adhere to some tough output standards.", - "I had to be sure to shift values that exceeded some high", - "voltage threshold. And if I was sending a low", - "value I had to make sure my values were lower than some", - "output low voltage threshold. Similarly, if I was the", - "receiver then I had to guarantee to recognize as a one all", - "voltages that where above some input high voltage threshold.", - "And similarly I had to guarantee to recognize as a zero", - "voltages that were below some input low voltage threshold.", - "So provided senders and receivers in a system adhere to", - "these voltage levels, to this discipline then they", - "would all very comfortably work correctly in a digital system.", - "Then we also said that once you deal with such values,", - "one you deal with digital values we can now postulate a", - "bunch of digital elements that process these values in a manner", - "very reminiscent of our analog circuits where we get analog", - "signals. And you've already learned how", - "to process analog signals. You've learned about resistor", - "dividers and so on and so forth. You feed in an analog signal", - "and you get an output analog signal as well.", - "Now, here the resistor in the analog domain,", - "elements like resistors and voltage sources were the symbols", - "that you dealt with. Here, in the digital domain,", - "the primitive elements that we will be using are called gates.", - "As one example, this is called the NAND gate.", - "So we looked at the AND gate in the previous lecture.", - "This is an example of another gate called the NAND gate.", - "The NAND gate has the following truth table.", - "Our two inputs A and B and this output C.", - "And the NAND gate works as follows.", - "The output -- In English I can describe its", - "properties as the output is a high at all times when at least", - "one of these inputs is a low value.", - "So it's high whenever at least one input is a low.", - "So it's high here. It's high here.", - "Oops, it's high here, high here.", - "And when, oops. And when both inputs are a high", - "the output is a low. This is a NAND gate.", - "Notice that these are exactly complimentary to the AND gate.", - "The AND gate outputs were 0-0-0-1.", - "And the AND gate symbol looked like this.", - "In general, notice that this little bubble here,", - "it's called a bubble. That bubble implies a negation,", - "an inversion. So we take the AND gate,", - "invert the output and negate the output and you get the NAND", - "gate. So these elements are", - "combinational gates. And in combinational gates they", - "adhere to two properties. One is that they must satisfy", - "the static discipline.", - "All the systems, all the elements in our", - "repertoire in the digital domain need to satisfy the static", - "discipline. And the properties of a", - "combinational gate are that its outputs are a function of inputs", - "alone.", - "In other words, it doesn't store any state or", - "doesn't store any history inside it.", - "You can figure out its output just by looking at the inputs at", - "that instant. Think of it as a completely", - "transparent entity where its output reflects some function of", - "the inputs at every instant of time.", - "So I'll show you an example of a digital circuit.", - "So much as I could interconnect resistors and voltage sources", - "and current sources to build analog circuits,", - "I can now build digital circuits using primitive", - "elements such as these. So, for example,", - "I could build a simple circuit that looked like this,", - "two inputs A and B here, I get an output.", - "And I feed that to another NAND gate with another input C.", - "This device is called an inverter.", - "The inverter simply flips the sense of the input.", - "So if C is a 1 the output is a 0, if C is a 0 the output", - "becomes a 1. It's an inverter.", - "It simply inverts its input. Yet another primitive device.", - "And this is my output D. So there are three gates in", - "this design. And I can quickly write down", - "what the output looks like using some very simple Boolean algebra", - "or dealing with Boolean values here.", - "So for AND gate the output is A and B.", - "Remember dot is a short form for and.", - "But there's a negation, inversion, so represent", - "inversions with a bar. So my output is A dot B bar.", - "There is a C here. So this is my output C bar.", - "And this is a NAND gate. So it takes one input A dot B.", - "It takes the second input C bar and ANDs those and inverts them.", - "So that's the output. So there are three gates in", - "this example. So you can think of building", - "very complicated circuits containing large numbers of", - "gates. In fact, the microprocessors", - "that you use in your laptop contain a large number of gates.", - "Can someone guess how many gates are in the Pentium IV,", - "roughly? Approximate,", - "how many? How many gates in a Pentium IV?", - "40 million. 100 million.", - "In the Pentium IV you have on the order of 20 million gates.", - "20 million gates in the Pentium IV.", - "And life begins in 002. Here you learn about onsies and", - "twosies, and in the real world you will be dealing with tens of", - "millions of gates. But this is for the Pentium IV.", - "My research group at Laboratory for Computer Science built a", - "chip called the Raw chip. And this chip has 3 million", - "gates. And so there are several", - "undergraduate students involved in this project in their third", - "year, and they're beginning to deal with millions of gates.", - "So the key thing to remember is that 002 provides the", - "foundations where you make the switch from the analog signal to", - "the digital signal or from continuous matter to lumped", - "matter. And learn about the foundations", - "of these primitive elements. And by the end of this course", - "you will begin dealing with small systems,", - "analog systems that contain on the order of 10 to 20 primitive", - "elements. You will also begin dealing", - "with small digital systems that contain tens of gates.", - "In your final project you will build a mixed signal circuit", - "involving an audio playback system.", - "You will have digital data stored in a memory chip and you", - "will build a circuit to extract that data, filter it and then", - "convert it to the analog domain and then play it on a set of", - "speakers. And that has on the order of", - "about 50 to 100 primitive elements.", - "So by the end of 002 you will have learned to deal with", - "hundreds of elements. And then you will take other", - "courses like 004 and so on where you will then make the leap to", - "learn further abstractions that will take you from subsystems to", - "systems with millions of gates. So the key is to manage the", - "complexity of dealing with millions of gates it's all about", - "abstractions. You have to build abstractions", - "and double abstractions so you can deal with complexity.", - "So the rest of EECS will take you from three gates to 20", - "million gates and software systems that operate on 20", - "million gates or whatever. So there is still a ways to go.", - "Lorenzo, our friend has gone to bring a demonstration that we", - "forgot to bring today. That will show you that little", - "digital circuit in a mock up form.", - "So what's today's lecture about?", - "Today's lecture is going to be about what's inside a gate?", - "How to build a gate. Once you build a gate you can", - "then put millions of them into computer systems or analog", - "systems or other sorts of systems.", - "And what we'll do here is understand what's inside this", - "abstraction. This is an abstract element", - "that looks like a little circle and a line with some stuff", - "inside it, with some properties. But someone's got to build", - "that. It doesn't come from nature.", - "You don't go and harvest gates from trees, you got to go build", - "that, and someone has got to do that.", - "So what to learn here is how do we go about building a gate?", - "And here you will see practically how do you deal with", - "voltage thresholds that satisfy a given static discipline?", - "So before I jump into building a gate, let me try to build up", - "some intuition. As is my usual practice,", - "I'd love to get you to build some intuition as to how to", - "build a gate. And then we'll go through the", - "mechanics of doing it. So to build intuition,", - "let me show you an analogous situation in fluids.", - "So let's say I have a cauldron of water.", - "This is like a power supply. And I need to feed this fluid", - "down at some output source. And what I do in the middle is", - "put in a couple of taps, faucets, all right?", - "And so what do these guys do? Under what condition do you", - "have fluid flow out of the tube at the other end?", - "You will have fluid flow if -- So let me call this A and B.", - "If A is on and B is on then C has water.", - "Otherwise, if both A and B are not on then C has no water.", - "So this is already beginning to sound like a AND gate,", - "correct, where you get water only if A and B are both turned", - "on. So we're going to use this", - "insight, a stream of some flow and I put things to obstruct the", - "flow. And when both the obstructions", - "are lifted I get the output. I want to use that intuition to", - "build an AND gate. Similarly, I could build a", - "system that allows me to build the following structure --", - "So in this scenario let me call this --", - "-- the signal of A and B here. And in this situation under", - "what conditions, provided the power supply has", - "water, under what conditions do I get water out?", - "In this situation, it is I get water if A or B are", - "turned on. So I don't need to turn both A", - "and B on. If either one of them is on,", - "I'm going to get fluid flow here.", - "So this will help us build the inside to build the OR gate.", - "So that's an analogy involving items we see in everyday life.", - "Let me now move into the electrical domain.", - "In the electrical domain my analogy would be something like", - "this. Let's say I have a power supply", - "and I have two switches A and B. And I build a little circuit", - "that connects this voltage source across the bulb using a", - "couple of switches. In this case,", - "the bulb is on if both switches A and B are on.", - "My bulb turns on. If I switch either one of them", - "off my bulb turns off. So notice that I can begin", - "implementing things like this if I had this element.", - "I had sources already. I know how to deal with bulbs.", - "I model them as resistors. So I need to do something about", - "this new element called a \"switch\".", - "So let me build an abstract device.", - "I'll tell you how to do that in real life in a second.", - "So if I had the switch I could build things like this.", - "I could put switches in series in a circuit and get myself", - "something that looks like a AND function.", - "So let me go ahead and build an equivalent circuit for a switch.", - "So the switch has a couple of terminals here and I have a", - "control. Switches have a control and", - "they have a pair of terminals. And the equivalent circuit for", - "this looks like this. This is for my switch.", - "So when control is a 0. Then my switch is open to give", - "me an open circuit in the circuit that I've shown you", - "here. And, by the same token,", - "if my control is a 1 then --", - "-- I have a connection between in and out.", - "And this is a short circuit. So, in other words,", - "if my switch has 0 at its control, I'll talk about how to", - "get that, I have an open circuit, and if it's a 1 then I", - "have a short circuit. This is a switch going on and", - "off. Now, in traditional switches", - "mechanical pressure is my control signal.", - "If I apply mechanical pressure my switch could turn on.", - "And if I take away the mechanical pressure then I could", - "get an off situation. So let's for now imagine that", - "we have a switch. I still haven't told you how I", - "am going to get a switch in real life.", - "Let's imagine you have a switch.", - "It's a three terminal device. There's a control thingamajig", - "coming in. Input and an output.", - "So let's build the following little circuit containing a", - "switch. So what I'm going to do,", - "I will take a resistance RL and plug it in here.", - "And connect my power supply like so.", - "So the little circuit that I build has a resistor.", - "And I connect the switch in this pattern and I get a VS.", - "Lorenzo, you can set that up there if you'd like.", - "No problem. So I get a VS here.", - "Now, a couple of lectures ago I told you that 6.002,", - "and for that matter, 004 and many of our other", - "courses deal with combinations of elements.", - "And we often deal with the same kinds of combinations again and", - "again and again. We see the same sorts of", - "patterns happening, and we need to begin to learn", - "to identify these patterns. This is an incredibly common", - "pattern. You'll see this pattern more", - "times in 6.002 than any other pattern, I promise you.", - "A power supply connected to a resistor and connected to a", - "couple of terminals of some interesting device.", - "I promise there will be at least one such pattern on the", - "quiz, for example. These patterns are incredibly", - "common. So let's take a look at the", - "interesting properties of this pattern.", - "Since this pattern occurs so commonly, I am going to create a", - "short form. I have already created a short", - "form which is this ground node here.", - "By putting ground 0 all I'm really saying is that there is a", - "wire connecting these two and that's my ground.", - "So I already have a short form here.", - "My second short form is when I connect a power supply to a", - "node. Then what I'm going to do is", - "come up with yet another short form that looks like this,", - "an up arrow with the voltage written there.", - "This symbol simply says that this node is connected to a", - "power supply with voltage, or a voltage source voltage VS.", - "So I just have come up with a slightly simpler representation", - "for the little pattern that I have.", - "Now let's take a look at the properties of this little", - "system. Let's first look at what", - "happens when C is 0. When C is 0,", - "let me draw the equivalent circuit for this using the open", - "circuit out there.", - "That's what I get, OK?", - "So when C is 0, if VS is a high voltage,", - "let's say 5 volts, what do you expect at the", - "output if C is a 0? This voltage VS appears at V", - "out because this is an open circuit here.", - "Remember, RL and this little device form a voltage divider.", - "But since it's an open circuit its resistance is infinity.", - "And so therefore in this resistor divider all the voltage", - "falls across this open circuit. So, in this case,", - "v out is a 1 or a high voltage. But let's take a look at what", - "happens when C is a 1. In this situation,", - "I have my RL, that's what I have.", - "It's a short circuit at the switch and C is a 1.", - "So what's the voltage v out in this case?", - "Not surprisingly, since I've shorted this node to", - "ground the voltage at this point is 0.", - "So if I have low voltage that's corresponding to logical 0s that", - "corresponds to a 0. So I can build a simple truth", - "table for C and use logical symbols here.", - "So when C is a 0 I get a high at the output and when C is 1 I", - "get a low at the output. Have you seen a device that", - "behaves like this so far? That's a little inverter.", - "That's the exact behavior of an inverter.", - "So this thing I've written here is a truth table for an", - "inverter. So notice with just a simple", - "little switch and a resistor, I have managed to build an", - "inverter. Before I go on,", - "I guess we have some things to show you.", - "And let me pause for a couple of seconds and do that.", - "First of all, what I want to show you is the", - "following idea. So as I was preparing for this", - "lecture last night I said, now here I am telling the 6.002", - "gang that you need to learn about analog circuits and", - "resistors and all of that stuff, and you also need to learn", - "about digital systems and all of that stuff.", - "And I said, because these two are very commonplace and often", - "times they occur together. So I said well,", - "if I really believe in my own BS then there should be", - "something around me where I can find both of them", - "instantaneously. So I said let me do the", - "following experiment. Let me close my eyes and reach", - "out and see what I touch. So I closed my eyes,", - "reached out, and guess what?", - "I touched the lonely mouse. The mouse.", - "So I said let me see what is in side the mouse.", - "And if I believe in my BS we should find analog,", - "little components and digital components in there,", - "right? So let's see what is inside the", - "mouse. All right.", - "There we go. Don't try this at home,", - "as with many other things we do in lecture.", - "Come on. Show me what I want to see.", - "OK, here we go. Not bad.", - "Let me show you what we have here in this poor shattered", - "mouse. That's my finger,", - "silly. You should recognize this", - "little resistor here. That thing with the little", - "bands, oh, here we go. We'll use this.", - "That's a resistor. And you'll see capacitors in", - "about four weeks. That's a capacitor.", - "And there is a digital IC here. That's a digital IC.", - "That contains a bunch of gates inside it.", - "So this mouse has not made a liar out of me.", - "So what I just showed you was a little device that we use in", - "everyday life that has both analog components and digital", - "components. A large number of devices that", - "we use in daily life are this way.", - "You can do the same thing to your laptop.", - "You could go try it out. And you will find a bunch of", - "analog components and a bunch of digital components.", - "And you really, really need to understand the", - "whole caboodle here. Let me show you a fun little", - "demo involving gates. Now, I want you to be very", - "careful here. Lots of caveats here.", - "If your grandmother asks you how big is a gate don't say this", - "big. This is how big gates used to", - "be, I would say, when they were first invented.", - "When they built gates out of discrete vacuum tubes and so on,", - "this is how big a gate used to be.", - "This is roughly that big. Today in a chip,", - "in a small VLSI, very large scaled integrated", - "circuit in a chip, which is about 1 cm on the", - "side, how many gates do you think I can fit in a thumbnail", - "sized chip? Any guesses?", - "With today's technology, how many gates can I fit on a", - "chip? It has to be more than a", - "million because I just told you that Pentium IV was 20 million", - "and that was a year ago. How many?", - "40 million is a good guess. So on the order of 40 to 80", - "million gates in a 1 square centimeter.", - "Intel just announced that they will be shipping a chip", - "containing 1 billion switches. Remember, this whole thing is a", - "gate, right? Inverter, a resistor and a", - "switch. This thing is a switch.", - "So Intel is going to be shipping something containing a", - "billion of those little elements.", - "Just keep those large numbers in mind.", - "So here is a little circuit that I showed you here,", - "A, B, the NAND gate, the NAND gate at the output and", - "the inverter. So this output A is going to be", - "1 whenever either A or B is off. So the output is a 1 in this", - "case when both A and B are off. I turn A to 1,", - "output is still a 1. So the moment I turn both of", - "these inputs into a 1, these are 1s,", - "the output goes to 0. That's behavior for NAND gate.", - "If I switch any one of the inputs to a 0 the output should", - "go to a 1. Similarly, for the inverter", - "here, when the input is a 0 the output is a 1.", - "And when I switch it so should the output.", - "Now imagine a circuit, a little chip containing", - "billions of these devices. And just imagine all of these", - "1s and 0s flying around. So one simple switch in the", - "input, like a click of a keystroke could actually cause a", - "billion signals in your circuit to be flipping around.", - "And that causes some fun stuff to happen, which we will learn", - "about a few months from now. But for now that's a quick show", - "of a little circuit that looks like that.", - "Let me go back to talking about building other types of gates.", - "So that was an inverter. So now you know.", - "You're almost halfway to being able to build a Pentium IV.", - "You've come all the way from nature to gates.", - "And Pentium IV contains 20 million of them so you now know", - "how gates are built. So that's an inverter.", - "Let's look at how we can build other forms of gates.", - "To build another gate let me do this.", - "How about this pattern? If I build a pattern like this", - "with A and B coming in here and I put two switches with their", - "inputs in and out, so two switches in series.", - "Let's write down the truth table for what this looks like.", - "Let's see. When A and B are both 0,", - "what should the output be? These are both off so the", - "output is directly VS which is a high.", - "When either of these switches is off 0-1 or 1-0.", - "If either switch is off then this node is cut off from", - "ground. There is no current flowing", - "here. So this entire voltage drops", - "across this infinite resistance here, and so I get 1s at the", - "output as well. If both switches are on what", - "happens? If both A and B are on then I", - "get a short circuit to ground and my output is a 0.", - "So can someone tell me what gate this is?", - "Awesome. We just build a NAND gate.", - "This is unbelievable. Five lectures and you've", - "already come all the way from nature to the primitive building", - "blocks of microprocessors. It's pretty amazing.", - "So what about this one here?", - "What's this? I haven't told you this before", - "but if an AND gate becomes a NAND gate, this is kind of an OR", - "arrangement, what should an OR become?", - "NOR. It's all completely logical.", - "So you can go home and practice a truth table for this.", - "A, B and C. I'll just fill in one of the", - "rows. So in this particular", - "situation, if both A and B are 0, if A is 0 and B is 0,", - "both the switches are off, so it's as if this little", - "sucker here is cut off from ground and VS falls across from", - "C to ground here and the output is a 1, so on and so forth.", - "So I can build other interesting forms of gates.", - "So let's say I build something that looks like this.", - "I build something like this.", - "You can write the truth table for this or you can look at this", - "and write down the function that this one supports.", - "Notice that this output here is going to be a high only when", - "both of these are not connected to ground.", - "And if you stare at it some more the function this one", - "presents, this is my AND function.", - "Suppose this one didn't exist, that would be my AND function.", - "But because this one exists that's in an OR configuration", - "and so I get a C. And so because of that I get", - "something that looks like this. So this is my A dot B,", - "this is my plus because of a parallel here,", - "and ultimately this caused an inversion in this gate.", - "So the primitive pattern has a generic inversion built into the", - "output. That is why they commonly end", - "up building NAND gates and NOR gates and so on as the simplest", - "gates. We don't build AND gates and OR", - "gates. How can I convert this one to", - "an AND gate? Anybody?", - "Put an inverter on the output. So what I can do is take this", - "little sucker here, put an inverter here and I get", - "an AND gate. So the real primitives in", - "circuits tend to be NANDs and NORs.", - "OK. So the real practical among you", - "should be saying at this point all right, all right,", - "I buy this, if there existed a switch.", - "I know exactly how to go from nature to building Pentium IVs", - "if there exists a switch. So that the obvious next step", - "for me is to show you a switch, a physical switch device.", - "And to introduce a switch device, let me show you a three", - "terminal element. Remember, the switch has three", - "terminals, an input, output and something called the", - "control, C. So I'm going to introduce a new", - "primitive element called \"The MOSFET Device\".", - "MOSFET stands for metal-oxide semiconductor field-effect", - "transistor. This is shortened to FET or", - "transistor. Now I'm going to show you that", - "this works like a switch. And before I do that,", - "in fact, let me do that first. Then I'll show you something", - "else. So this device has the", - "following symbol. It has a terminal called a", - "gate, the drain and the source. Gate, drain and source.", - "Three terminals. This is the primitive element", - "that forms virtually every electronic component built", - "today. This is the foundation of the", - "universe. So this little MOSFET device,", - "we can look at how it behaves. I'll show you this thing on the", - "screen in a second, but this guy behaves very much", - "like this device I was postulating earlier.", - "Let's take a look at this device on the scope.", - "To do so let me label some voltages and currents.", - "So let me label this voltage as vDS.", - "Let me label this voltage as vGS between the gate and the", - "source. And let me label the current", - "coming into this node iG. In this device,", - "the physical device that I'm going to show you,", - "the current going into the gate is always 0.", - "So iG is always going to be 0 for 6.002.", - "In real life there is some leakage and so on.", - "But in 6.002 for now we deal with a very simple abstract", - "model, iG is 0. And let me label the current", - "here as iDS. To be correct with the", - "nomenclation, the current into node D should", - "be labeled iD, but because iG is 0 iD flows", - "out through the source as well, so I would simply call it iDS", - "just so that I can show that vDS and iDS are the two voltages and", - "currents that I am going to deal with.", - "So that's my little device here.", - "And notice that the source terminal is common.", - "I use the source both for the control GS and I use the source", - "for the drain as well. So you can view this as input,", - "view this as out, and you can view this,", - "if you like, as the control abstractly.", - "So let me show you a plot of how this behaves.", - "To understand how it behaves, I can draw an equivalent", - "circuit for it. So in this particular", - "situation, if its behavior is characterized by the voltage", - "applied to vGS. Much like the control on the", - "switch, vGS is my control. So if vGS is 0,", - "oh, I'm sorry. If vGS is greater than or equal", - "to some threshold voltage VT -- So vGS, the voltage applied", - "here is greater than some voltage, VT, a threshold", - "voltage, or the pressure of the switch is greater than some", - "threshold pressure then this guy behaves like a short circuit.", - "This is iDS, this is my drain and this is my", - "source. So if the voltage applied", - "between the gate and the source is higher than some threshold", - "then this behaves like a short circuit.", - "Similarly, if the voltage vGS is less than some threshold VT", - "then in that situation --", - "-- I get an open circuit. And when I have an open circuit", - "between D and S then the current iDS is going to be 0.", - "So this is the idealized model. And this idealized model is", - "called \"the switch model of the MOSFET\".", - "The switch model or the S model of the MOSFET.", - "Well, if you want to see the internals of the MOSFET,", - "I won't cover that in lecture or recitation.", - "You can look at the section, I believe Section 6.7 of the", - "course notes. That has the internal structure", - "of the MOSFET and how you physically construct such a", - "device. So what I can do here is step", - "back and stare at the device for a second or two.", - "And what it says is that if I apply a lot of pressure,", - "if vGS is greater than a threshold VT then I get a short", - "circuit here just like my switch.", - "When in doubt think faucet. If you put pressure on the", - "faucet, think of this as closing, and when I open it,", - "when vGS goes less than VD, less than a threshold,", - "I take off the pressure and then it becomes an open circuit.", - "So I can plot the following.", - "Much like I plotted the iV characteristics of two terminal", - "elements, I can plot the iV characteristics of this three", - "terminal element in the following way.", - "I can focus on two terminals and look at vDS and iDS for that", - "terminal pair and draw the curves for how it will behave as", - "I change vGS that I applied. So what I'm going to show you", - "is that if vGS is less than a threshold then this behaves like", - "a open circuit. So no matter what the voltage", - "is the current is 0. Similarly, if vGS greater than", - "equal to some threshold voltage then I get the behavior iV curve", - "of a short circuit where the current can be anything and", - "controlled by external forces like in any short circuit.", - "So let me show you on the screen.", - "Lorenzo has kindly put the graph up already.", - "So I'm showing the iV curve of a switch.", - "Notice that when vGS is greater than VT, greater than a", - "threshold I get the vertical line corresponding to a short", - "circuit. Is it this one?", - "This one. There we go.", - "So what I'm going to do here is I'm going to reduce vGS to below", - "VT. What should you see happening?", - "The curve, from being a short circuit, should hammer down to", - "becoming an open circuit. That's the curve for an open", - "circuit as I drew out there for you.", - "VGS pressure ain't enough. Lots of pressure,", - "boom, it's a short circuit. I really like to think of this", - "pressure analogy if I get confused whenever I look at a", - "MOS transistor and I need to look at vGS and so on I always", - "think vGS is greater than VT. Lots of pressure on the switch", - "it turns on. Just remember that,", - "and then you won't forget this vGS thing here.", - "So that's the behavior of a switch.", - "And so viola, there's our switch.", - "So I've given you a three terminal element that is a", - "switch that is controlled like a mechanical switch.", - "So I can build a, if I replace --", - "This was my switch earlier. And what I can do is replace", - "this with my MOSFET and that's what I get.", - "And I won't bother showing you this is your inverter.", - "All of that has replaced the abstract switch with a physical", - "switch which behaves as shown in the graph up there.", - "And so I apply an input here and I take the output here.", - "So as 6.002 you could look at this and say ah-ha,", - "that is an inverter. When you go to 004 what you", - "will do is build this triangle and a circle around it and you", - "will ignore what's inside and just look at that.", - "So in 002 we showed you that the internals look like a", - "pattern with a MOSFET and a resistor, but it's really the", - "abstract inverter looking in from the outside.", - "I'm just going to close the loop inside the digital gate,", - "and this was inside your little inverter with a resistor and a", - "switch. Let me continue with this for a", - "little longer here --", - "-- and do something that we like to do a lot,", - "which is plot what are called input / output curves.", - "So let's say the voltage applied here is v in and let's", - "call this v out. For fun let's plot a v in", - "versus v out for this inverter. So when input is a 0,", - "let's say VT is 1 volt for the inverter.", - "The threshold voltage is 1 volt.", - "The threshold pressure is 1 volt.", - "So when input is a 0, and let's say VS is 5 volts.", - "So when the input is a 0, this guy is turned off.", - "So what's the output? What's the output voltage?", - "If this is turned off, what's the output voltage?", - "It's the supply. The supply directly shows up", - "here. And so as long as the input is", - "0 the output is at 5 volts. And this is true until the", - "input reaches 1 volt. As long as the input is less", - "than 1 volt my output stays high.", - "And then when my input exceeds or hits 1 volt then at that", - "point the switch turns on and the MOSFET turns on and shorts", - "the output to ground in which case boom, this is what I get.", - "And then, no matter how much I increase the input,", - "my switch stays on and the output follows a zero volts at", - "the output. So this is my v in versus v out", - "curve for the inverter. One of the interesting things", - "that we do a lot is see whether this satisfies some voltage", - "threshold. So let's say I have a VOL of", - "0.5 volts, VOH of 4.5, VIL of 0.9 and VIH of 4.1", - "volts. So VOL says in its low value is", - "the output less than 0.5? Yup, output less than 0.5.", - "In its high is it more than 4.5?", - "Yup, it's more than 4.5. Does it recognize all values", - "below VIL as a low input? Yup.", - "So anything below 0.9 or 1 for that matter is viewed as a low.", - "That's good. So these pass.", - "And high, anything above 4.1, is that treated as a high?", - "Yes. So anything above 4.1 is", - "treated as a high and the output goes low.", - "So therefore this inverter that I've designed for you here", - "satisfies the static discipline and this inverter can be used in", - "circuits or other devices that conform to this value here.", - "In your recitation, you will look at a slightly", - "more detailed model of the switch where the switch behaves", - "like a resistor." - ] -} \ No newline at end of file diff --git a/subs/wNuBD4PYWvs.srt.sjson b/subs/wNuBD4PYWvs.srt.sjson deleted file mode 100644 index 2e74e81caf..0000000000 --- a/subs/wNuBD4PYWvs.srt.sjson +++ /dev/null @@ -1,2117 +0,0 @@ -{ - "start": [ - 0, - 4137, - 24000, - 28142, - 32865, - 36511, - 39991, - 44051, - 48028, - 53000, - 57514, - 60548, - 64840, - 68170, - 71426, - 74829, - 78012, - 81712, - 85560, - 95000, - 99992, - 103715, - 111000, - 115016, - 118351, - 122979, - 126393, - 128820, - 131400, - 136027, - 139213, - 143310, - 147406, - 151553, - 156750, - 160096, - 164852, - 170224, - 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OK.", - "The topic for today is Energy and Power.", - "Most of the time this semester, up to now at least,", - "we focused a lot on speed. We have been truly speed freaks", - "looking at how fast can we switch the signal,", - "what does a time domain waveform look like?", - "We also looked at frequency responses of circuits.", - "This week we will spend on something a little bit", - "different, and that relates to energy and power.", - "Energy and power is gaining a lot more importance in certainly", - "this decade, and will do so in the future.", - "And I am going to work out a little example towards the end", - "of the lecture. And there you will see that if", - "you do things naively, your handheld devices,", - "your cell phone, laptops and so on will just up", - "and explode. You have got to be a little bit", - "careful in terms of how to manage energy and power.", - "Before I get into that, I just want to wrap up with a", - "quick review of what we covered last week.", - "We ended last week by looking at positive feedback in analog", - "circuits using an op amp. And, in particular,", - "we built an oscillator.", - "We built an oscillator that allowed us to charge a", - "capacitor. And when the voltage across the", - "capacitor equaled that at the minus terminal it would flip and", - "keep doing so. And at the output you would get", - "a waveform that looked like this.", - "You would get a square wave output.", - "Now, throughout the course we have talked about getting square", - "wave inputs. And this is one example of how", - "you can actually produce a square wave pretty much from", - "first principles using a capacitor, resistors and an op", - "amp. Now, I just wanted to wrap up", - "this little item here by talking about one application of an", - "oscillator. And this application of the", - "oscillator really nicely closed the loop on the body of", - "knowledge relating to digital circuits that we have covered in", - "this course. What I want to talk about", - "briefly is a small digital system with a sender and a", - "receiver. And the sender is sending a", - "signal, the receiver receives a signal, and in this course we", - "have talked about senders sending a sequence of ones and", - "zeros. Say, for example,", - "the sender wants to send some sort of a signal like this.", - "We have seen that this is quite a legitimate signal.", - "We get some kind of oscillatory behavior because of the", - "inductance and capacitance associated with the wire.", - "And what you have done is that you pretty much believed me when", - "I said that this really corresponds to a one,", - "one, zero. The sender wants to send a one,", - "one, zero signal to the receiver, and the receiver gets", - "it. So this is a one,", - "this is a one, this is a zero.", - "But if I am a receiver, I am going to look at the", - "square wave. There is no such thing as", - "sending a one on a wire. You cannot send a one on a", - "wire. You send a voltage signal or a", - "current signal on a wire. So, the receiver receives a", - "voltage signal. It is going to be zero for some", - "time and then maybe 5 volts or 3 volts or whatever is your high", - "and then zero again. How does my receiver know it's", - "a one, one, zero? Why can't it be a one,", - "one, one, one, zero, zero, zero?", - "It doesn't know. How does the receiver know it's", - "a one, one, zero sequence and not 50 ones followed by 40", - "zeros? It doesn't know.", - "What we need is -- For senders to be able to", - "communicate with receivers, we need some kind of agreed", - "upon time when receivers sample the signal coming in and decide", - "whether it's a one or a zero. They both have to agree on", - "certain time bases when to look at the input.", - "One way to deal with this is I can have a clock,", - "a square wave signal that we call a clock in digital systems", - "and ship it to the other side in the following manner.", - "This clock signal can be applied to this sender and to", - "this receiver. For more details on this,", - "let me recommend Page 735 of the course notes that talks", - "about a detailed example of the use of a clock in a digital", - "system. What I can do is create a clock", - "that looks like the square wave. The clock provides a notion of", - "time to the circuit. And I have some kind of a clock", - "signal generator. And I connect that to the", - "sender and connect that to the receiver.", - "And now both the receiver and the sender have a notion of", - "time. And what I can do is I can tell", - "my receiver, the sender and the receiver can have an agreement", - "between them that says that look at the signal at your input when", - "on the rising edge of the clock. Whenever the clock rises,", - "when you see a rising edge look at the value in the wire and", - "that's the value I sent. By doing so,", - "what I can do is that the receiver can look at the signal.", - "At this rising edge it sees a zero, this is vOH,", - "looks up here, sees a one here,", - "sees a one here and sees a zero.", - "So, it correctly sampled one, one, zero at the receiving end.", - "And the sender can send the same sequence here once we have", - "this time base. This little brief foray", - "circuits was simply to give you an application of a circuit that", - "can produce a square wave. I can create a clock with a", - "time base. Also, interestingly much more", - "fundamental is we looked at various abstractions throughout", - "the course. We talked about discretizing", - "space by looking at lumped signals.", - "What I also want to point out is that a clock can be viewed as", - "another fundamental abstraction in the digital domain where what", - "I am doing is discretizing time. What I am saying is that,", - "look, in the digital domain we have already discretized value", - "into zeros and ones, but we still had continuous", - "time until now. And what you do in digital", - "systems is to say that look, let's digitize everything,", - "or rather discretize everything.", - "And let's discretize time as well into these points that", - "happen on the rising edge of the clock which means that the", - "circuit has meaning, signals have meaning only when", - "the clock is rising. That tends to discretize time", - "which means that I really don't care what happens to signals in", - "this time, as long as on the rising edge of the clock I get", - "the right value. This concept is called", - "discretizing time. And a clock lets you do that.", - "Remember that in digital systems, which you will learn", - "about in 004 I am really discretizing two things,", - "discretizing values into zeros and ones, and at the same time", - "also discretizing time into a time when I sample things and a", - "time when I ignore values on the wires.", - "I think you will get to clocks in 6.004 after about a month,", - "so initially you would just be focusing on the statics of the", - "system without worrying about any dynamic clock introduced in", - "the circuit. OK, that's just a brief little", - "interlude. With that let me get into", - "today's topic of energy and power.", - "Why is this important? The reason this is important is", - "that what really determines the size of your handheld?", - "You may think oh, gee, electronics in the", - "handheld. Some of you may think,", - "oh, the antenna in the handheld.", - "No. What really,", - "really determines the size and weight of your handheld devices,", - "your PDAs, your cell phones, your laptops and so on is by", - "and large the battery. On Page 2 I have a little", - "cartoon that shows you that if we did not have you learn about", - "energy and power, that's what we would all be", - "doing in order to use cell phones.", - "Not surprisingly the very first wireless phones ended up in", - "automobiles because you had a big battery.", - "And so you had these wireless phones only in cars.", - "Because of a huge amount of research based on the knowledge,", - "the technologies I am going to talk about in today's lecture", - "and Thursday's lecture, you will see very simple and", - "elegant ways of reducing the amount of battery you need to be", - "able to get some kind of function out of analog or", - "digital devices. I also want you to take a look", - "at Page 2 of the handout that I have given you here,", - "handout 63. This handout talks about the", - "absolute latest in digital fabrication technology out", - "there. This is not a paid commercial", - "for IBM. IBM has a technology called", - "CU08. It is called Blue Logic.", - "It is called the Copper 08 Process.", - "And in this process, if you look down on Page 1,", - "for example, IBM claims that it can build up", - "to 72 million gates in a single chip.", - "With this technology they are able to build 70 to 80 million", - "gates where a gate is, unless otherwise mentioned,", - "pretty much defined as a two input NAND gate equivalent.", - "So, your inverter, your NAND gate and so on count", - "as a gate. And they can build close to 80", - "million of these little suckers on a single chip.", - "Just imagine that. And the biggest chip they can", - "build is on the order of 18 to 19 millimeters on a side,", - "roughly two centimeters on a side.", - "On a chip that's about one square inch.", - "You can put down 80 million gates.", - "What is more important for today is what is on Page 2,", - "actually. I have circled two things on", - "Page 2. One thing that I have circled", - "is power supply range in the 0.7 to 1.3 volts.", - "Notice that that voltage, the power supply voltage for", - "these chips is significantly lower than the 5 volts that we", - "have been normally talking about in this course.", - "When in doubt our problems have used 5 volts.", - "But notice that in this technology they're talking about", - "using voltages for the power supply VS in the range of 0.7 to", - "1.3. Why is it so much lower?", - "Well, you will find out. The second thing I've circled", - "is something called power dissipation.", - "And you say power dissipation is said to be 0.006 microwatts", - "per megahertz per gate. It says power dissipation is 6", - "nanowatts per megahertz per gate.", - "What that says is that each gate off your circuit will", - "dissipate this much power at a 1 megahertz frequency.", - "And the implication of that is that you should be able to", - "convert that single number to the power dissipation in any", - "chip that you might build depending on the number of gates", - "that you have, the frequency you run the", - "circuit at, the voltage that you use and so on and so forth.", - "By the end of today's lecture you will be able to take this", - "number and correlate that into the power dissipation of any", - "chip that you might want to build with this.", - "That just serves as the motivation that by the end of", - "this lecture you will understand how to very quickly in five", - "seconds or less, boom, given a chip,", - "oh, yeah, that should consume about 30 watts of power.", - "And what you will also do, based on some examples here,", - "estimate the power of not the Pentium IV but a chip following", - "the Pentium VI, let's call it the Pentium V", - "would consume if it ran at 1 gigahertz.", - "We will come up with some absolutely shocking numbers", - "based on what you have learned. With that kind of motivation", - "let me get into talking about some theory and get into the", - "foundations of energy and power.", - "Let's go to Page 3.", - "To drive the theoretical discussion, I would like to", - "focus on the energy dissipated in a MOSFET gate.", - "And fundamentally we will talk about looking at energy and", - "power in circuits containing switches, resistors and", - "capacitors. The MOSFET gate is simply an", - "illustrative example to drive the theory.", - "But fundamentally what I am going to show you,", - "or lead you through today, I will tell you how to compute", - "the power and energy when you have capacitors,", - "resistors, voltage sources and switches in your circuit.", - "We will look at a circuit that looks like this.", - "Your vanilla inverter circuit.", - "My inverter. I apply some vIN signal here.", - "It could be a square wave. It could be some sequence of", - "ones and zeros. And this is an inverter that we", - "all know and love. And this guy here is,", - "stuck in a capacitor here. And this capacitor is meant to", - "model the input gate capacitance of whatever this inverter drives", - "plus any capacitance of the wire leading up to that gate and so", - "on. It is just a lumped capacitor", - "that I have stuck on there. I am interested in determining", - "a few things. One is what we call the standby", - "power. You will see all these terms", - "being used in cell phones and so on.", - "In your cell phone, your cell phone manufacturer", - "gives you two numbers. Of course both are over", - "exaggerations, but they give you two numbers", - "nonetheless. One number is the number of", - "days that the cell phone battery will last when in standby mode,", - "right? That's exactly where standby", - "comes from. In standby mode,", - "how much power does your cell phone or how long will the", - "battery last, that's the standby power.", - "And the second thing is what we call active use power.", - "Active use is when you are making a phone call and so on,", - "what is the power consumed? And there again your", - "manufacturer of your cell phone will give you a much smaller", - "number for the active use power of your cell phone.", - "What I am going to do is assume for discussion that the inverter", - "is driven by a square wave signal of the following sort.", - "This is vIN. And I am going to drive this", - "with a signal of this sort. The period applied at the", - "input, so I am switching the inverter on and off,", - "on and off, on and off. And T1 seconds for the high,", - "T2 seconds for the low. This is the inverter,", - "this is the input signal, and we'll keep coming back to", - "that again and again. Rather than directly taking", - "this circuit and analyzing its power, I would like to do things", - "in a slightly roundabout manner. What I would like to do is show", - "you some very simple circuits and analyze their standby and", - "active powers. And then show you that this", - "circuit simply is a combination of some of the simple things", - "that you have seen. Example 1.", - "I would like to take a simple circuit that looks like this.", - "A voltage source V applied across a resistor R,", - "some current I. And if I apply a voltage across", - "this resistor, that voltage would simply", - "appear across the resistor. And the power is simply given", - "by VI which is simply V squared divided by R.", - "This is 6.002 101 in the very first chapter.", - "That is the power that is dissipated by this resistor,", - "simply V squared divided by R. That's the power dissipated by", - "the resistor. Where does that power come", - "from? The voltage source supplies the", - "power. So, this guy here supplies this", - "power and this guy here dissipates it.", - "What is the energy that I dissipate in T time?", - "Remember, power is the rate of energy dissipation.", - "And so energy is simply power multiplied by time.", - "For a circuit like this, energy dissipated in time T is", - "simply VIT. For our gate remember we have", - "two situations. We have VS, we have RL we have", - "RON, vO and vIN. So, vIN is high.", - "If vIN is high with respect to ground then RON,", - "the switch is on, and this is the circuit that I", - "see. In this situation the power", - "consumed is simply V squared divided by the resistance here.", - "It is simply VS squared divided by RL plus RON.", - "Let me mark that with an asterisk.", - "I will refer to this later. Similarly, when vIN is low the", - "MOSFET is off. And the power is simply zero.", - "I have no current flowing down and the power is zero.", - "Absolutely basic stuff. Absolutely basic.", - "So, the power, when I have the MOSFET on,", - "for the kind of inverters you have seen so far,", - "this is the power consumed by the inverter.", - "And this asterisk here is simply to say hold that thought,", - "we will get back to it a little later.", - "Let me work out a second example.", - "In this second example, I would like to consider the", - "following circuit, a voltage source VS with a", - "strange arrangement of switches, S1 with a resistance R1,", - "a capacitor C in this manner, a switch S2 and a resistor R2.", - "For now don't worry about how the circuit comes about.", - "Just assume that I have drawn the circuit for you.", - "And what I want to do is compute the power under certain", - "conditions. Notice that if this is off and", - "this is off, there is no current flowing either in this loop or", - "this loop, and the power dissipated by the circuit is", - "zero. But there are some arrangement", - "of switches for which I do consume power.", - "And so let me show you that arrangement of switches.", - "And what I am going to do is assume that the switches open", - "and close with the following periodic cycles.", - "Let's assume that when this is high S1 is closed and S2 is", - "open, and when this is low assume that S1 is open,", - "S2 is closed. And let's assume this is T,", - "this is T1, this is T2. That sequence should be", - "reminiscent of this input that I am feeding to this inverter.", - "All I am telling you here is that I am giving you the", - "circuit. I want to compute the power", - "consumption of the circuit. And what I am telling you is", - "that with the frequency, with a time period of capital", - "T, for the first T1 seconds this switch is closed and that is", - "open. So, this circuit applies.", - "In the second half of the clock this switch is open so this", - "circuit applies. And what I am interested in", - "finding out is what is the energy dissipated in each cycle", - "of time capital T? And I also want to find out the", - "average power. Just spend about five seconds", - "just staring at this and kind of intuit what is going on here.", - "I start by putting a voltage source here and I close the", - "switch. That is open.", - "Start by closing this, what happens?", - "When I close the switch VS is going to charge up this", - "capacitor. I get current flowing through", - "my resistor, so I am going to be charging up this capacitor here.", - "Then let's say I allow T1 to be as large as possible,", - "and so this capacitor is going to be charged up to all of VS.", - "After a long time this guy gets to be VS in the capacitor.", - "And as it is charging up I have current flow through the", - "resistor, so it is sitting there dissipating power.", - "Notice that this sucker does not dissipate energy.", - "It simply stores energy. So, the energy supplied by the", - "voltage source comes in, some of it gets stored in the", - "capacitor and some of it is being dissipated by the", - "resistor. That gets me to the end of T1.", - "At the end of T2 I open the switch and close this switch.", - "When I close the switch I have some energy on the capacitor,", - "and the voltage across the capacitor begins to drive a", - "current through this resistor R2.", - "And now the capacitor supplies its stored energy,", - "and its stored energy then begins to dissipate through", - "resistor R2. And if T2 is very long then all", - "the charge in the capacitor drains out.", - "And the voltage in the capacitor at the end will be", - "zero. So, that is just sort of a high", - "level description of what goes on.", - "Now let's go ahead and compute from first principles the", - "energetics of this little circuit.", - "Let's look at the entire period capital T, and as a first step", - "look at T1. When T1 is in place S1 is", - "closed and S2 is open. Accordingly,", - "the circuit that applies looks like this.", - "I have VS, S1 is closed, so that is closed,", - "and I have this resistance R1, I have this capacitance C,", - "some voltage VC across the capacitor.", - "You can go ahead and assume that VC of zero is zero.", - "That I start off my life with no voltage across the capacitor.", - "First of all, let me plot the waveforms and", - "write the expressions down and then compute the energy supplied", - "by the voltage source and then look at where the energy goes.", - "You all know, or should know by now,", - "if I plot VC as a function of time, remember,", - "this is really easy to do. VC as a function of time goes", - "like this. At time T equal to zero I am", - "telling you that the capacitor voltage is zero.", - "I am telling you that. So, it is at zero.", - "And then the capacitor charges up until it reaches VS.", - "I also know that after a long time this will be VS,", - "after a long time that will be VS, and between those two I have", - "a rising function that looks like this.", - "I can similarly plot the current for you.", - "At time T equal to zero instantaneously the capacitor", - "looks like a short, and so the current that I start", - "off with is going to be VS divided by R1.", - "The voltage across the capacitor is zero.", - "All the voltage falls across the resistor R1.", - "So, VS divided by R1 is the initial instantaneous current.", - "And after a long time, because VC reaches VS,", - "the current is going to be zero.", - "And between those two points I get an exponential decay.", - "I could very quickly write down the expression for the current.", - "And that is simply the initial value VS divided by R1 times the", - "exponential decay minus T divided by the time constant for", - "the circuit R1C. You have seen this stuff", - "before. Here comes the part that we", - "care about for now. Let's find out what is the", - "total energy provided by the source.", - "When dealing with energy computations you have to be", - "incredibly careful of these words here, supply,", - "provided versus dissipated. Dissipated implies that the", - "resistor is burning energy. Provided means that the source", - "is supplying that energy. So, energy provided by source", - "during T1. Let's go ahead and compute that", - "very quickly. The energy supplied by the", - "source is simply the voltage across the source multiplied by", - "the current being supplied by the source.", - "This is i. Remember, by associated", - "variables convention, if I have a voltage across some", - "element and the current into the element is positive then that", - "element dissipates power. If the voltage here is,", - "say, 1 volt and it is supplying current, if the i is out in the", - "other direction then it is supplying power.", - "In this case, the current i is going to be on", - "the outside, heading outside. The total energy is going to be", - "the instantaneous power integrated over time,", - "and that is simply VS. Remember, the instantaneous", - "power is VS times the current i, so the instantaneous power is", - "simply VS times i, that is the instantaneous", - "power. To get the energy provided by", - "source and some time, I have to integrate that", - "instantaneous power over the period of interest T1.", - "That gives me the energy supplied by the source during", - "T1. And let me go ahead and", - "substitute for i with this expression here.", - "It is VS times i, and i is VS divided by R1 times", - "this expression here. That gives me", - "(VS^2/R1)e^(-t/R1C) dt. Let me carry out the", - "integration there. I get -1/RC,", - "so I get this outside. And I also get to write down,", - "oops, let me do that a little bit more carefully.", - "VS^2/R1 simply comes out and I get a -R1C in the numerator.", - "If I differentiate it then I get R1C in the denominator.", - "I have an integral that comes up here.", - "And then I write down e^-t/R1C, zero and T1.", - "So, this R1 and this R1 cancel out.", - "And I end up getting something that looks like this.", - "I get CVS^2. And so there is a minus sign", - "out here, so at zero this thing goes to a one,", - "so I get a one. And because of minus sign I get", - "e to the -T1/R1C. All I have done here is simply", - "go through the math to do this integration here.", - "What I am also going to do is assume that if T1,", - "if the time that the switch is closed is much,", - "much bigger than the time constant of the circuit,", - "T1 is much, much greater than R1C, if this is much,", - "much greater than R1C then this term goes to zero.", - "And this becomes more or less equal to CVS^2.", - "What do we have here? What we have here is that if I", - "let the switch stay closed for a long time and S to be open then", - "the voltage source is going to supply some amount of energy.", - "That energy will equal CVS^2. The voltage across the", - "capacitor will be VS and all that energy would have been", - "supplied by this guy. Let me pose the following", - "conundrum here. If the voltage across the", - "capacitor is VS, because we know the energy", - "stored in the capacitor is half CV^2.", - "So, the energy in the capacitor is half CVS^2.", - "At the end of the day, since the voltage across the", - "capacitor is VS, \u00bdCV@2 is the energy stored", - "here. But we know,", - "from this calculation, the source has supplied CVS^2.", - "Source has supplied twice that energy.", - "This guy has supplied twice that energy and only half of", - "that is stored here. Who ate up the other half?", - "The resistor, exactly.", - "The resistor has walloped half the energy.", - "Let me just show it to you. It dissipated \u00bdCVS^2.", - "It's pretty interesting. It's a pretty simple result.", - "If T1 is very large compared to time constant then half the", - "energy is in the capacitor and half of it has been burned by", - "R1. This energy has not been", - "burned. It is simply stored.", - "It is stored by the capacitor.", - "And if you do simple energy conservation arithmetic here,", - "the energy dissipated in the resistor plus that stored in the", - "capacitor equals the energy supplied by the source.", - "All right. Let's go to T2 now.", - "At T2, S2 is closed and S1 is open.", - "Let's look at the second part of the cycle when S1 is open and", - "S2 is closed. And what is going to happen now", - "is the left-hand part of the circuit can be ignored and I can", - "focus on this part. So, S2 is closed.", - "This is RC, my capacitor, this is vC.", - "This is the circuit of interest.", - "What is the initial condition on this?", - "What is the value of vC initially?", - "Start off, because remember, I allowed this capacity to", - "charge up fully, and so initially I have VS on", - "the capacitor. And so the energy on the", - "capacitor initially is \u00bdCVS^2. That is the energy on the", - "capacitor. This time around I won't go", - "through an integration process like that, but you can if you", - "like, and do it in a much similar manner to say that now", - "let's suppose that T2 is much greater than this time constant.", - "If T2 is much greater than R2C, this time constant.", - "If that time is much greater than this entire,", - "the initial voltage VS drives a current through the resistor,", - "and after some amount of time the voltage across the capacitor", - "goes to zero and all the energy in the capacitor gets dissipated", - "in R. So, if T2 is much greater than", - "R2C then energy dissipated in R2 is simply \u00bdCVS^2.", - "Notice that the energy dissipated in R1,", - "in the first half cycle is \u00bdCVS^2 and the second half cycle", - "during T2, if T2 is large enough, all this energy gets", - "dissipated in this resistor R2. And I have that expression", - "here.", - "So let me just say that this is E1 and let me say that this is", - "E2. So, E1 is dissipated in the", - "resistor and E2 is dissipated in R2 in the second half cycle.", - "A couple of interesting things to note at this point.", - "One is that E1 and E2 are independent of R.", - "If the time constant is small enough compared to the time that", - "I charge the capacitor then half the energy gets lots in the", - "resistor, and that is simply \u00bdCVS^2.", - "And if I let this discharge completely it doesn't matter", - "what resistor I am discharging it through.", - "That's the intuition. If I have certain energy here", - "and I let it discharge completely it doesn't matter", - "what this resistor is. Small or large,", - "it doesn't matter. All this energy gets dissipated", - "there. The rate at which the energy", - "gets dissipated will change depending on R2.", - "If R2 is very small then I get a burst of power initially and", - "then a rapid decay after that, but if R2 is very large then I", - "have a much slower release of energy.", - "But suffice it to say that the energy dissipated,", - "the total energy in T2 is simply \u00bdCVS^2.", - "All right.", - "Let's put T1 and T2 together and look at the total energy", - "dissipated --", - "Total energy dissipated. E is simply E1 plus E2.", - "Dissipated in each cycle. Assuming T1 and T2 are much", - "larger than the respective time constants.", - "And I know that this is \u00bdCVS^2, \u00bdCVS^2, so this is simply", - "CVS^2. If I have an arrangement of", - "switches and capacitors like that, I charge the capacitor,", - "discharge the capacitor, charge the capacitor,", - "discharge the capacitor. What it is saying is that in a", - "charge/discharge cycle I am using up CVS^2 of energy.", - "\u00bdCVS^2 when I charge it up and \u00bdCVS^2 when I discharge it.", - "That is what I get. Let's compute the average power", - "dissipated, P average in a cycle is simply E/T where T is the", - "period of the square wave sequence that I have shown you", - "out there. This is simply CVS^2 divided by", - "T. If the period of the square", - "wave is capital T, I can express that as a", - "frequency. Let's say for example the", - "period of the square wave is T, so let's say the frequency of", - "the square wave is simply 1/T. I can also express this as", - "C(VS^2)f.", - "What does this say? Let me mark that as a thing to", - "remember, the second thing to remember.", - "One was the power that was the static power.", - "And second is this power relating to this frequency f and", - "the charging and discharging of the capacitor in that little", - "circuit shown up there. So, this average power is", - "CVS^2f. What this is saying is that if", - "f is high, if I have high frequency of charging and", - "discharging the capacitor then I am charging and discharging much", - "more frequently so I am going to consume more power.", - "Notice that at any given time there is no direct connection", - "between the power supply and the ground.", - "What I am doing is my capacitor is an intermediary.", - "I am dumping some charge in the capacitor and the capacitor is", - "dumping the charge into ground. It behaves like a switch to", - "capacitor. And what it is doing is it is", - "being charged and discharged at frequency f.", - "So, it makes sense that the amount of average current that I", - "am pumping through relates to the frequency at which I am", - "charging and discharging the capacitor.", - "And similarly the average power also relates to the value of the", - "capacitor. If C is larger I dissipate more", - "energy. And the same way with the", - "voltage. If the voltage is higher then", - "the power in that period, or the average power relates to", - "CVS^2. Spend a few seconds staring at", - "the two expressions. This power here relating to", - "just this connection between the power supply and ground and that", - "power out there relating to charging and discharging", - "capacitors. Let's get back to our inverter", - "right now.", - "This is our inverter circuit. Let us say that I drive the", - "input with the waveform shown here.", - "Well, I go back to the same situation as here.", - "I drive the input with a square wave, with T1 and T2 as the high", - "time and the low time. The equivalent circuit for this", - "is not exactly what we saw there.", - "The equivalent circuit for this would look like this.", - "I have a VS. And the VS supply is connected", - "through RL, VS connected through RL to a capacitor C.", - "This is my voltage vO. So, VS is always connected to", - "ground through this resistor and capacitor in this manner.", - "And then I have a resistor here RON corresponding to that", - "MOSFET. And there I am switching it on", - "and off in a way that it is on during T1 and off during T2.", - "So, the situation here is a bit different from that simple", - "situation I computed there. Much like I computed the power", - "dissipation in that circuit, I can go ahead and compute the", - "total power dissipated in this circuit.", - "I won't do it here. The algebra tends to be a big", - "more grubbier than what I have been through.", - "And suffice it to say that you can show that the average power", - "is given by (VS^2)/(2(RL+RON))+(CVS^2)f", - "(RL^2)/(RL+RON)^2.", - "OK? And for details I suggest that", - "you look at section 12.3 of the course notes.", - "Section 12.3 goes through the algebra to compute the total", - "power dissipated by this specific circuit,", - "and here is the expression we get.", - "And let's take the specific situation where RL is much", - "greater than RON. If RL is much greater than RON", - "then I can ignore this RON here.", - "And I get this. And out here,", - "if I ignore RON, then RL and RL will cancel out", - "and I get CVS^2f. If I ignore RON compared to RL", - "this is the expression I get. Now you can see why I went", - "through those two examples. This is exactly the power", - "consumed by the connection between power supply and ground.", - "And this CVS^2f is the power consumed in charging and", - "discharging the capacitor. If you look at the circuit here", - "it is consuming two kinds of power.", - "One kind of power is due to the current flowing directly from VS", - "through RL and RON to ground. Oh, this also assumes,", - "by the way, that T1 is equal to T2.", - "So, in this circuit there are two kinds of power.", - "One is the power when the switch is on and I have a", - "current flowing from VS to RL to ground.", - "Notice I get an extra factor of two in the denominator here.", - "And that two comes about because the connection to ground", - "only happens half the time. It's half that power out there", - "because I am connected to ground only when the switch is on.", - "And that happens only half the time, and so therefore I get the", - "VS^2/2RL. And then CVS^2f is simply the", - "power that I consumed because I am charging and discharging the", - "capacitor C. Notice that in this inverter", - "circuit there are two kinds of power.", - "One is called the standby power which is static power being", - "consumed by the circuit, and the second power is the", - "dynamic power because the circuit is switching up and", - "down. This relates to star and this", - "relates to the double star. And to demonstrate that,", - "I have a little demonstration here that has an inverter.", - "And I am going to up the frequency of the square way of", - "driving the inverter. I am going to show you a few", - "numbers so hang on for two minutes after this demo.", - "I will give you some numbers, but I want you to go ahead and", - "compute the numbers based on what we have seen here.", - "And you will get suitably impressed, I promise you.", - "This is the input fed to the inverter.", - "This is the output of the inverter.", - "Notice that the output of the inverter reflects some sort of", - "an RC time constant because of the output driving the", - "capacitor, and the same way here.", - "I start off by showing you that on the left-hand side I am", - "simply measuring the power being consumed by the circuit.", - "Notice that the power being consumed is expressed by the", - "needle being at this point here. This is a very low frequency so", - "this is almost all standby power consumed by the inverter.", - "The inverter is on half the time, and when it is on it is", - "consuming power. What I am going to now is", - "increase the frequency. As I increase the frequency", - "driving the inverter what should happen to this needle?", - "As I increase the frequency there that waveform should", - "become closer and closer together.", - "And what should happen to the needle?", - "That should begin to go up. If I increase the frequency it", - "should consume more and more power and the needle should", - "start going up. So, let me do that for you.", - "In terms of numbers there it is on top of the four on the scale", - "in the middle. I am going to increase the", - "frequency very slowly. Unfortunately,", - "the sampling scope messes up the waveform.", - "Ignore the waveform for now. Just look at the meter as I", - "increase the frequency.", - "Notice that I have increased the frequency by about a factor", - "of 2 or 3. And notice here that this meter", - "has moved. The needle has moved to the", - "right. And I can keep doing that and", - "the needle keeps moving to the right as I am consuming more and", - "more power because I'm driving the inverter faster and faster", - "and faster. That should convince you that", - "there is a standby power and there is some power component", - "related to frequency. This relates to your standby", - "power in your cell phone. This relates to active use.", - "Let me show you some numbers, and you can plug those numbers", - "in yourself and see how much power this converter is going to", - "consume and see if it makes sense.", - "Assume that I have a chip with 10^8 gates.", - "F is 1 gigahertz. That is 10^9.", - "Assume C is 0.1 femtofarads which is 10^-16 farads.", - "Assume VS is 5 volts. Assume RL is 10 kilo ohms.", - "Use these numbers. Plug these numbers in here and", - "get a sense if our modern-day circuitry used that inverter,", - "what would be the power consumed by a chip that contains", - "10^8 of these gates? You will find out that you may", - "have to use a nuclear power reactor to actually drive that", - "chip, but go check it out for yourselves.", - "In the next lecture we will see then how do our cell phones", - "work, how does life go on despite this horrendous", - "calculation here." - ] -} \ No newline at end of file diff --git a/subs/wO-WqB_k9QQ.srt.sjson b/subs/wO-WqB_k9QQ.srt.sjson deleted file mode 100644 index 4061525c2e..0000000000 --- a/subs/wO-WqB_k9QQ.srt.sjson +++ /dev/null @@ -1,272 +0,0 @@ -{ - "start": [ - 410, - 3130, - 7160, - 9660, - 12020, - 15930, - 19810, - 23480, - 26240, - 28450, - 33260, - 36660, - 40420, - 41770, - 44840, - 47260, - 51110, - 54160, - 56780, - 59990, - 64470, - 67762, - 68900, - 72300, - 73340, - 75660, - 78530, - 81620, - 84910, - 86050, - 91100, - 94680, - 96400, - 99420, - 100900, - 103800, - 107460, - 114830, - 118120, - 119350, - 123220, - 124600, - 126980, - 130310, - 132020, - 135180, - 136990, - 138860, - 144970, - 146860, - 149330, - 153420, - 157580, - 161500, - 164040, - 165950, - 167635, - 169320, - 170550, - 172780, - 177670, - 179560, - 182670, - 184370, - 185610, - 187270, - 189890, - 191325, - 195050, - 200140, - 204810, - 209390, - 213530, - 215270, - 219950, - 223760, - 224360, - 225620, - 228980, - 231670, - 235915, - 240830, - 244580, - 247860, - 248640, - 251430, - 254530, - 256560 - ], - "end": [ - 3130, - 7160, - 9660, - 12020, - 15930, - 19810, - 23480, - 26240, - 28450, - 33260, - 36660, - 40420, - 41770, - 44840, - 47260, - 51110, - 54160, - 56780, - 59990, - 64470, - 67762, - 68900, - 72300, - 73340, - 75660, - 78530, - 81620, - 84910, - 86050, - 91100, - 94680, - 96400, - 99420, - 100900, - 103800, - 107460, - 114830, - 118120, - 119350, - 123220, - 124600, - 126980, - 130310, - 132020, - 135180, - 136990, - 138860, - 144970, - 146860, - 149330, - 153420, - 157580, - 161500, - 164040, - 165950, - 167635, - 169320, - 170550, - 172780, - 177670, - 179560, - 182670, - 184370, - 185610, - 187270, - 189890, - 191325, - 195050, - 200140, - 204810, - 209390, - 213530, - 215270, - 219950, - 223760, - 224360, - 225620, - 228980, - 231670, - 235915, - 240830, - 244580, - 247860, - 248640, - 251430, - 254530, - 256560, - 258410 - ], - "text": [ - "SPEAKER 1: So before I wrap up the node method, I wanted to", - "take some time and show you something interesting, largely", - "for your cultural interest. This is not required for the", - "course, and so this is optional.", - "I want to show you how these equations are really solved in", - "real life and how computers can be used to do this for us.", - "So if you go back to step four of the node method, you recall", - "we had these two equations and two unknowns, where the", - "unknowns were e1 and e2.", - "I can turn these into matrix form, like so, where I have", - "matrix times a column vector equals another column vector,", - "and where I get a two-by-two matrix called the", - "conductivity matrix.", - "I get a column vector of the unknown node voltages.", - "And I get a column vector of the source voltages.", - "So I've taken my system of equations and converted them", - "into the matrix notation, like so.", - "And the way this works is each of these equations can be", - "obtained by doing a row column multiply.", - "So if I multiply the first row with this column here, I take", - "e1, multiply that by G1 plus G2 plus G3, I get", - "the first term here.", - "I take e2, multiply that by minus G3, I", - "get the second term.", - "And I equate that to G1V0.", - "Similarly, to get the second equation, I would take the", - "second row and multiply that by the same column vector.", - "Now, let's take a look at how things like", - "this might be solved.", - "So here is my matrix equation again, with a two-by-two", - "matrix multiplying a column vector equal", - "another column vector.", - "So we can use many sophisticated techniques to", - "analyze systems like this.", - "And if you've done courses in linear algebra, you would've", - "noticed that linear algebra spends a lot of time trying to", - "analyze systems of this sort, where A is some matrix, x is a", - "column vector of unknowns, and b is a", - "column vector of knowns.", - "And so you often have to go and solve for the column", - "vector of unknowns.", - "Now, with circuit analysis, if I have a circuit containing", - "millions of elements, I would have a column vector here,", - "which had a million elements.", - "And so clearly we would love to use computers to do that.", - "And not surprisingly, that is what to", - "do in circuit analysis.", - "In fact, the lab that you work on in 6002-X has the schematic", - "capture system where you can build circuits.", - "But for the analysis, the computer programs that are", - "used to analyze the voltages and so on, and show them to", - "you, use methods very similar to this, where you use these", - "sophisticated linear algebraic solvers that solve systems of", - "equations of the form Ax equals b.", - "So back to our system.", - "I can go ahead and solve the system.", - "I won't bore you with the details of", - "the agony of algebra.", - "I've gone ahead and solved these equations for you.", - "And so I get e1 and e2 are expressed as fairly big", - "equations of the sort.", - "So one interesting fact that I mentioned to you was you end", - "up with systems of equations that you", - "can solve with computer.", - "There's one other interesting fact.", - "Notice that the circuit that we used, our demo", - "circuit, was linear.", - "It was composed of linear elements and so on.", - "And so notice here that e1 is also related to a set of", - "linear terms. So notice that this equation here is linear", - "in V0, i1, V0, and so on.", - "And it is all in linear terms. Also note that there are no", - "negatives in the denominator.", - "So the fact that this is linear in the constant sources", - "will be used in a later sequence that we will cover in", - "a few days.", - "So watch out for that.", - "So just to wrap up and just go through the motions here, let", - "me just go ahead and solve for e2 just for kicks.", - "And I'll do it for values G1, G5, and then so on and so", - "forth, given here, and for i1 chosen to be 0, just for fun.", - "And so if I plug these numbers into the equation for e2 that", - "I just showed you, I'm going to get e2 as a function of V0,", - "as follows.", - "Then e2 is going to be 0.6 times V0.", - "And so if I pick V0 to be three volts, then e2 is going", - "to be 1.8 volts.", - "So there you have it." - ] -} \ No newline at end of file diff --git a/subs/wlcwr1VIQ7Y.srt.sjson b/subs/wlcwr1VIQ7Y.srt.sjson deleted file mode 100644 index 5206cd416f..0000000000 --- a/subs/wlcwr1VIQ7Y.srt.sjson +++ /dev/null @@ -1,422 +0,0 @@ -{ - "start": [ - 250, - 4310, - 6240, - 7610, - 11120, - 12830, - 15980, - 18220, - 20770, - 23710, - 27110, - 28320, - 31150, - 34250, - 36250, - 40670, - 43060, - 44530, - 49040, - 51560, - 56130, - 59000, - 60130, - 64519, - 67280, - 73230, - 76100, - 78905, - 81230, - 83840, - 87660, - 91495, - 95020, - 97830, - 100230, - 103160, - 106980, - 108970, - 111320, - 113640, - 114490, - 117130, - 119560, - 121640, - 123220, - 126660, - 129860, - 135490, - 139050, - 142580, - 144355, - 145520, - 150010, - 153280, - 154240, - 156190, - 162220, - 165540, - 168010, - 170820, - 176620, - 178940, - 182510, - 185120, - 186480, - 190160, - 194290, - 197430, - 200070, - 203330, - 205930, - 208550, - 214080, - 217300, - 217940, - 221700, - 225215, - 228900, - 230690, - 233510, - 236260, - 239890, - 244060, - 245800, - 247680, - 248520, - 251730, - 252870, - 255210, - 257060, - 258610, - 259970, - 261980, - 263460, - 264960, - 265690, - 267360, - 269270, - 272860, - 277250, - 279590, - 282410, - 285280, - 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203330, - 205930, - 208550, - 214080, - 217300, - 217940, - 221700, - 225215, - 228900, - 230690, - 233510, - 236260, - 239890, - 244060, - 245800, - 247680, - 248520, - 251730, - 252870, - 255210, - 257060, - 258610, - 259970, - 261980, - 263460, - 264960, - 265690, - 267360, - 269270, - 272860, - 277250, - 279590, - 282410, - 285280, - 288140, - 289090, - 292500, - 296050, - 297910, - 304180, - 309050, - 310280, - 313280, - 317240, - 319240, - 320990, - 323790, - 324380, - 327770, - 330880, - 334910, - 338530, - 340440, - 344585, - 345700, - 347750, - 350080, - 353520, - 356025, - 359990, - 363370, - 366270, - 369300, - 370690, - 374130, - 375570, - 378240, - 380200, - 383470, - 384720 - ], - "text": [ - "SPEAKER 1: So the fourth loop really is this outer loop here", - "that goes like so.", - "That is four.", - "So notice that I have four nodes, and I have four loops,", - "and I have 12 unknowns.", - "And the goal of the method will be to find out the values", - "of each of these 12 unknowns.", - "If you're ready, now that you've labeled the circuit,", - "let's go to step one of the KVL, KCL method.", - "And our overall goal will be to find out the values of", - "these 12 unknowns.", - "You see the circuit on the right-hand side, and then", - "notice that all the branch variables have been assigned", - "as we did in the previous step.", - "So the first step of the KVL, KCL method is to write down", - "all the element v, i relationships so", - "there are six elements--", - "one, two, the R2, R3, R4, R5, so six elements.", - "So let's write down six v, i relationships.", - "So for the volted source, I get V0 is capital V0.", - "And this is given because I know the value", - "of the voltage here.", - "I can do V1 is i1R1.", - "V2 is i2R2.", - "And then for resistor three, I can write V3 is i3R3.", - "V4 is i4R4.", - "And V5 is i5R5.", - "So notice that there are six equations here.", - "So we're done with the element relationships.", - "And let me now go on to the next step of the KVL, KCL", - "method, which is to write KCL at each of the nodes.", - "So I have four nodes, A, B, C, and D. So let's start by", - "writing KCL for node eight.", - "So let's write KCL for node eight.", - "So at node eight, notice that I have three currents deal", - "with, i0, i1, and i4.", - "So here, again, I'm going to use a little bit of a", - "convention in how I sum up currents.", - "And as a rule, I can sum currents going in or", - "currents going out.", - "But again, I'm just going to use a convention.", - "I am going to sum currents leaving the node.", - "So for every node, I'm just going to sum currents leaving", - "the node if they should add up to 0.", - "So for node eight, notice that current i0 is leaving the", - "node, i1 is leaving the node, and i4 is leaving the node.", - "So I can sum them all up to be i0 plus i4 plus i1 equals 0.", - "Similarly, for node b, I have currents--", - "let's see, we have i2 leaving the node, so i2.", - "Then we have i3 leaving the node.", - "So I write i3.", - "And then, notice that i1 is coming into the node.", - "So there, it's not a plus, but it's a minus i1", - "coming into the node.", - "And that equals 0.", - "Then, similarly, at the next node, b, I can write down i5", - "leaving the node minus i4 leaving the node.", - "And then I have i3 coming into the node.", - "So it is minus i3 leaving the node.", - "Finally, for c, I have minus i0 minus i2 minus i5 equals 0.", - "So in this case, I have four equations.", - "But notice that even though there's four equations,", - "because of the circuit topology, there is one", - "dependent equation.", - "So I really end up getting three independent equations.", - "So as you're doing the analysis, you will find that", - "there's only three independent equations, given these four", - "nodes in a circuit.", - "OK, let's go to step three of the KVL, KCL method.", - "And the step three says write down the Kirchhoff's Voltage", - "Law, KVL, for each of the nodes.", - "So here, again, let me start by writing KVL for loop one.", - "So what I'm going to do is I'm going to follow loop one in", - "this direction.", - "I'm going to go around clockwise for loop one.", - "So here, again, I have a convention to follow.", - "As I go down the loop, how do I write down the voltages?", - "There's many conventions people follow.", - "But the convention that I follow and I recommend, which", - "is very simple, is as you go around the loop, you simply", - "assign to each voltage the first encountered sign.", - "So as you go around this loop here, I get the v0 voltage.", - "And the sign encountered is minus.", - "So I'm going to assign that a minus sign.", - "So let's do that.", - "So for the loop one, I'm going to go around the", - "loop in this direction.", - "And the first encountered voltage is v0.", - "And the first encountered sign is a minus.", - "So I write minus v0.", - "And I continue down this way.", - "And I hit v1.", - "In this case, I hit the plus sign.", - "So it is plus v1.", - "And I go down.", - "And then I hit plus v2.", - "And that sums to 0.", - "Similarly, for loop two, I'm going to go around the loop.", - "Why don't I say just for fun, for this loop, why don't I go", - "around in a counterclockwise manner.", - "So in this case, I'm going to hit the positive terminal of", - "v1 first. So I write plus v1.", - "Then I'm going to hit the positive terminal of v3.", - "So I write plus v3.", - "Then the minus terminal of v4, so minus v4.", - "So similarly, for loop three, I get v3 plus v5", - "minus v2 equals 0.", - "And for loop four, I get minus v0 plus v4 plus v5 equals 0.", - "And again, because of the circuit topologies, there's", - "three independent loops.", - "And so I get three independent equations.", - "And so this last equation is redundant.", - "OK, so putting it all together, I'm in", - "the KVL, KCL method.", - "You saw that we developed six equations for the element", - "relationships.", - "And then we had three independent equations from the", - "KCL at the nodes and three more KVL at the nodes.", - "So in all, notice that we ended up with 12 equations.", - "And recall we had 12 unknowns, v0 through v5", - "and i0 through i5.", - "So now you can take these 12 equations and put them into a", - "hopper and turn the crank.", - "And you can go and get the answer.", - "However, this is very grubby.", - "But even a simple circuit like this, now, with just a small", - "number of elements, three inner loops and one outer", - "loop, I had a horrible mess, 12 equations, 12 unknown.", - "And so this works, but this is a real pain.", - "We will see that the node method, which builds on the", - "KVL, KCL method, will be much, much better", - "and will be way simpler.", - "And we'll have far fewer equations than", - "the KVL, KCL method.", - "But it's good to know about the KVL, KCL method, because", - "it's the simplest method that there is.", - "Just that it ends up with a whole boatload of equations", - "that you have to solve." - ] -} \ No newline at end of file diff --git a/subs/xal6k2pwvgA.srt.sjson b/subs/xal6k2pwvgA.srt.sjson deleted file mode 100644 index d96b61df2d..0000000000 --- a/subs/xal6k2pwvgA.srt.sjson +++ /dev/null @@ -1,635 +0,0 @@ -{ - "start": [ - 270, - 3520, - 5500, - 8910, - 11210, - 14260, - 17840, - 21030, - 23940, - 26650, - 29010, - 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672060 - ], - "text": [ - "PROFESSOR: In this segment, we will develop a second method", - "that will work for linear circuits.", - "This method is called the Thevenin method, and its", - "complementary method, the Norton method.", - "So in order to develop this method for linear circuits,", - "suppose you have some arbitrary network, N. And", - "let's say in this arbitrary network you have a whole bunch", - "of resistors, you have a whole bunch of voltage sources, Vm,", - "and a whole bunch of current sources as well.", - "OK, so you have a bunch of voltage sources.", - "And these are all independent voltage sources for now.", - "V1, V2, V3, all the way through VM.", - "You have a whole bunch of current sources, I1, I2, I3,", - "all the way through to In.", - "Suppose I am interested in applying some kind of", - "excitation due to an external current source with current i.", - "And let us say that all I care to do is to determine the", - "voltage, V. So the setup here is I have an arbitrary", - "network, N, with a ton of resistors and voltage sources", - "and current sources, all independent.", - "And I apply an external excitation, and", - "it's a current i.", - "And just assume that all I want to do is to determine the", - "voltage, V. Assume that I don't care about any internal", - "voltages, Vi, or any internal currents, Ij, and so on.", - "Let's say I don't care about any of", - "those internal currents.", - "All I care about is the voltage, V.", - "So in a situation like this where you care about some", - "voltage or current at some point, you can use the", - "property of linearity and the resulting superposition", - "property to develop an extremely powerful method to", - "get you to your answer very quickly.", - "So in order to develop this method, let me use the", - "superposition technique and try to figure out the voltage,", - "V. So the voltage V will be some combination of the linear", - "sources in this linear circuit.", - "So let's say, for example, I want to figure out the", - "contribution to the voltage V due to the voltage source, Vm.", - "What I would then do is I would set i to 0, I would set", - "all the currents, I1 through In, to 0, and I would set all", - "the voltages, V1 through Vm minus 1, to 0 as well, and", - "just look at the impact on V due to Vm acting alone.", - "So the impact on V due to Vm acting alone, and notice that", - "once all the currents have been turned off and all the", - "other voltages have been turned off, I'm left with a", - "big resistor network.", - "And I'm going to get some multiplier here.", - "Let's label that alpha m.", - "So that will be the result of the source Vm acting alone on", - "the output voltage, V.", - "Similarly, I can do the same thing for all the voltages.", - "I can do it for V1 acting alone.", - "I can do it for V2 acting alone, and so on and so forth.", - "For each of those voltages, V1, V2, and so on, I get a", - "term that looks like this.", - "I get alpha 1 V1, alpha 2 V2, and so on and so forth, all", - "the way through alpha m Vm.", - "And so what I get is a sum over m of all of these terms.", - "By applying V1 acting alone and V2 acting alone and so on,", - "I get a term, alpha 1 V1, alpha 2 V2, and so on.", - "Next, I'll move on to the currents, and in this case,", - "supposing I set all the currents, say, for In--", - "I'm going to set the small i to 0, and I'm going to set all", - "the Vm's to 0, and I'm going to set all the currents, I1", - "through In minus 1, to 0.", - "So in that situation, I'm going to get some factor, Bn,", - "that applies to In.", - "So I've got some factor Bn, beta n, that applies to In.", - "And that is the result of In acting alone.", - "Similarly, I can have I1 acting alone, I2 acting alone,", - "and so on, and for each of them, I get a term, beta 1 I1", - "plus beta 2 I2 and so on and so forth.", - "And I sum them all up as well over all n.", - "So with i acting alone, I'm going to set all of the other", - "In's and Vm's to 0, and just have i acting alone.", - "And so therefore I will get an i, and I'm going to have some", - "multiplier.", - "And in this case, notice that when all the Vm's and all the", - "In's are set to 0, I'm just left with a big resistor", - "network here.", - "And so it will look like a big effective resistor looking", - "into this port.", - "And so let me write that down as some R multiplied", - "by the current i.", - "So notice now that the voltage V is a sum of a bunch of", - "components that arise from the voltages acting alone, the", - "currents acting alone, and also the external excitation", - "acting alone.", - "And just recall, how did I get this?", - "How did I get each of these terms?", - "So this term which sums up all the voltages I got by setting", - "all the In's to 0 and by setting the external", - "excitation to 0.", - "Similarly, I got the second term here by setting all the", - "voltage sources to 0, and also by setting the external", - "excitation to 0.", - "And finally, this last term, I got that by setting all the", - "currents to 0 and all the voltages to 0.", - "So what we're going to do now is by using this insight,", - "we're going to build up a new technique.", - "And to give you a preview to that technique, I'm going to", - "show you a trick that will enable you to replace this", - "network, N, by something very, very simple.", - "In fact, I'm going to show you that we're going to be able to", - "replace that entire network by some voltage source and some", - "resistor acting in series.", - "And this will be able to replace this entire network,", - "N, for the purpose of computing the voltage, V. So", - "just think of that as a preview of upcoming", - "attractions.", - "So moving on, let's take a look at the equation that we", - "just developed and understand that a little bit more.", - "So if you look at the equation here that we developed, V is", - "some component related to Vm's, some component related", - "to In's, and some component related to the external", - "excitation, i.", - "So if you look at this term here, if you look at the alpha", - "m term here, that has no units.", - "It has no units because I have a voltage on the left-hand", - "side and it's multiplying a voltage.", - "Similarly, beta and In must result in a voltage, and so", - "therefore beta n must have resistance units.", - "And then similarly, R that is multiplying i must have", - "resistance units as well.", - "So notice that if you look at the Vm-related term and the", - "In-related term, then what you see is that together they are", - "independent of the external excitation, and the behave", - "like a voltage.", - "Similarly, if you look at the right-hand term here, Ri,", - "that's a resistance multiplied by a current, and of course,", - "that also has resulting voltage units.", - "So let's look at the first part here, the part comprising", - "the Vm's and the In's.", - "That behaves like a voltage, and it is independent of", - "external excitation.", - "And so what I'm going to do is I am going to call it VTH.", - "And don't worry about why I'm calling it VTH right now, but", - "let's assume that I call it VTH.", - "So that's a first component that is independent of", - "external excitation and behaves like a voltage.", - "Now if you look at the second component, as I said earlier,", - "the second component clearly depends on the current, i.", - "But if you look at the multiplier R, then that is", - "also independent of external excitation and", - "behaves like a resistor.", - "So let's call that RTH.", - "So again, if you look at the term that gives you V, it will", - "now comprise a portion that we've called VTH.", - "And it has a second component that relates to the external", - "excitation, i, by is multiplied by something we", - "call RTH, where the RTH is independent of the external", - "excitation, i.", - "So what I've just done is I've written down the excitation as", - "a sum of a voltage here that I decided to call VTH, and I've", - "also said that the second part is RTH times i.", - "And that is equal to the voltage, V. So notice V equals", - "VTH plus RTH i.", - "So in other words, if you look at this expression here, as", - "far as the external world is concerned-- and again, for the", - "purpose of computing the voltage, our network N is", - "completely indistinguishable from another network.", - "What does that network look like?", - "So this whole network, N, can be replaced by the following", - "network that I'm going to show you in a quick second.", - "So I have a voltage, VTH, here, and I have", - "a resistance, RTH.", - "And this is my voltage, V. And what I've done here is,", - "according to this equation, V equals VTH plus RTH i--", - "I have simply expressed that in circuit form as a little", - "pattern showing a VTH and then with an RTH in series.", - "And this is easy to see, that when i is 0, the voltage at", - "the output here is VTH.", - "And then if I have a short circuit where V is 0, then the", - "current through that short circuit will simply be given", - "by VTH divided by RTH.", - "And so this little pattern here can now replace my", - "network N for the purpose of computing V.", - "This network is called the Thevenin equivalent network.", - "And so I can take this network, replace the arbitrary", - "network N with this network, the Thevenin equivalent", - "network, and then I can connect my external", - "excitation, i, and then compute the voltage V that", - "appears across the terminals.", - "In other words, what I've done is, using the Thevenin method,", - "I can take an arbitrary network N. I can figure out", - "the VTH and RTH that relate solely to that network's", - "properties, and then replace that network with", - "VTH and RTH in series.", - "And the series connection is called the", - "Thevenin equivalent network.", - "So you will see this is another pattern.", - "This is called the Thevenin pattern.", - "So in circuits and electronics courses, you will see the", - "Thevenin pattern very often.", - "And in this pattern, you have a voltage source in series", - "with a resistor.", - "And again, it's easy to see that when you have I being 0,", - "then the Thevenin voltage, VTH, appears at the output", - "terminal as a VTH.", - "And similarly, if you short the terminal pair here where V", - "is 0, then your current is going to be given by the", - "expression, VTH divided by RTH.", - "And since the current is going to be in the direction", - "opposite to this current, i, there will be a negative.", - "But essentially you can see why this expression, V equals", - "VTH plus RTH i, directly relates to the Thevenin", - "pattern with the voltage source in series with the", - "resistance." - ] -} \ No newline at end of file diff --git a/subs/xnoAyQeGZis.srt.sjson b/subs/xnoAyQeGZis.srt.sjson deleted file mode 100644 index 3ae839c3ce..0000000000 --- a/subs/xnoAyQeGZis.srt.sjson +++ /dev/null @@ -1,101 +0,0 @@ -{ - "start": [ - 220, - 2350, - 5830, - 6620, - 10540, - 11340, - 14990, - 15770, - 17520, - 21780, - 24120, - 27340, - 30806, - 33570, - 36820, - 41220, - 42670, - 45770, - 50260, - 54610, - 59660, - 63350, - 66980, - 68980, - 72420, - 75760, - 78140, - 80830, - 83090, - 85530, - 87760 - ], - "end": [ - 2350, - 5830, - 6620, - 10540, - 11340, - 14990, - 15770, - 17520, - 21780, - 24120, - 27340, - 30806, - 33570, - 36820, - 41220, - 42670, - 45770, - 50260, - 54610, - 59660, - 63350, - 66980, - 68980, - 72420, - 75760, - 78140, - 80830, - 83090, - 85530, - 87760, - 89010 - ], - "text": [ - "SPEAKER 1: OK, let me go ahead and give you the answer.", - "In this case, I equals V divided by R is a linear", - "relationship.", - "And notice that the I here and this V here, it's linear", - "relationship.", - "And the slope of the straight line is given by 1 divided by", - "R.", - "So the resistor is one element.", - "And we have enumerable elements in EECS.", - "And another element is a voltage source.", - "A voltage source is an idealistic model of a battery.", - "Again, you can see that there's a voltage, V, and", - "current, I, that I've defined for the element.", - "And the voltage, V, the capital V written inside the", - "element, that is the voltage supplied by the element itself", - "for a typical battery.", - "It might be, for example, 1.5 volts.", - "But the properties of the element are described by its", - "V-I relation, and so this is given by capital V.", - "So notice the small v in this equation here is related to", - "the V-I for the element, while capital V, which could be one", - "1.5 volts, is the voltage supplied by the element.", - "So just make sure to distinguish between what I", - "call up variable V and I that describe through an I-V", - "relation, the element behavior with the element's internal", - "properties, such as the resistance or the voltage.", - "Much like we did with the resistor, we could also plot", - "V-I relation for the voltage source.", - "And before I show it, let me pause for a couple of seconds", - "so you could think about what it might look like before I", - "give you the answer." - ] -} \ No newline at end of file diff --git a/subs/ypX20WnHNQw.srt.sjson b/subs/ypX20WnHNQw.srt.sjson deleted file mode 100644 index 76f51183dc..0000000000 --- a/subs/ypX20WnHNQw.srt.sjson +++ /dev/null @@ -1,2120 +0,0 @@ -{ - "start": [ - 0, - 3552, - 8341, - 16837, - 23016, - 31512, - 40933, - 46380, - 51304, - 57380, - 62166, - 66416, - 71250, - 74500, - 79416, - 82333, - 96000, - 98622, - 103390, - 107761, - 112450, - 115549, - 120000, - 123033, - 126257, - 128911, - 132451, - 134916, - 137318, - 140731, - 144207, - 148000, - 151410, - 156372, - 158232, - 161100, - 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Good morning,", - "all. So we take another big step", - "forward today and get onto a new plane of understanding,", - "if you will. In the last week and a half,", - "our focus was on the storage element or storage elements", - "called inductors and capacitors. And capacitors stored change", - "and inductors essentially stored energy in the field,", - "the magnetic flux. And the state variable for an", - "inductor was the current while that for a capacitor was the", - "capacitor voltage. We also looked at circuits", - "containing a single storage element, we looked at RC", - "circuits and we also looked at circuits containing a single", - "inductor. And this was a single inductor", - "with a resistor and a current source or a voltage source and", - "so on. What we are going to do today", - "is do what are called \"second-order systems\".", - "So they are on the next plane now.", - "And with this second-order of systems, they are characterized", - "by circuits containing two independent storage elements.", - "They could be an inductor and a capacitor or two independent", - "capacitors. And you will see towards the", - "end what I mean by two independent capacitors.", - "If I have two capacitors in parallel, they can be", - "represented as a single equivalent capacitor so that", - "doesn't count. It has to be two independent", - "energy storage elements and resistors and voltage sources", - "and so on. And what we end up getting is", - "what is called \"second-order dynamics\".", - "And much as first order circuits were represented using", - "first order differential equations, this kind you end up", - "getting second-order differential equations.", - "Before we go into this, I would like to start", - "motivating this and give you one example of why this is important", - "to study. There are many,", - "many examples but I will give you one.", - "What I would like to do is draw your attention to our good old", - "inverter driving a second inverter.", - "The same circuit that we used to motivate RC studies,", - "one inverter driving another. So let me draw the circuit.", - "Here is one inverter. This is, let's say,", - "5 volts and this is, let's say, 2 kilo ohms.", - "And I connect the output of this inverter to a second", - "inverter. And what we saw in the last few", - "lectures was that in this specific example there was a", - "parasitic capacitor or a capacitor associated with the", - "gate of this MOSFET. And that could be modeled by", - "sticking a capacitor CGS between the gate of the MOSFET and", - "ground. And we saw that the waveforms", - "here, if I had some kind of step here.", - "Let's say, for example, a step that went from high to", - "low. Then out here I would have a", - "transition that instead of going up rapidly like this would", - "transition a little bit more slowly.", - "And this transition was characterized by an RC time", - "constant. And this is what gave rise to a", - "delay in the eventual output. So that is what we saw", - "previously, single energy storage element.", - "Today what we are going to do is we are going to look at the", - "same circuit, the exact same circuit,", - "and have some fun with it. What we are going to say is", - "look, this thing is pretty slow, so what I would like to do is", - "-- why don't we go ahead and put that up.", - "What we are going to see is that the yellow waveform is the", - "waveform at the input here. And the green waveform here is", - "the waveform at this intermediate node.", - "And notice that this waveform here is characterized by the", - "slowly rising characteristics that are typical of an RC", - "circuit. There are some other", - "weirdnesses and so on going on here like a little bump and", - "stuff like that. You can ignore all of that for", - "now. It happens because of certain", - "other very subtle circuit effects that you won't be", - "dealing with, called Miller effects and so on", - "that you won't be dealing with in 6.002.", - "So focus then on this part here.", - "It is pretty slow. And because of that slow", - "rising, I get a very slow transition and I get some delay", - "in my inverter. So you say ah-ha,", - "we learned about this in 6.002, I can make it go faster.", - "How can you make the circuit go faster?", - "What could you do? This is rising very slowly.", - "How can you make it go faster? Anybody?", - "You have multiple choices, actually.", - "What are your choices here? Pardon.", - "Decrease the time constant. And how would you decrease the", - "time constant? The capacitance is connected to", - "this MOSFET gate here. I didn't want it in the first", - "place but it is there, I cannot help it,", - "so I can decrease the resistance.", - "Good. Let me go ahead and do that.", - "What I will do is I am going to knock this sucker out and stick", - "in a new resistance that is say 50 ohms, a much smaller", - "resistance. That should speed things up,", - "right? That should make things go much", - "faster because this is a smaller time constant because R is", - "smaller, correct? OK, let's go do it.", - "And let's see if we get what we expect.", - "I have a little switch here. And using that switch,", - "I am going to switch in this little resistance.", - "Whoa, what on earth is happening out there?", - "This is so much fun. What I did is I switched in a", - "small resister here to decrease the time constant,", - "but it looks like I got a whole bunch of crapola that I did not", - "bargain for. This is certainly very fast,", - "it goes up really fast, but I am not sure where it is", - "going, though. Let's stare at that a little", - "while longer. Let me expand the time scale", - "for you. Look at this.", - "Instead of a nice little smooth thing going up.", - "I get something that looks like this.", - "It looks something like a sinusoid.", - "It looks sinusoidal, but then it is a sinusoid that", - "kind of gives up and kind of gets tired and kind of goes", - "away. Right?", - "It kind of dies out. So nothing that you have", - "learned so far has prepared you for this.", - "And, trust me, when I first did some circuit", - "designs myself a long, long time ago I got nailed by", - "that. I looked at my circuit,", - "and what ended up happening was I was noticing these sharp lines", - "at all my transitions. When I looked at my scope,", - "I expected to see nice little square waves but I saw these", - "little nasty spikes sitting out there.", - "And then when I stared at it more carefully,", - "those spikes were really sinusoids that seemed to kind of", - "get tired and kind of go away. So those are nasty,", - "those are real and they happen all the time.", - "And what we will do today is try to get into that and", - "understand why that is the case. We will understand how to", - "design that away. And that is a real problem,", - "by the way. And the reason that is a real", - "problem is the following. Look at this.", - "Look down here. Because this intermediate", - "voltage is meandering all over the countryside here,", - "at this particular point the intermediate voltage dips quite", - "low. And because it dips quite low", - "look at the output. The output has a bump here.", - "And it is quite possible for this output bump to now go into", - "the forbidden region. Or worse.", - "If this swing here was higher, this could have actually gone", - "onto a one, so I would have gotten a false one pulse here.", - "Instead of having a nice one to zero transition,", - "I would have gotten a one to zero, oh, back to one,", - "oh, back to zero and then back down to zero.", - "So this is nasty stuff, really, really nasty stuff.", - "What we will do is understand why that is the case today and", - "see if we can explain it. What is going on here?", - "What is really going on here is take a look at this circuit", - "here. I will take a look at this path", - "here. So this is your VS voltage", - "source. Path kind of goes like this and", - "around. It turns out that this circuit", - "is a loop here. And when there is current flow,", - "going down to basic physics you remember that I also enclose", - "some amount. So there is a current flowing", - "in a loop. And because of that there is an", - "effective inductance here. And, in fact,", - "any current flowing through a wire above a ground plane,", - "for that matter, can be characterized by the", - "inductance. So I can model that by sticking", - "a little inductor here. So my real circuit is not", - "exactly a resistor and a capacitor, but my real circuit", - "is an inductor as well that comes into play because of this", - "wire. Every wire, when there is a", - "current flow, has an inductance associated", - "with it. And because of that the real", - "circuit is resistor, inductor and capacitor.", - "So I end up with two storage elements now,", - "and the dynamics of that are very different from that with a", - "single storage element. That is just a bit of", - "motivation for why our study of inductors is important.", - "And I can draw a quick circuit here.", - "If you look at the circuit, start from ground,", - "the voltage VS and there is a resistor here.", - "And then I have an inductor and then I have a capacitor.", - "So it is a voltage source, resistor, inductor and", - "capacitor. For this whole week we will be", - "looking at circuits like this. Today what I would like to do", - "is start very simple, start with the simplest", - "possible form of this so that you can begin building up your", - "insight and then go into more complicated cases.", - "Today what I will do is simply begin with a case where I don't", - "have a resistor here and simply study a voltage source,", - "an inductor and a capacitor and understand what the voltage", - "looks like out here. So we look at the dynamics of a", - "little system like this. Before we go on,", - "I want to caution you about something.", - "It is just happenstance that I have introduced for you", - "capacitors based on the parasitic capacitance here and", - "inductance based on parasitic inductance.", - "I would hate to leave you with the impression that inductors", - "and capacitors are \"bad\". Because when you think of a", - "parasitic, you know, parasites.", - "These are parasitic. You didn't expect them there,", - "didn't expect this here and we got the weird behavior.", - "So parasitics have a bad connotation to them.", - "I do not want to leave you with a bad taste in your mouth about", - "capacitors and inductors that these are just bad things.", - "We just have to deal with them and deal with second-order", - "differential equations and all that stuff because they're just", - "bad stuff and we just have to deal with them.", - "I don't want you to end up going through life hating", - "capacitors and inductors. Just because of my choice of", - "examples, it just happened to be introducing them as capacitors.", - "I want to point out that these are fundamental lumped elements", - "in their own right. They are very,", - "incredibly important and useful circuits where we designed", - "capacitors and inductors because we want to have them in there.", - "There are many circuits that we will look at where we really", - "want the inductor in there. We will design an inductor by", - "wrapping wire around in a coil and get bigger inductances and", - "so. Just remember that this can be", - "parasitic in some cases, but in many cases it's good,", - "inductors are good, so just stick with that", - "thought. These are mostly good so don't", - "go around hating them. All right.", - "Let's go on and analyze a basic circuit like this.", - "And what I would like to cover in the next hour are the", - "foundations of something like that.", - "I will take you through the foundations so you understand", - "how it works. And, as always,", - "what I am going to end up with is build up the foundations,", - "help you understand why we got where we were and then help you", - "build intuition. And then show you a really,", - "really simple intuitive way of doing things in terms of how", - "experts do it. And the real cool thing about", - "EECS is that the way experts do things, things are really,", - "really very simple in the end. But you need to build up some", - "intuition to get there. So our circuit looks like this", - "in terms of my two storage elements.", - "I have a voltage vI, inductor L, capacitor C and I", - "am going to look at the voltage across the capacitor and my", - "current through the capacitor. So v(t) is the voltage across", - "the capacitor and my current is the current through this loop", - "here, which is the same as the current through the capacitor or", - "the current through the inductor.", - "And we are going to proceed in exactly the same manner as we", - "did for first order differential equations, write the equations", - "down and just boom, boom, boom, boom,", - "go down the same sets of steps but just get to some place", - "different. We are going to start by", - "writing a node equation for this node here.", - "That's the only node for which I have an unknown voltage.", - "The node here is vI, so I need to find this,", - "there's just one unknown node voltage.", - "And I am going to need some element laws.", - "For the capacitor I know the iV relation is given by the i for", - "the capacitor is Cdv/dt. And just to show the capacitor", - "I am just calling it dvc/dt. Similarly, for an inductor,", - "L, the voltage across the inductor is given by Ldi/dt.", - "So this is the vI relation for the capacitor,", - "the vI relation for an inductor.", - "It also suits us to write this in an integral form.", - "So if I integrate both sides of this equation and I bring L down", - "to this side, I end up getting something like", - "this, 1/L minus infinity to t, VLdt, and that is simply iL.", - "I am just simply replacing this with an integral form.", - "So this is a VI relationship for the inductor and this is for", - "the capacitor. So let me now go ahead and", - "apply the node method for my circuit here.", - "Here, for the node method, I have to equate the currents", - "coming into the node or sum the currents coming into the node", - "and equate that to zero. And while I do that I simply", - "replace the currents by the corresponding voltages using the", - "element laws. So what do I get?", - "I get the current going in here to the inductor is equal to the", - "current going through the capacitor.", - "What is the current going the capacitor?", - "In terms of its v relationship it is Cdv/dt.", - "And the current going to the inductor is given by this", - "relation here, which is simply 1/L minus", - "infinity to t. The voltage across the", - "capacitor is simply (vI-v)dt. I have just written down the", - "node quotation for this node here.", - "Now I will just apply a bit of math and simplify it and get the", - "resulting equation. What I can do is simply", - "differentiate with respect to t here.", - "And get this to be Cd^2v/dt^2, the second derivative of v.", - "And here what I end up getting is 1/L(vI-v).", - "So I just differentiated the whole thing by d/dt here.", - "And then I just move L up here. I bring d^2v/dt^2 out here.", - "And then I get a minus v here, and that will be equal to,", - "oh, I'm sorry. Let me leave this here.", - "Bring the minus v to this side so it becomes a plus and leave", - "vI on this side. So I end up getting", - "LCd^2v/dt^2. I bring L up here.", - "And then I take v to the other side.", - "Plus v and leave vI here so I get vI.", - "That is second order differential equation that", - "governs the characteristics of the voltage, v.", - "So much as the voltage across the capacitor was a state", - "variable in our RC circuits or the current through the inductor", - "was a state variable in our RL circuits, out here both the", - "current through the inductor and the voltage across the capacitor", - "are my two state variables. And so here I have a", - "second-order equation in my voltage, v.", - "Again, going through the foundations here,", - "I am now going to go through a bunch of math.", - "Up to here it was circuit analysis, and now I am just", - "going to do math. For the next three or four", - "blackboards just math. You can solve this second-order", - "differential equation any which way you want.", - "But just to keep things as simple as possible,", - "in 6.002 I solve all the differential equations,", - "it turns out we are fortunate enough we can do that,", - "using the exact same method again and again and again,", - "the same thing can be applied. And the method that we use to", - "solve it is the method of homogenous and particular", - "solutions. So the first step we are going", - "to find the particular solution, vP.", - "Second step we find the homogenous solution,", - "vH. And the third step we are going", - "to find the total solution as the sum of, v is simply the", - "particular plus the homogenous solution and then solve for", - "constants based on the initial conditions and the applied", - "voltage. So let's write down initial", - "conditions. Let's assume,", - "for simplicity, that my initial conditions are", - "simply the voltage across the capacitor is zero to begin and", - "the current through my inductor is also zero as I begin life.", - "Now, this is what is called \"zero state\".", - "v and i are both zero, and so the response of my", - "circuit for some input is going to be called ZSR.", - "You've probably heard this term in one of your recitations.", - "So zero state response simply says I start with my circuit at", - "rest and looks at how it behaves for some given input.", - "That is a little term you may end up using.", - "My input next. I am going to use the following", - "input. vI of t is going to be a step,", - "is going to look like this. My input is at t=0 v is going", - "from zero to some voltage VI and then stay at that voltage.", - "It is going to be a step. Kaboom.", - "And you can see why I am going with this set of variables,", - "because I want make this situation as close as possible", - "to the funny behavior we observed there.", - "Remember we had a step, and because of the step we had", - "some behavior at that node? So I will try to bring you as", - "close to that. In tomorrow's lecture,", - "I am going to close the loop around that and derive for you", - "exactly the behavior we saw on the scope.", - "And to get there I am going to be try to be as close as", - "possible to the constants and other parameters in the demo.", - "So VI is a step and zero state. Just in terms of notation,", - "this kind of a step input occurs pretty frequently.", - "And we just have a special notation for it.", - "We simply call it VI is the final value here.", - "And we call it u(t). So VIu(t), u(t) simply", - "represents a step at time t=0, steps from zero volts to VI.", - "That is just a little more notation that will come in handy", - "at some point. More math now.", - "Three steps, particular solution,", - "homogenous solution, total solution/constants.", - "This is almost like a mantra here, like a chorus.", - "Homogenous solution we compute using a four-step method.", - "And four-step method for homogenous solutions,", - "it turns out that it happens to be that way for all the", - "equations we will see in our course.", - "The first step would be assume a solution of the form Ae^st.", - "Exactly as with RCs. If you close your eyes and do", - "exactly what you did for RCs you will get to where you want to", - "be. You assume a solution of the", - "form Ae^st. Substitute that into your", - "homogenous equation. Obtain the characteristic", - "equation. Solve for the roots.", - "And then write down your homogenous solution.", - "Same sort of steps again and again and again until you get", - "bored to tears. Particular solution.", - "For the particular solution, I simply need to find a", - "solution, any solution, if not the most general one but", - "any solution that satisfies the particular equation which", - "satisfies that equation. LCd^2vP/dt^2+vP=VI.", - "My input is a step and I am going to look for the solution", - "for time t greater than zero. Notice that for time t less", - "than or equal to zero, v is going to be zero.", - "So I am looking for a solution greater than t=0.", - "Here, if I substitute vP=VI, that is a particular solution.", - "Because if I substitute VI here this goes to zero and then I get", - "VI=VI, so this works. I promised you this was going", - "to be simple. You cannot get any simpler than", - "that. I have done my first step.", - "I found the particular solution.", - "And VI is a good enough particular solution so I will", - "use it, I will take it. As my second step I am going to", - "find vH or the solution to the homogenous equation.", - "And the homogenous equation is simply that equation with drive", - "set to zero. What I get here is", - "LCd^2vH/dt^2+vH=0. That is my homogenous equation.", - "I simply set the drive to be zero.", - "And to find the solution here, I go through my four-step", - "method. Again, in 6.002 following the", - "kind of Occam's principle, we just show you the absolute", - "minimum necessary to get to where you want.", - "The absolute minimum necessary is it turns out that we can", - "solve all our differential equations that we use here by", - "using the methods of homogenous and particular solutions.", - "And every homogenous solution can be solved by a four-step", - "method. That is about as minimal as it", - "can get. So no extraneous stuff there.", - "The four-step method, four steps.", - "The first step is assume a solution of the form vH=Ae^st.", - "What I have noticed is that students starting out are", - "usually scared of differential equations.", - "I know I was when I was a student.", - "And the trick with differential equations is that it is all a", - "matter of psych. Just because you see some", - "squigglies and squagglies and a bunch of math and so on you say", - "oh, that must be hard. But differential equations are", - "actually the simplest thing there is because in a large", - "majority of cases the way you solve them is you assume you", - "know the answer, someone tells you the answer.", - "And then all you are left to do is shove the answer into the", - "equation and find out the constants that makes it the", - "answer. Just a matter of psych.", - "Psych yourselves that this stuff is easy,", - "because I am telling you what the solution is.", - "All you have to do is substitute and verify.", - "If you think about differential equations that way or a large", - "majority of them, it really is very simple if you", - "can just get past the squigglies here.", - "Just get past the squigglies and then just simply stick in", - "some simple stuff and it works. I mean it just cannot get any", - "easier. I cannot think of any other", - "field where the way you find a solution is assume you know the", - "solution and stick it in. It has never made any sense to", - "me but that is how it is. So we assume the solution to", - "the form Ae^st, you stick it in there,", - "and you have to find out the A and s that make it so.", - "It cannot get any simpler than that.", - "Let's stick the sucker in here and see what we can get.", - "Substitute Ae^st here I get LCA, and second derivative,", - "so it's s^2 e^st. And Ae^st on this one here.", - "And that equals zero. And then let me just solve for", - "whatever I can find. Assuming I don't take the", - "trivial case A=0, I cancel these guys out.", - "And what I am left with is simply LCs^2+1=0.", - "In other words, what I end up getting is B,", - "s^2=-1/LC. My first step was,", - "I am giving you solutions, stick them in there,", - "assume a solution of this form. Second step is get the", - "characteristic equation. And the way you get the", - "characteristic equation is that you simply stick this guy in", - "there. And what you end up getting is", - "some equation in s^2. Do you remember what you got", - "for first order circuits? What s was?", - "What is s? For first order circuits,", - "what did you get as a characteristic equation?", - "s+1/RC=0. The same thing.", - "Just remember to blindly apply the steps.", - "It will lead you to the answer. This is called the", - "\"characteristic equation\". This is incredibly important.", - "You will see in about a couple weeks from now that once you", - "write the characteristic equation down for a circuit,", - "it tells you all there is to know about the circuit.", - "And often times you can stop solving right here.", - "To experienced circuit designers this tells me", - "everything there is to know. This is really key.", - "That's why it's called a characteristic equation.", - "I believe in problem number three of the homework that will", - "be coming out this week, that is exactly what you are", - "going to do. I am going to give you a", - "circuit, ask you to get to the characteristic equation quickly", - "and then from there intuit the solution.", - "Write the characteristic equation and then just intuit", - "solution, it's that simple. So, step A, assume a solution", - "of the form, step B, write the characteristic", - "equation down. And let me just simplify that a", - "little bit. I go ahead and find my roots.", - "And my roots here, remember that j is the square", - "root of minus one. And so what I end up getting", - "is, my two roots here are, plus j square root of 1/LC and", - "minus j square root of 1/LC. Two roots.", - "And just as a shorthand notation, much like I had a", - "shorthand notation for RC, what was my shorthand notation", - "for RC? Tau.", - "Just as tau was big in first order, we have a corresponding", - "thing that is big in second order and that is omega nought.", - "Omega nought is simply square root 1/LC.", - "Just as tau was RC, omega nought is a shorthand", - "here. And so s is simply plus or", - "minus j omega nought. Notice that in this equation", - "here, if you take the square root of LC there that has units", - "of time, so one divided by that has units of frequency.", - "Notice that this guy is a frequency in radians.", - "I end up getting my roots of the homogenous equation,", - "and that is my third step. And as my fourth step,", - "I simply write down the homogenous solution as", - "substituting s with its roots and writing the most general", - "possible form of the solution, and that would be A1e^(j omega", - "nought t)+A2e^(-j omega nought t).", - "Done. Some constant times this", - "solution plus some other constant times,", - "the other solution. Plus zero omega nought.", - "Remember it comes from here, Ae^st.", - "I assume the solution of this form, so my solution in this", - "most general case would be s being j omega nought in one", - "case, minus j omega nought in the other case,", - "and I sum the two to get the most general solution.", - "So blasting ahead. I now have my homogenous", - "solution. And as my third step of", - "solution to differential equations I write down the total", - "solution, v=vP+vH, particular plus the homogenous", - "solutions. And v=VI, was my particular", - "solution, +A1e^(j omega nought t)+A2e^(-j omega nought t) is my", - "complete solution. The final step,", - "write down the total solution and find the constants from the", - "initial conditions. To find the constants from the", - "initial conditions, let's start with,", - "the voltage is zero to begin with.", - "This equation governs the characteristics of v,", - "so I need to find the initial conditions.", - "First of all, I know that know that v(0)=0.", - "From there I substitute t=0. And so this goes to one,", - "this goes to one, and I end up getting", - "0=VI+A1+A2. That is my first expression.", - "And then I am also given that i(0)=0.", - "And so I can get that as well. How do I get i?", - "This is v. I know that i=Cdv/dt,", - "so I can get i by simply multiplying by C and", - "differentiating this with respect to t.", - "I get C, this guy vanishes so I get d/dt of this.", - "So it is CA1(j omega nought) e^(j omega nought t)+CA2(-j", - "omega nought)e^(-j omega nought t).", - "From here I am given that that is zero, and so therefore this", - "guy becomes a one, this guy becomes a one,", - "j omega nought, j omega nought cancel out.", - "What I end up getting is A1=A2. From the second initial", - "condition I get A1=A2. From these two,", - "if I substitute here for A2, I get VI + 2A1 = 0,", - "or A1=-VI/2. That is also equal to A2.", - "Therefore, my total solution now can be written in terms of", - "the actual values of the constants I have obtained.", - "I get VI-VI/2. So A1 and A2 are equal.", - "I just pull them outside. I pull VI-2 outside and I stick", - "these two guys in parenthesis in.", - "Again, I promised you no more circuits from here on until the", - "very last board or something like that.", - "It is all math, so not much else happening", - "there. More math.", - "If you would like, I could skip all the way to the", - "end and show you the answer. But I just love to write", - "equations on the board so let me just go through that.", - "I am going to simplify this a little further here.", - "And we should remember this form by the Euler relation,", - "ejx=cos x+j sin x. And by the same token,", - "(e^jx + e^-jx)/2=cos x. You all should know this from", - "the Euler relation. So were are using this guy", - "here, ej^x + e^-jx=2cos x. And so this one is 2 cosine of", - "omega nought t, 2 and 2 cancel out,", - "and what I am left with is v(t)=VI-VI cos( omega nought t).", - "And the current is Cdv/dt, which is simply CVI sin( omega", - "nought t). Just remember that omega nought", - "is the square root of 1/LC. We are done.", - "In fact, I did not give that answer the importance that was", - "due so let me just draw.", - "There. That is better.", - "Enough math. In a nutshell,", - "what did we do. We wrote the node method,", - "it's a very simple circuit, to write down the equation", - "governing that circuit. And then we grunged through a", - "bunch of math. Not a whole lot here.", - "It is pretty simple. And ended up with a relation", - "that says the voltage across the capacitor for a step input,", - "assuming zero state, is a constant VI-VI cos omega", - "t. Notice that even though I have", - "a step input, the circuit dynamics are such", - "that I get a cosine in there. You can begin to see where", - "these cosines are coming from now.", - "They come in here. And if you recall the example I", - "showed you earlier of the inverter circuit,", - "remember there was a cosine that decayed,", - "that was sort of losing energy and kind of dying out?", - "So you can see where the cosines are coming from.", - "And just to draw you a little sketch here.", - "Let me draw v and i for you and let me plot omega t,", - "pi/2, pi and so on. Let me plot VI.", - "When time t=0, VI=0, cosine omega t is one,", - "and so VI-VI=0. That is simply a cosine that", - "starts out at zero here, and at pi I get cosine omega t", - "is minus one, so I get plus VI on the other", - "side. So I end up at +2VI.", - "At this point the voltage is here.", - "And notice that this guy looks like this.", - "It is a cosine that is translated up so that its mean", - "value is not zero but VI. It is just a translation up of", - "a cosine. Similarly, in this case for the", - "current it is a sinusoidal characteristic.", - "And it looks something like this where the peak is given by", - "CVI, oh, I messed up.", - "When I differentiated this is missed the omega nought out", - "there.", - "What I would like to do now -- This is the form of the output", - "for a step input. What I would like to do next is", - "show you a demo. But before I show you a demo,", - "I always found it strange that I have a step input and then I", - "have two little elements, how can I get a sine coming out", - "of the output? I would like to get some", - "intuition as to why things behave the way they are.", - "I could go and pray to find out, but let me just give you", - "some very basic insight as to why this behaves the way it", - "does. Let me draw the circuit for you", - "here. And this is my inductor L and", - "capacitance C. Remember this is v.", - "Let me just walk you through what is happening there and get", - "you to understand this. Now, you have seen sines occur", - "before. If you go and write down the", - "equation of motion of a pendulum, you know,", - "you have a pendulum, you move it to one side,", - "let go. It is also governed by", - "sinusoidal characteristics. And you will find that the", - "equation governing its motion is very much of the same form,", - "and you get the sinusoid where you have energy that is sloshing", - "back and forth between maximum potential energy to maximum", - "kinetic energy and zero potential energy back to maximum", - "potential energy, zero kinetic.", - "So it is energy sloshing back and forth.", - "The same way here. Capacitors and inductors store", - "energy. Let's walk through and see what", - "happens. I start off with both of them", - "having the stage zero, zero current,", - "zero voltage. I apply a step here.", - "Boom, the step comes instanteously to VI.", - "I notice that the capacitor voltage cannot change instantly", - "unless there is an infinite pulse of a sort,", - "so this guy cannot change instantly.", - "And so its voltage starts off being zero.", - "So the entire voltage here, KVL must be true no matter", - "what. They are absolutely fundamental", - "principles from Maxwell's equations.", - "KVL must hold, which means that the entire", - "voltage VI must appear across the inductor.", - "I put a big voltage across the inductor and its current begins", - "to build up. There you go.", - "A voltage across the inductor, its current begins to build up.", - "As its current begins to build up that current must flow", - "through the capacitor, too.", - "And as current flows through a capacitor it is depositing", - "charge into the capacitor. As the capacitor begins to get", - "charge deposited on it, its voltage begins to rise.", - "Let's see what happens here. Its voltage keeps rising.", - "At some point, the voltage across the", - "capacitor is equal to VI. But then VI equals this VI", - "here. So when the two become VI,", - "the inductor has zero volts across it.", - "So there is no longer a potential difference that is", - "increasing the current in that direction.", - "At that point, at pi divided by 2,", - "I have some current going into the inductor so there is no", - "longer a pressure that is forcing more current through the", - "inductor because this voltage reaches VI.", - "But remember capacitors like to sit around holding voltages.", - "Just remember that demo. That rinky-dink capacitor sat", - "there stubbornly holding its voltage.", - "And it had a huge spark towards the end.", - "It just sat there holding its voltage.", - "In the same manner, inductors love to sit around", - "holding a current. They will do whatever they can", - "to keep the current going through them.", - "It has got the current going through.", - "And few forces on earth can change that.", - "And so therefore, even though the capacitor", - "voltage is VI and the voltage drop across the inductor is", - "zero, it still keeps supplying a current.", - "It has got the current. It's got inertia.", - "It keeps going. It is like a runaway train.", - "You may not be pushing the train from the back,", - "but once it is running it has got kinetic energy and is going", - "to run no matter what for a least some more time,", - "even if you take away the force on the train.", - "So I have taken away the force on the punching more current", - "through, but it has kinetic energy.", - "It has current flowing through it so it continues to supply a", - "current. Because it continues to supply", - "the current the capacitor voltage keeps increasing.", - "This is a subtle insight which is absolutely spectacular that", - "with zero volts across it, it still keeps pumping that", - "current. Capacitor voltage has gone up.", - "And guess what? The voltage on this side is", - "higher now but this guy is still pumping a current.", - "Man, I have been born to do this, you know,", - "I shall pump a current. However, because the voltage", - "has now gone up here gradually the current begins to diminish.", - "So the capacitor is concerned. You pump a current into me,", - "my voltage goes up. At some point,", - "like a runaway train, it comes to a halt.", - "The current through the capacitor drains and now goes to", - "zero and the capacitor voltage reaches 2VI.", - "So this is at 2VI now and this is at VI.", - "Now the situation is not in equilibrium.", - "At this point there is zero current through it,", - "but guess what? I have a VI pumping in this", - "direction now. I have the same VI punching in", - "this direction. So guess what?", - "Its current must now build up in this direction and its", - "current begins to build up in that direction.", - "That begins to discharge the capacitor and the capacitor then", - "goes on to a negative, or the current goes down to a", - "maximum negative current, and this process continues.", - "What you are seeing here is energy.", - "It is sloshing back and forth between the two,", - "and that is kind of a key. I will just quickly put up a", - "demo that you can watch as you are walking out.", - "With a step input, notice the green is the voltage", - "across the capacitor and the orange is the current through", - "the capacitor." - ] -} \ No newline at end of file diff --git a/subs/z4Bw9Vvx7es.srt.sjson b/subs/z4Bw9Vvx7es.srt.sjson deleted file mode 100644 index 243a726425..0000000000 --- a/subs/z4Bw9Vvx7es.srt.sjson +++ /dev/null @@ -1,569 +0,0 @@ -{ - "start": [ - 120, - 2540, - 3310, - 6590, - 7500, - 11040, - 16100, - 18490, - 19390, - 24450, - 28923, - 29910, - 33840, - 36510, - 38810, - 42210, - 46060, - 50180, - 52280, - 54600, - 58820, - 62380, - 64290, - 66460, - 69690, - 73330, - 77340, - 78390, - 80960, - 83950, - 86870, - 89980, - 93140, - 95340, - 96780, - 99670, - 102155, - 103640, - 105280, - 109240, - 112850, - 114820, - 118260, - 121460, - 123990, - 127220, - 131060, - 131520, - 133780, - 136430, - 136680, - 139000, - 143990, - 146730, - 149680, - 150690, - 152690, - 155430, - 158330, - 161100, - 163720, - 165940, - 169060, - 169800, - 174000, - 177060, - 177740, - 180880, - 182820, - 187110, - 190110, - 193180, - 196430, - 197710, - 200740, - 203810, - 205420, - 207050, - 210170, - 213230, - 214030, - 216230, - 219510, - 223370, - 226280, - 229130, - 232750, - 235370, - 238110, - 241220, - 243820, - 245450, - 250510, - 252410, - 257959, - 260260, - 262970, - 264640, - 265630, - 268580, - 270970, - 273300, - 275780, - 280010, - 281210, - 285620, - 289860, - 290700, - 293520, - 296660, - 299540, - 302500, - 305590, - 307940, - 310200, - 311840, - 314690, - 318000, - 322040, - 322690, - 325050, - 326950, - 329650, - 332130, - 332800, - 336400, - 340020, - 342710, - 344645, - 347780, - 350980, - 352770, - 356010, - 358925, - 364450, - 368350, - 370710, - 373860, - 377620, - 381470, - 384160, - 386530, - 389070, - 391950, - 396610, - 398890, - 402680, - 407260, - 410100, - 413710, - 417740, - 421360, - 424170, - 428450, - 429330, - 430150, - 432410, - 435730, - 437850, - 439420, - 441750, - 444840, - 447230, - 450530, - 454240, - 456780, - 457960, - 459030, - 463770, - 465980, - 469200, - 470760, - 473930, - 476100, - 477660, - 479000, - 480370, - 482990, - 486610, - 491680, - 495680, - 499130, - 502260, - 506170, - 509720, - 511390, - 515020 - ], - "end": [ - 2540, - 3310, - 6590, - 7500, - 11040, - 16100, - 18490, - 19390, - 24450, - 28923, - 29910, - 33840, - 36510, - 38810, - 42210, - 46060, - 50180, - 52280, - 54600, - 58820, - 62380, - 64290, - 66460, - 69690, - 73330, - 77340, - 78390, - 80960, - 83950, - 86870, - 89980, - 93140, - 95340, - 96780, - 99670, - 102155, - 103640, - 105280, - 109240, - 112850, - 114820, - 118260, - 121460, - 123990, - 127220, - 131060, - 131520, - 133780, - 136430, - 136680, - 139000, - 143990, - 146730, - 149680, - 150690, - 152690, - 155430, - 158330, - 161100, - 163720, - 165940, - 169060, - 169800, - 174000, - 177060, - 177740, - 180880, - 182820, - 187110, - 190110, - 193180, - 196430, - 197710, - 200740, - 203810, - 205420, - 207050, - 210170, - 213230, - 214030, - 216230, - 219510, - 223370, - 226280, - 229130, - 232750, - 235370, - 238110, - 241220, - 243820, - 245450, - 250510, - 252410, - 257959, - 260260, - 262970, - 264640, - 265630, - 268580, - 270970, - 273300, - 275780, - 280010, - 281210, - 285620, - 289860, - 290700, - 293520, - 296660, - 299540, - 302500, - 305590, - 307940, - 310200, - 311840, - 314690, - 318000, - 322040, - 322690, - 325050, - 326950, - 329650, - 332130, - 332800, - 336400, - 340020, - 342710, - 344645, - 347780, - 350980, - 352770, - 356010, - 358925, - 364450, - 368350, - 370710, - 373860, - 377620, - 381470, - 384160, - 386530, - 389070, - 391950, - 396610, - 398890, - 402680, - 407260, - 410100, - 413710, - 417740, - 421360, - 424170, - 428450, - 429330, - 430150, - 432410, - 435730, - 437850, - 439420, - 441750, - 444840, - 447230, - 450530, - 454240, - 456780, - 457960, - 459030, - 463770, - 465980, - 469200, - 470760, - 473930, - 476100, - 477660, - 479000, - 480370, - 482990, - 486610, - 491680, - 495680, - 499130, - 502260, - 506170, - 509720, - 511390, - 515020, - 517880 - ], - "text": [ - "PROFESSOR: Let's move on from here, now that we've seen the", - "Thevenin pattern.", - "What I'd like to do is continue analyzing this a", - "little bit more.", - "As I said earlier, the Thevenin pattern replaces the", - "arbitrary network, N. And VTH here in the Thevenin network", - "is simply the open circuit voltage seen at", - "the terminal pair.", - "In other words, if I looked at network N and I simply", - "measured the voltage at the terminal pair, it has to be an", - "open circuit voltage.", - "That is, without anything connected there, then whatever", - "voltage I measure there would be the Thevenin voltage.", - "Notice that you can see the same thing here.", - "If I measure the voltage at that point, without any", - "external excitation, with an open circuit here, then VTH", - "would directly appear at the terminal, and I would be able", - "to measure the Thevenin voltage.", - "Similarly, what is RTH ?", - "RTH is simply the resistance of the network seen at the", - "terminal there, with all the voltages, Vm's, and all the", - "currents, In's, set to 0.", - "In other words, the way you can find the Thevenin", - "resistance of a network is simply set all the voltages", - "engines and all the currents to 0, and then go ahead and", - "simply measure the resistance looking into", - "that terminal pair.", - "And that will give you RTH.", - "Again, as a quick summary, given any network n, and this", - "case a network with independent voltage and", - "current sources, I can find a Thevenin equivalent which", - "comprises a Thevenin voltage, VTH, and a", - "resistance, RTH, as follows.", - "I open-circuit the connection.", - "In other words, I don't connect anything to the", - "terminal pair when I'm measuring the voltage V. I", - "measure the open circuit voltage there,", - "and that is my VTH.", - "Then I turn off all my current sources and voltage sources", - "inside the network N, and simply measure its resistance.", - "And that is RTH.", - "So that's how I can get RTH and VTH by measurement.", - "And for the purpose of computing some property such", - "as the voltage when an external excitation is", - "applied, I can use those values of VTH and RTH to", - "replace the entire arbitrary network N with this Thevenin", - "equivalent pattern.", - "This is a very, very powerful technique, and we will see", - "some examples of this shortly.", - "OK.", - "So we are ready to define the Thevenin method.", - "So in the Thevenin method, you are given some network N,", - "maybe a horrendous network with a whole bunch of voltage", - "sources and current sources and resistors and", - "so on and so forth.", - "And you have some other external", - "network, E. E for external.", - "Then what I can do is, by the Thevenin method, I can break", - "this down into a simpler problem as follows.", - "What I would do as a first step is I would replace the", - "network N with this Thevenin equivalent.", - "And then as my second step, I would solve with the external", - "network, E.", - "So in other words, what I would do is I would replace", - "the network N with its Thevenin equivalent as my", - "first step.", - "And then I would go ahead and solve with the external", - "network E in my second step.", - "And notice that I can compute RTH and VTH for the Thevenin", - "equivalent using the discussion from a few minutes", - "ago, where I can measure it by measuring the open circuit", - "voltage and the effective resistance of the network with", - "all sources turned off.", - "Or I can also compute it by using superposition and", - "turning off each of the voltages one by one.", - "I can do it in either way.", - "So this is the Thevenin method.", - "Again, as a first step, I replace the network N with a", - "Thevenin equivalent, and then I solve for the external", - "network, E.", - "Now you might wonder, when is this useful?", - "So it turns out that in many cases where all you're", - "interested in is some value, V for example, and you don't", - "really care about what's going on inside this horrendous", - "network N, then you can simplify your life", - "tremendously by replacing that entire network with its", - "Thevenin equivalent, and then solving the circuit for the", - "voltage V based on that Thevenin equivalent.", - "Again, this is a process where we divide up the problem into", - "two simpler components, finding a Thevenin and then", - "solving the resulting circuit.", - "So let us now move on to an example and go to our old", - "faithful little circuit here.", - "And in this example, let us say that my goal here is to", - "find out the current, I1.", - "All I care about is to find out the current, I1.", - "Now of course I can go ahead and apply the Norton", - "method and do it.", - "But let us say that in this case I want to apply the", - "Thevenin method and use this as an example, and I'm going", - "to show you how simple it can get.", - "So to apply the Thevenin method, remember the first", - "part was to identify some sub-network and replace that", - "by its Thevenin equivalent.", - "So what I'm going to do is I'm going to identify this network", - "here as the arbitrary network N whose Thevenin equivalent", - "I'm going to find.", - "And then I'm going to view the network on the left-hand side,", - "the voltage and resistance, as the network E. And the reason", - "I'm going to do that is, notice that if I replace", - "network N with a Thevenin equivalent, which would be", - "simply a resistance and a voltage, notice that the", - "resulting circuit would be very simple to analyze,", - "because it would have pair of voltages and a pair of", - "resistances in series.", - "Let me we go ahead and find the Thevenin equivalent for", - "network one in step one of the Thevenin method.", - "So I'm going to replace network N by its Thevenin", - "equivalent.", - "So my network E is going to stay the same.", - "So E hasn't changed.", - "I'm trying to figure out the value of I1.", - "And I'm going to replace the network N with this Thevenin", - "equivalent.", - "So the Thevenin equivalent will fit in here into this", - "box, and let me draw the Thevenin pattern, just to be", - "clear, where this is R Thevenin", - "and this is V Thevenin.", - "And we'll replace network N with its Thevenin equivalent,", - "and in order to do that, I need to find all the values of", - "RTH and VTH.", - "And let me go ahead and do that next.", - "Continuing with step one of the Thevenin method, I have my", - "network N. And I need to find out VTH and RTH for that", - "network N. And again, as a reminder, this is what I have", - "for VTH and RTH.", - "So let me first find out the VTH.", - "And as I told you earlier, VTH is simply the open circuit", - "voltage of the network N. So how do I find out what the", - "open circuit voltage of that network N is?", - "Well, it's pretty straightforward.", - "Let me draw the network here.", - "Let's have an R2 here, and I have a current here.", - "And the open circuit voltage is my Thevenin voltage, VTH.", - "So here's your simple pattern.", - "I have a current I that is flowing into a resistance R2.", - "And so therefore VTH is simply I times R2.", - "So that gives me VTH.", - "So the second step, I need to find out RTH.", - "And the way I'm going to find out RTH is I'm going to turn", - "off all the independent sources inside network N, and", - "then measure the resistance looking in.", - "So this was my network from before.", - "This corresponds to this network.", - "I'll do the same now.", - "So I'm going to put my network in there.", - "And the difference is that I'm going to turn off all the", - "voltages and currents that are", - "independent inside that network.", - "So as I draw it out, R2 stays the same.", - "But here, what I'm going to do is I'm going to turn off my", - "current source and open-circuit that.", - "So I'm going to turn off my current source, and so now,", - "RTH will simply be the resistance looking in.", - "That is easy enough to do.", - "So RTH is simply R2.", - "So there you have it.", - "I've computed VTH and RTH, and that lets me develop my", - "Thevenin network, and I'm ready for step two.", - "So as I said earlier, VTH and RTH are given", - "by these two values.", - "And what I'm going to do is I'm going to replace the", - "network N with its Thevenin equivalent.", - "Network E stays the same.", - "I show that here.", - "That hasn't changed.", - "But now what I'm going to do is I'm going to replace the", - "network N with its Thevenin equivalent like so.", - "But I get the RTH in series with the VTH, and the VTH is", - "given by IR2 and RTH is given by R2.", - "So in step two, I now need to solve with the external", - "network E applied to the Thevenin equivalent network", - "that as replaced the original network N. So this is, again,", - "a very simple circuit, and recall all that I", - "cared about was I1.", - "And so, let me let you think for a couple of seconds about", - "what the value of I1 is before I go and do it myself." - ] -} \ No newline at end of file diff --git a/subs/zpzcLzD2dV4.srt.sjson b/subs/zpzcLzD2dV4.srt.sjson deleted file mode 100644 index f6de185a12..0000000000 --- a/subs/zpzcLzD2dV4.srt.sjson +++ /dev/null @@ -1,527 +0,0 @@ -{ - "start": [ - 1176, - 6660, - 11910, - 18130, - 25890, - 29310, - 31300, - 35050, - 38130, - 40690, - 44320, - 47910, - 50490, - 53430, - 59720, - 64300, - 68200, - 71920, - 75196, - 83400, - 88850, - 91850, - 95680, - 96630, - 101150, - 104760, - 109530, - 115689, - 122270, - 126810, - 131150, - 133790, - 140560, - 147800, - 153010, - 156860, - 162357, - 164010, - 166990, - 170490, - 173520, - 176870, - 183290, - 187140, - 191490, - 196180, - 201730, - 206460, - 209050, - 214100, - 215590, - 218280, - 220180, - 224170, - 227720, - 233510, - 238260, - 241690, - 244694, - 249930, - 254050, - 258720, - 263340, - 268055, - 271880, - 276940, - 281560, - 286860, - 288910, - 294310, - 299090, - 303870, - 310460, - 313896, - 317010, - 324480, - 326600, - 330280, - 336500, - 342630, - 345310, - 346330, - 346920, - 350060, - 350810, - 353190, - 359180, - 365600, - 369410, - 372760, - 374640, - 379380, - 383320, - 387100, - 394000, - 395080, - 398780, - 402600, - 405330, - 407410, - 417210, - 423730, - 427250, - 428420, - 436400, - 441790, - 444180, - 448630, - 452510, - 455710, - 463570, - 465430, - 470480, - 474490, - 480380, - 482740, - 487990, - 490800, - 493030, - 498370, - 504070, - 505660, - 507760, - 510610, - 511650, - 514809, - 518190, - 521630, - 525350, - 529710, - 533790, - 538120, - 543420, - 545920, - 548725, - 553010, - 556820, - 564220, - 570020, - 575360, - 576120, - 582960, - 589840, - 593700, - 598650, - 604560, - 606850, - 608650, - 612260, - 616070, - 619336, - 621680, - 622480, - 624430, - 627700, - 630220, - 634778, - 638070, - 645120, - 648206, - 651920, - 653550, - 654990, - 655830, - 659170, - 664330, - 668605, - 676080, - 677945, - 679720, - 685200, - 690660, - 694700 - ], - "end": [ - 6660, - 11910, - 18130, - 21870, - 29310, - 31300, - 35050, - 38130, - 40690, - 44320, - 47910, - 50490, - 53430, - 59720, - 64300, - 68200, - 71920, - 75196, - 83400, - 88850, - 91850, - 95680, - 96630, - 101150, - 104760, - 109530, - 115689, - 122270, - 126810, - 131150, - 133790, - 140560, - 147800, - 153010, - 156860, - 162357, - 164010, - 166990, - 170490, - 173520, - 176870, - 183290, - 187140, - 191490, - 196180, - 201730, - 206460, - 209050, - 214100, - 215590, - 218280, - 220180, - 224170, - 227720, - 228970, - 235715, - 241690, - 244694, - 249930, - 254050, - 258720, - 263340, - 268055, - 271880, - 276940, - 278190, - 286860, - 288910, - 294310, - 295770, - 301330, - 307960, - 313896, - 317010, - 318260, - 326600, - 330280, - 336500, - 342630, - 345310, - 346330, - 346920, - 350060, - 350810, - 353190, - 359180, - 365600, - 369410, - 372760, - 374640, - 379380, - 383320, - 387100, - 394000, - 395080, - 398780, - 402600, - 405330, - 407410, - 417210, - 423730, - 427250, - 428420, - 436400, - 441790, - 444180, - 445430, - 452510, - 455710, - 463570, - 465430, - 466680, - 474490, - 480380, - 482740, - 487990, - 490800, - 493030, - 498370, - 504070, - 505660, - 507760, - 510610, - 511650, - 514809, - 518190, - 521630, - 525350, - 529710, - 533790, - 535040, - 543420, - 545920, - 548725, - 549975, - 556820, - 564220, - 570020, - 575360, - 576120, - 582960, - 589840, - 593700, - 598650, - 604560, - 606850, - 608650, - 612260, - 616070, - 619336, - 621680, - 622480, - 624430, - 627700, - 630220, - 634778, - 638070, - 641765, - 648206, - 651920, - 653550, - 654990, - 655830, - 659170, - 664330, - 668605, - 676080, - 677945, - 679720, - 685200, - 690660, - 694700, - 697520 - ], - "text": [ - "SPEAKER 1: In this unit, we're going to study several new", - "tools in our tool chest. These include the superposition", - "method, the Thevenin method, and the Norton method.", - "The recommended reading is chapter three of the textbook.", - "Before we begin, let's do a quick review of what we've", - "seen so far.", - "So recall we've been building up our tool chest, a tool", - "chest of techniques that can analyze circuits.", - "We've seen several.", - "First, we've seen the KVL/KCL method, where, given the", - "KVL/KCL rules, you would write a bunch of equations to", - "circuits and go and solve them.", - "Then, you looked at the circuit composition rules", - "method, where you simplified circuits into more composed", - "circuits and analyzed them much more simply.", - "The third method was the Node method.", - "The Node method is the workhorse of 6.002 and pretty", - "much all of circuit analysis.", - "The key idea behind the Node method is that KCL at the", - "nodes is applied using all voltages referenced to ground,", - "where the ground is taken as zero.", - "That enables substantial simplicity in", - "how the Node method--", - "in how the rules are applied, giving you way better and", - "efficient techniques.", - "So these are three methods in your tool chest.", - "So today, we are going to look at how to build up your tool", - "chest. And I'm going to introduce a new technique, or", - "a set of two techniques, the superposition method, the", - "Thevenin method, and the Norton method.", - "I'll start with the superposition method.", - "Now, these methods apply only to linear circuits.", - "Now recall, when we did the analysis of various circuits--", - "recall that we had looked at this playground of ours.", - "And in this playground, all our techniques applied.", - "Now it turns out, there's a region of the playground in", - "which circuits are linear.", - "It's a subset of the playground.", - "Within this playground, some extremely", - "powerful tools apply.", - "Imagine that, within this playground, you are able to", - "use a bazooka as a weapon, while you can't use it outside", - "this little piece of playground.", - "This subset of the playground that we've been used to so far", - "is the playground containing only linear circuits.", - "So in this unit, I would like to introduce linear circuits.", - "Then I'll talk about the properties of linearity.", - "What does it buy us?", - "And then I will talk about the superposition method.", - "The superposition method applies", - "only for linear circuits.", - "And we'll look at how that can substantially", - "simplify circuit analysis.", - "So in this video segment, let's start with introducing", - "linear circuits.", - "I would like to introduce a technique with an example.", - "This is a very simple circuit containing two sources, the", - "voltage source and the current source.", - "I'm going to apply the Node method to analyze this.", - "So according to the Node method, I am going to start", - "with introducing a ground node.", - "So I want to pick this node as my ground node.", - "And the reason I'm doing that is, as is our usual practice,", - "this ground node connects to one terminal of both of our", - "sources, and many edges of the circuit come", - "together at that point.", - "The voltage at this node here is V, because there's a", - "voltage source connected there.", - "And the voltage at this node is labeled e. e is my unknown.", - "And my goal is to find e.", - "So how do I apply the Node method?", - "I'm going to start by adding a node equation for the node e.", - "So here is my node equation.", - "How do I get that?", - "Let's look at the first term.", - "The first term, e minus V divided by", - "R1, arises as follows.", - "So recall, I have to apply KCL at the node with voltage e,", - "and sum the currents coming into the node,", - "and set them to 0.", - "So--", - "I'm sorry.", - "I'm summing the currents leaving the node and setting", - "them to be 0.", - "I could do either.", - "So there's a current leaving this node in this direction.", - "In that direction, the current leaving that node is e minus", - "the voltage V divided by R1.", - "So it's e minus V divided by R1 is the current", - "leaving this node.", - "The current leaving this node through R2 is simply e divided", - "by R2, and that's this piece.", - "Finally, the current leaving this node in this direction is", - "simply minus I. And these three currents sum to 0.", - "OK.", - "That gives us the node equation, or the", - "node at voltage e.", - "You've already noticed some very interesting things in", - "this equation.", - "notice that the equation is linear in e, V, and I. Notice", - "that you don't see any terms involving the product eV, or V", - "squared, VI, and so on.", - "So [UNINTELLIGIBLE PHRASE]", - "this equation is linear in e, V, and I.", - "Let's go on and stir this equation a little more.", - "And I'm going to rearrange the terms.", - "So I take this equation--", - "I'm going to take this equation and rearrange the", - "terms a little bit.", - "And if you look at the equation here, 1 by R1, is", - "multiplying the inverse.", - "We divide by R1.", - "And that's shown here.", - "And then, similarly, 1 divided by R2 is multiplying e here.", - "And I show that here.", - "I move I to the right hand side, so that's here.", - "Similarly, we divide by R1.", - "Shows up here.", - "So by rearranging terms, I show the unknown voltage e to", - "be some function of the voltages V and I.", - "This turned out to be a canonic", - "representation of equations.", - "And in this representation, in this case, I", - "have a single voltage.", - "But in general, this could be multiple voltages, which I", - "could collect into a matrix form", - "This matrix here is called the conductance matrix.", - "I could stick my vector of node voltages here.", - "And on the right hand side, I have a linear sum of sources,", - "where V and I are my voltage and current sources,", - "respectively.", - "In matrix form, this matrix is commonly called G. The vector", - "of unknown voltages is called e.", - "And on the right hand side, I have the", - "linear sum of sources.", - "So let's take it one step further.", - "And in this equation, here is what I am doing.", - "I have taken this component and I have moved it over to", - "the right hand side, exposing e all by itself.", - "OK.", - "As I simplify the equation, here is what I get.", - "Notice that when I move this to the side, my V here is now", - "multiplied by R2 divided by R1 plus R2.", - "And I is multiplied by R1 and R2 divided by R1 plus R2.", - "So all I've done here is taken this part and simply moved it", - "to the right hand side and divided the right", - "hand side with that.", - "And this is what I get.", - "This should make it very clear that my unknown node voltage e", - "is a straight linear--", - "is a linear sum of the sources.", - "V is my source.", - "I is a source.", - "And I have some constant multiplier", - "multiplying those voltages.", - "So this should make it clear that this is a constant.", - "This is a constant.", - "And I have a V and a I, and so I get a linear sum of sources.", - "I can do it a little bit more clearly.", - "Looks like I've scribbled around, unfortunately, so", - "let's see if this eraser thingy works.", - "Ah.", - "There you go.", - "That works pretty nicely.", - "And let me get some color back into my pen here.", - "And so notice that in general, for any circuit, any node", - "voltage e can be represented as a linear combination of all", - "the sources, whether they're voltage", - "sources or current sources.", - "But a1, a2, b1, b2 and so on are constants that are", - "independent of the source voltages and source currents.", - "And so, in general, I end up with my unknown being a linear", - "combination of the various source voltages." - ] -} \ No newline at end of file From cc0418ca73e5cae623a13ce8bd0fe35c9adc0765 Mon Sep 17 00:00:00 2001 From: Ernie Park Date: Wed, 1 Feb 2012 12:03:22 -0500 Subject: [PATCH 3/4] updated sass --- css/application.css | 1445 ++++++++++++++++++------------------------- css/marketing.css | 140 +++-- 2 files changed, 679 insertions(+), 906 deletions(-) diff --git a/css/application.css b/css/application.css index 32e43ac3fa..517da22856 100644 --- a/css/application.css +++ b/css/application.css @@ -86,19 +86,50 @@ hr { input, select { vertical-align: middle; } +/* Generated by Font Squirrel (http://www.fontsquirrel.com) on January 25, 2012 05:06:34 PM America/New_York */ @font-face { - font-family: 'Droid Sans'; - font-style: normal; - font-weight: normal; - src: local("Droid Sans"), local("DroidSans"), url("http://themes.googleusercontent.com/static/fonts/droidsans/v3/s-BiyweUPV0v-yRb-cjciL3hpw3pgy2gAi-Ip7WPMi0.woff") format("woff"); } + font-family: 'Open Sans'; + src: url("/static/fonts/OpenSans-Regular-webfont.eot"); + src: url("/static/fonts/OpenSans-Regular-webfont.eot?#iefix") format("embedded-opentype"), url("/static/fonts/OpenSans-Regular-webfont.woff") format("woff"), url("/static/fonts/OpenSans-Regular-webfont.ttf") format("truetype"), url("/static/fonts/OpenSans-Regular-webfont.svg#OpenSansRegular") format("svg"); + font-weight: 600; + font-style: normal; } @font-face { - font-family: 'Droid Sans'; - font-style: normal; - font-weight: bold; - src: local("Droid Sans Bold"), local("DroidSans-Bold"), url("http://themes.googleusercontent.com/static/fonts/droidsans/v3/EFpQQyG9GqCrobXxL-KRMXbFhgvWbfSbdVg11QabG8w.woff") format("woff"); } + font-family: 'Open Sans'; + src: url("/static/fonts/OpenSans-Italic-webfont.eot"); + src: url("/static/fonts/OpenSans-Italic-webfont.eot?#iefix") format("embedded-opentype"), url("/static/fonts/OpenSans-Italic-webfont.woff") format("woff"), url("/static/fonts/OpenSans-Italic-webfont.ttf") format("truetype"), url("/static/fonts/OpenSans-Italic-webfont.svg#OpenSansItalic") format("svg"); + font-weight: 400; + font-style: italic; } -.clearfix:after, .topbar:after, div.course-wrapper section.course-content ol.sequence-nav:after, div.book-wrapper section.book nav:after, div.wiki-wrapper section.wiki-body header:after, body.askbot .secondary-nav nav:after, html body div.header-wrapper header:after, html body div.header-wrapper header nav ul:after, html body section.main-content:after, html footer:after, div.course-wrapper section.course-content ol.vert-mod > li:after, div.book-wrapper section.book nav ul:after, div.wiki-wrapper div#wiki_panel div#wiki_create_form:after, body.askbot footer div.footer-wrapper:after { +@font-face { + font-family: 'Open Sans'; + src: url("/static/fonts/OpenSans-Bold-webfont.eot"); + src: url("/static/fonts/OpenSans-Bold-webfont.eot?#iefix") format("embedded-opentype"), url("/static/fonts/OpenSans-Bold-webfont.woff") format("woff"), url("/static/fonts/OpenSans-Bold-webfont.ttf") format("truetype"), url("/static/fonts/OpenSans-Bold-webfont.svg#OpenSansBold") format("svg"); + font-weight: 700; + font-style: normal; } + +@font-face { + font-family: 'Open Sans'; + src: url("/static/fonts/OpenSans-BoldItalic-webfont.eot"); + src: url("/static/fonts/OpenSans-BoldItalic-webfont.eot?#iefix") format("embedded-opentype"), url("/static/fonts/OpenSans-BoldItalic-webfont.woff") format("woff"), url("/static/fonts/OpenSans-BoldItalic-webfont.ttf") format("truetype"), url("/static/fonts/OpenSans-BoldItalic-webfont.svg#OpenSansBoldItalic") format("svg"); + font-weight: 700; + font-style: italic; } + +@font-face { + font-family: 'Open Sans'; + src: url("/static/fonts/OpenSans-ExtraBold-webfont.eot"); + src: url("/static/fonts/OpenSans-ExtraBold-webfont.eot?#iefix") format("embedded-opentype"), url("/static/fonts/OpenSans-ExtraBold-webfont.woff") format("woff"), url("/static/fonts/OpenSans-ExtraBold-webfont.ttf") format("truetype"), url("/static/fonts/OpenSans-ExtraBold-webfont.svg#OpenSansExtrabold") format("svg"); + font-weight: 800; + font-style: normal; } + +@font-face { + font-family: 'Open Sans'; + src: url("/static/fonts/OpenSans-ExtraBoldItalic-webfont.eot"); + src: url("/static/fonts/OpenSans-ExtraBoldItalic-webfont.eot?#iefix") format("embedded-opentype"), url("/static/fonts/OpenSans-ExtraBoldItalic-webfont.woff") format("woff"), url("/static/fonts/OpenSans-ExtraBoldItalic-webfont.ttf") format("truetype"), url("/static/fonts/OpenSans-ExtraBoldItalic-webfont.svg#OpenSansExtraboldItalic") format("svg"); + font-weight: 800; + font-style: italic; } + +.clearfix:after, .topbar:after, div.course-wrapper section.course-content ol.sequence-nav:after, div.book-wrapper section.book nav:after, div.wiki-wrapper section.wiki-body header:after, body.askbot .secondary-nav nav:after, html body div.header-wrapper header:after, html body div.header-wrapper header nav ul:after, html body section.main-content:after, html footer:after, div.course-wrapper section.course-content ol.vert-mod > li:after, section.course-content div.video-wrapper section.video-controls:after, section.course-content div.video-wrapper section.video-controls div#slider:after, div.book-wrapper section.book nav ul:after, div.wiki-wrapper div#wiki_panel div#wiki_create_form:after, body.askbot footer div.footer-wrapper:after { content: "."; display: block; height: 0; @@ -136,7 +167,7 @@ input, select { border: 1px solid #6f6f6f; padding: 4px 8px; color: #fff; - font: bold 14px "Droid Sans", "Lucida Grande", "Lucida Sans Unicode", "Lucida Sans", Geneva, Verdana, sans-serif; + font: bold 14px "Open Sans", "Lucida Grande", "Lucida Sans Unicode", "Lucida Sans", Geneva, Verdana, sans-serif; cursor: pointer; -webkit-font-smoothing: antialiased; } .button:hover, input[type="submit"]:hover, input[type="button"]:hover, button:hover, .button:focus, input[type="submit"]:focus, input[type="button"]:focus, button:focus { @@ -179,7 +210,7 @@ input, select { background: #e3e3e3; border-right: 1px solid #d3d3d3; display: table-cell; - font-family: "Droid Sans", "Lucida Grande", "Lucida Sans Unicode", "Lucida Sans", Geneva, Verdana, sans-serif; + font-family: "Open Sans", "Lucida Grande", "Lucida Sans Unicode", "Lucida Sans", Geneva, Verdana, sans-serif; text-shadow: 0 1px 0 #f1f1f1; vertical-align: top; width: 23.482%; @@ -253,25 +284,30 @@ input, select { font-size: 12px; text-shadow: 0 1px 0 #fff; } .topbar a, div.course-wrapper section.course-content ol.sequence-nav a, div.book-wrapper section.book nav a, div.wiki-wrapper section.wiki-body header a, body.askbot .secondary-nav nav a { - -webkit-box-shadow: inset 1px 0 0 #faf7e9; - -moz-box-shadow: inset 1px 0 0 #faf7e9; - -ms-box-shadow: inset 1px 0 0 #faf7e9; - -o-box-shadow: inset 1px 0 0 #faf7e9; - box-shadow: inset 1px 0 0 #faf7e9; - background: #f2e7bf; - border-left: 1px solid #e4d080; - color: #292309; - padding: 16.989px; - text-transform: uppercase; - display: block; } + color: #292309; } .topbar a:hover, div.course-wrapper section.course-content ol.sequence-nav a:hover, div.book-wrapper section.book nav a:hover, div.wiki-wrapper section.wiki-body header a:hover, body.askbot .secondary-nav nav a:hover { color: #7e691a; - text-decoration: none; - background: none; } + text-decoration: none; } + .topbar a.block-link, div.course-wrapper section.course-content ol.sequence-nav a.block-link, div.book-wrapper section.book nav a.block-link, div.wiki-wrapper section.wiki-body header a.block-link, body.askbot .secondary-nav nav a.block-link, .topbar div.course-wrapper section.course-content ol.sequence-nav a, div.course-wrapper section.course-content ol.sequence-nav .topbar a, div.course-wrapper section.course-content ol.sequence-nav a, div.book-wrapper section.book nav div.course-wrapper section.course-content ol.sequence-nav a, div.course-wrapper section.course-content ol.sequence-nav div.book-wrapper section.book nav a, div.wiki-wrapper section.wiki-body header div.course-wrapper section.course-content ol.sequence-nav a, div.course-wrapper section.course-content ol.sequence-nav div.wiki-wrapper section.wiki-body header a, body.askbot .secondary-nav nav div.course-wrapper section.course-content ol.sequence-nav a, div.course-wrapper section.course-content ol.sequence-nav body.askbot .secondary-nav nav a, .topbar div.book-wrapper section.book nav a, div.book-wrapper section.book nav .topbar a, div.course-wrapper section.course-content ol.sequence-nav div.book-wrapper section.book nav a, div.book-wrapper section.book nav div.course-wrapper section.course-content ol.sequence-nav a, div.book-wrapper section.book nav a, div.wiki-wrapper section.wiki-body header div.book-wrapper section.book nav a, div.book-wrapper section.book nav div.wiki-wrapper section.wiki-body header a, body.askbot .secondary-nav div.book-wrapper section.book nav a, div.book-wrapper section.book body.askbot .secondary-nav nav a, .topbar div.wiki-wrapper section.wiki-body header a, div.wiki-wrapper section.wiki-body header .topbar a, div.course-wrapper section.course-content ol.sequence-nav div.wiki-wrapper section.wiki-body header a, div.wiki-wrapper section.wiki-body header div.course-wrapper section.course-content ol.sequence-nav a, div.book-wrapper section.book nav div.wiki-wrapper section.wiki-body header a, div.wiki-wrapper section.wiki-body header div.book-wrapper section.book nav a, div.wiki-wrapper section.wiki-body header a, body.askbot .secondary-nav nav div.wiki-wrapper section.wiki-body header a, div.wiki-wrapper section.wiki-body header body.askbot .secondary-nav nav a { + -webkit-box-shadow: inset 1px 0 0 #faf7e9; + -moz-box-shadow: inset 1px 0 0 #faf7e9; + -ms-box-shadow: inset 1px 0 0 #faf7e9; + -o-box-shadow: inset 1px 0 0 #faf7e9; + box-shadow: inset 1px 0 0 #faf7e9; + background: #f2e7bf; + border-left: 1px solid #e4d080; + padding: 16.989px; + text-transform: uppercase; + display: block; } + .topbar a.block-link:hover, div.course-wrapper section.course-content ol.sequence-nav a.block-link:hover, div.book-wrapper section.book nav a.block-link:hover, div.wiki-wrapper section.wiki-body header a.block-link:hover, body.askbot .secondary-nav nav a.block-link:hover, .topbar div.course-wrapper section.course-content ol.sequence-nav a:hover, div.course-wrapper section.course-content ol.sequence-nav .topbar a:hover, div.course-wrapper section.course-content ol.sequence-nav a:hover, div.book-wrapper section.book nav div.course-wrapper section.course-content ol.sequence-nav a:hover, div.course-wrapper section.course-content ol.sequence-nav div.book-wrapper section.book nav a:hover, div.wiki-wrapper section.wiki-body header div.course-wrapper section.course-content ol.sequence-nav a:hover, div.course-wrapper section.course-content ol.sequence-nav div.wiki-wrapper section.wiki-body header a:hover, body.askbot .secondary-nav nav div.course-wrapper section.course-content ol.sequence-nav a:hover, div.course-wrapper section.course-content ol.sequence-nav body.askbot .secondary-nav nav a:hover, .topbar div.book-wrapper section.book nav a:hover, div.book-wrapper section.book nav .topbar a:hover, div.course-wrapper section.course-content ol.sequence-nav div.book-wrapper section.book nav a:hover, div.book-wrapper section.book nav div.course-wrapper section.course-content ol.sequence-nav a:hover, div.book-wrapper section.book nav a:hover, div.wiki-wrapper section.wiki-body header div.book-wrapper section.book nav a:hover, div.book-wrapper section.book nav div.wiki-wrapper section.wiki-body header a:hover, body.askbot .secondary-nav div.book-wrapper section.book nav a:hover, div.book-wrapper section.book body.askbot .secondary-nav nav a:hover, .topbar div.wiki-wrapper section.wiki-body header a:hover, div.wiki-wrapper section.wiki-body header .topbar a:hover, div.course-wrapper section.course-content ol.sequence-nav div.wiki-wrapper section.wiki-body header a:hover, div.wiki-wrapper section.wiki-body header div.course-wrapper section.course-content ol.sequence-nav a:hover, div.book-wrapper section.book nav div.wiki-wrapper section.wiki-body header a:hover, div.wiki-wrapper section.wiki-body header div.book-wrapper section.book nav a:hover, div.wiki-wrapper section.wiki-body header a:hover, body.askbot .secondary-nav nav div.wiki-wrapper section.wiki-body header a:hover, div.wiki-wrapper section.wiki-body header body.askbot .secondary-nav nav a:hover { + background: none; } :focus { outline-color: #ccc; } +h1 a, h2 a, h3 a, div.wiki-wrapper div#wiki_panel input[type="button"] a, h4 a, h5 a, h6 a { + color: #000; } + h1 { font-size: 1.6em; margin: 20px 0 10px 0; } @@ -287,8 +323,7 @@ p { margin-bottom: 22.652px; } em { - font-style: italic; - font-family: Georgia, serif; } + font-style: italic; } input[type="email"], input[type="number"], input[type="password"], input[type="search"], input[type="tel"], input[type="text"], input[type="url"], input[type="color"], input[type="date"], input[type="datetime"], input[type="datetime-local"], input[type="month"], input[type="time"], input[type="week"], textarea { -webkit-box-shadow: 0 -1px 0 white; @@ -304,7 +339,7 @@ input[type="email"], input[type="number"], input[type="password"], input[type="s background-image: -o-linear-gradient(top, #eeeeee, white); background-image: linear-gradient(top, #eeeeee, white); border: 1px solid #999; - font: 14px "Droid Sans", "Lucida Grande", "Lucida Sans Unicode", "Lucida Sans", Geneva, Verdana, sans-serif; + font: 14px "Open Sans", "Lucida Grande", "Lucida Sans Unicode", "Lucida Sans", Geneva, Verdana, sans-serif; padding: 4px; } input[type="email"]:focus, input[type="number"]:focus, input[type="password"]:focus, input[type="search"]:focus, input[type="tel"]:focus, input[type="text"]:focus, input[type="url"]:focus, input[type="color"]:focus, input[type="date"]:focus, input[type="datetime"]:focus, input[type="datetime-local"]:focus, input[type="month"]:focus, input[type="time"]:focus, input[type="week"]:focus, textarea:focus { border-color: #993333; } @@ -313,24 +348,18 @@ html { margin-top: 0; } html body { color: #333333; - font: 14px "Droid Sans", "Lucida Grande", "Lucida Sans Unicode", "Lucida Sans", Geneva, Verdana, sans-serif; + font: 14px "Open Sans", "Lucida Grande", "Lucida Sans Unicode", "Lucida Sans", Geneva, Verdana, sans-serif; text-align: center; margin: 0; - background: #f3f3f3; } + background: #f6f6f6; } html body div.header-wrapper { - -webkit-box-shadow: inset 0 1px 0 #bf4040, 0 1px 1px #cccccc; - -moz-box-shadow: inset 0 1px 0 #bf4040, 0 1px 1px #cccccc; - -ms-box-shadow: inset 0 1px 0 #bf4040, 0 1px 1px #cccccc; - -o-box-shadow: inset 0 1px 0 #bf4040, 0 1px 1px #cccccc; - box-shadow: inset 0 1px 0 #bf4040, 0 1px 1px #cccccc; - background-color: #ac3939; - background-image: -webkit-gradient(linear, left top, left bottom, color-stop(0%, #ac3939), color-stop(100%, #862d2d)); - background-image: -webkit-linear-gradient(top, #ac3939, #862d2d); - background-image: -moz-linear-gradient(top, #ac3939, #862d2d); - background-image: -ms-linear-gradient(top, #ac3939, #862d2d); - background-image: -o-linear-gradient(top, #ac3939, #862d2d); - background-image: linear-gradient(top, #ac3939, #862d2d); - border-bottom: 1px solid #732626; } + -webkit-box-shadow: inset 0 -1px 2px #732626; + -moz-box-shadow: inset 0 -1px 2px #732626; + -ms-box-shadow: inset 0 -1px 2px #732626; + -o-box-shadow: inset 0 -1px 2px #732626; + box-shadow: inset 0 -1px 2px #732626; + background: #993333; + border-bottom: 1px solid #fff; } html body div.header-wrapper header { -webkit-box-sizing: border-box; -moz-box-sizing: border-box; @@ -340,36 +369,42 @@ html { padding: 0 22.652px; } html body div.header-wrapper header h1 { border-right: 1px solid #862d2d; - font-size: 14px; - font-weight: bold; - margin: 0 2.024% 0 0; - padding: 15px 2.024% 15px 0; + color: #000; display: block; float: left; - color: #000; - text-shadow: 0 1px 0 #bf4040; } - html body div.header-wrapper header h1 em { - display: -moz-inline-box; - -moz-box-orient: vertical; - display: inline-block; - vertical-align: baseline; - zoom: 1; - *display: inline; - *vertical-align: auto; - padding-right: 22.652px; } + font-size: 20px; + font-weight: 800; + margin: 0 22.652px 0 0; + padding: 17px 22.652px 17px 0; + text-shadow: 0 1px 0 #bf4040; + line-height: 22.652px; } html body div.header-wrapper header nav { float: left; display: block; margin: 0; - text-shadow: 0 -1px 0 #732626; } + padding: 0; + text-shadow: 0 -1px 0 #732626; + -webkit-font-smoothing: antialiased; } + html body div.header-wrapper header nav h2 { + float: left; + margin: 0 22.652px 0 0; + padding: 19px 22.652px 12px 0; + line-height: 22.652px; + border-right: 1px solid #862d2d; } + html body div.header-wrapper header nav h2 a { + color: #fff; } + html body div.header-wrapper header nav h2 a:hover { + color: rgba(255, 255, 255, 0.7); + text-decoration: none; } html body div.header-wrapper header nav ul { display: inline-block; - padding: 15px 0; + padding: 19px 0 12px; margin: 0; } html body div.header-wrapper header nav ul li { margin-right: 22.652px; display: inline-block; - margin-bottom: 0; } + margin-bottom: 0; + line-height: 22.652px; } html body div.header-wrapper header nav ul li a { color: #fff; } html body div.header-wrapper header nav ul li a:hover { @@ -377,19 +412,27 @@ html { background-color: none; text-decoration: none; } html body section.main-content { - -webkit-box-shadow: 0 1px 0 white; - -moz-box-shadow: 0 1px 0 white; - -ms-box-shadow: 0 1px 0 white; - -o-box-shadow: 0 1px 0 white; - box-shadow: 0 1px 0 white; + -webkit-box-shadow: 0 0 4px #dddddd; + -moz-box-shadow: 0 0 4px #dddddd; + -ms-box-shadow: 0 0 4px #dddddd; + -o-box-shadow: 0 0 4px #dddddd; + box-shadow: 0 0 4px #dddddd; -webkit-box-sizing: border-box; -moz-box-sizing: border-box; -ms-box-sizing: border-box; -o-box-sizing: border-box; box-sizing: border-box; background: #fff; - border: 1px solid #ccc; - border-top: 0; } + border-bottom: 1px solid #bbb; } + @media screen and (min-width: 1400px) { + html body section.main-content { + margin-top: 11.326px; + -webkit-border-radius: 3px; + -moz-border-radius: 3px; + -ms-border-radius: 3px; + -o-border-radius: 3px; + border-radius: 3px; + border: 1px solid #bbb; } } html body img { max-width: 100%; height: auto; } @@ -498,7 +541,7 @@ div.leanModal_box { color: #666; font-size: 14px; float: none; } - div.leanModal_box form input[type="button"] { + div.leanModal_box form input[type="button"], div.leanModal_box form input[type="submit"] { border: 1px solid #691b1b; -webkit-border-radius: 3px; -moz-border-radius: 3px; @@ -526,7 +569,7 @@ div.leanModal_box { -webkit-background-clip: padding-box; font-size: 18px; padding: 11.326px; } - div.leanModal_box form input[type="button"]:hover { + div.leanModal_box form input[type="button"]:hover, div.leanModal_box form input[type="submit"]:hover { -webkit-box-shadow: inset 0 1px 0 0 #a44141; -moz-box-shadow: inset 0 1px 0 0 #a44141; -ms-box-shadow: inset 0 1px 0 0 #a44141; @@ -540,7 +583,7 @@ div.leanModal_box { background-image: -ms-linear-gradient(top, #823030, #691c1c); background-image: -o-linear-gradient(top, #823030, #691c1c); background-image: linear-gradient(top, #823030, #691c1c); } - div.leanModal_box form input[type="button"]:active { + div.leanModal_box form input[type="button"]:active, div.leanModal_box form input[type="submit"]:active { border: 1px solid #691b1b; -webkit-box-shadow: inset 0 0 8px 4px #5c1919, inset 0 0 8px 4px #5c1919, 0 1px 1px 0 #eeeeee; -moz-box-shadow: inset 0 0 8px 4px #5c1919, inset 0 0 8px 4px #5c1919, 0 1px 1px 0 #eeeeee; @@ -623,7 +666,8 @@ div.course-wrapper div#accordion ul.ui-accordion-content { div.course-wrapper div#accordion ul.ui-accordion-content li a { text-decoration: none; margin-bottom: 11.326px; - display: block; } + display: block; + color: #000; } div.course-wrapper div#accordion ul.ui-accordion-content li a:hover { color: #666; } div.course-wrapper div#accordion ul.ui-accordion-content li a p { @@ -686,12 +730,12 @@ div.course-wrapper section.course-content ol.sequence-nav { background-color: #f9f4e1; } div.course-wrapper section.course-content ol.sequence-nav li.seq_video_visited { width: 14px; - background: #ece5cb url("/static/images/video-icon.png") -64px 15px no-repeat; } + background: #ece5cb url("/static/images/video-icon.png") -81px 15px no-repeat; } div.course-wrapper section.course-content ol.sequence-nav li.seq_video_visited:hover { background-color: #F6EFD4; } div.course-wrapper section.course-content ol.sequence-nav li.seq_video_active { width: 14px; - background: #fffbeb url("/static/images/video-icon.png") -25px 15px no-repeat; + background: #fffbeb url("/static/images/video-icon.png") -32px 15px no-repeat; -webkit-box-shadow: inset -1px 0 0 #e4d080, inset 1px 0 0 #e4d080; -moz-box-shadow: inset -1px 0 0 #e4d080, inset 1px 0 0 #e4d080; -ms-box-shadow: inset -1px 0 0 #e4d080, inset 1px 0 0 #e4d080; @@ -767,28 +811,93 @@ section.course-content div.video-wrapper { left: 0; width: 100%; height: 100%; } - section.course-content div.video-wrapper section ul { - display: inline-block; } - section.course-content div.video-wrapper section ul li { - margin-top: 5px; - display: inline-block; - cursor: pointer; - border: 0; - padding: 0; } - section.course-content div.video-wrapper section ul li div:empty { - display: none; } - section.course-content div.video-wrapper section div#slider { - margin: -14px 0 10px 60px; } - section.course-content div.video-wrapper section div#vidtime { - float: left; } - section.course-content div.video-wrapper section div#video_speeds { - float: right; - cursor: pointer; } - section.course-content div.video-wrapper section div#video_speeds span:hover { - color: #993333; } + section.course-content div.video-wrapper section.video-controls { + background: #333; + border: 1px solid #000; + color: #ccc; } + section.course-content div.video-wrapper section.video-controls div#slider { + -webkit-border-radius: 0; + -moz-border-radius: 0; + -ms-border-radius: 0; + -o-border-radius: 0; + border-radius: 0; + -webkit-box-shadow: inset 0 1px 0 #eeeeee, 0 1px 0 #555555; + -moz-box-shadow: inset 0 1px 0 #eeeeee, 0 1px 0 #555555; + -ms-box-shadow: inset 0 1px 0 #eeeeee, 0 1px 0 #555555; + -o-box-shadow: inset 0 1px 0 #eeeeee, 0 1px 0 #555555; + box-shadow: inset 0 1px 0 #eeeeee, 0 1px 0 #555555; + background: #c2c2c2; + border: none; + border-bottom: 1px solid #000; + height: 20px; } + section.course-content div.video-wrapper section.video-controls div#slider a.ui-slider-handle { + -webkit-border-radius: 0; + -moz-border-radius: 0; + -ms-border-radius: 0; + -o-border-radius: 0; + border-radius: 0; + background: #993333 url(/static/images/slider-handle.png) center center no-repeat; + border: 0; + border-right: 1px solid #4d1919; + border-left: 1px solid #4d1919; + cursor: pointer; + height: 20px; + margin: 0; + top: 0; + width: 20px; } + section.course-content div.video-wrapper section.video-controls ul.vcr { + float: left; + margin-right: 22.652px; } + section.course-content div.video-wrapper section.video-controls ul.vcr li { + float: left; } + section.course-content div.video-wrapper section.video-controls ul.vcr li a { + -webkit-box-shadow: 1px 0 0 #555555; + -moz-box-shadow: 1px 0 0 #555555; + -ms-box-shadow: 1px 0 0 #555555; + -o-box-shadow: 1px 0 0 #555555; + box-shadow: 1px 0 0 #555555; + border-right: 1px solid #000; + display: block; + cursor: pointer; + height: 14px; + padding: 16.989px 22.652px; + text-indent: -9999px; + width: 14px; } + section.course-content div.video-wrapper section.video-controls ul.vcr li a.play { + background: url("/static/images/play-icon.png") center center no-repeat; } + section.course-content div.video-wrapper section.video-controls ul.vcr li a.play:hover { + background-color: #444; } + section.course-content div.video-wrapper section.video-controls ul.vcr li a.pause { + background: url("/static/images/pause-icon.png") center center no-repeat; } + section.course-content div.video-wrapper section.video-controls ul.vcr li a.pause:hover { + background-color: #444; } + section.course-content div.video-wrapper section.video-controls div#vidtime { + float: left; + font-weight: bold; + line-height: 46px; + -webkit-font-smoothing: antialiased; } + section.course-content div.video-wrapper section.video-controls div.speeds { + float: right; + line-height: 46px; + margin-right: 22.652px; + -webkit-font-smoothing: antialiased; } + section.course-content div.video-wrapper section.video-controls div.speeds div#video_speeds { + display: -moz-inline-box; + -moz-box-orient: vertical; + display: inline-block; + vertical-align: baseline; + zoom: 1; + *display: inline; + *vertical-align: auto; + font-weight: bold; } + section.course-content div.video-wrapper section.video-controls div.speeds div#video_speeds span { + cursor: pointer; } + section.course-content div.video-wrapper section.video-controls div.speeds div#video_speeds span:hover { + color: #993333; } section.course-content ol.subtitles { float: left; - width: 31.522%; } + width: 31.522%; + min-height: 570px; } section.course-content ol.subtitles li { margin-bottom: 0px; cursor: pointer; @@ -810,10 +919,30 @@ div.book-wrapper ul#booknav { -moz-box-sizing: border-box; -ms-box-sizing: border-box; -o-box-sizing: border-box; - box-sizing: border-box; - padding: 22.652px; } - div.book-wrapper ul#booknav li ul { - background: none; } + box-sizing: border-box; } + div.book-wrapper ul#booknav a { + color: #000; } + div.book-wrapper ul#booknav a:hover { + color: #666; } + div.book-wrapper ul#booknav li { + background: none; + padding-left: 30px; } + div.book-wrapper ul#booknav li div.hitarea { + margin-left: -22px; + background-image: url("/static/images/treeview-default.gif"); } + div.book-wrapper ul#booknav li div.hitarea:hover { + opacity: 0.6; + filter: alpha(opacity=60); } + div.book-wrapper ul#booknav li ul { + background: none; } + div.book-wrapper ul#booknav > li { + border-bottom: 1px solid #d3d3d3; + -webkit-box-shadow: 0 1px 0 #eeeeee; + -moz-box-shadow: 0 1px 0 #eeeeee; + -ms-box-shadow: 0 1px 0 #eeeeee; + -o-box-shadow: 0 1px 0 #eeeeee; + box-shadow: 0 1px 0 #eeeeee; + padding: 7px 7px 7px 30px; } div.book-wrapper section.book nav ul li.last { float: left; display: block; } @@ -1000,22 +1129,35 @@ form#wiki_revision { display: block; width: 50%; } form#wiki_revision #submit_delete { - float: right; } + -webkit-box-shadow: none; + -moz-box-shadow: none; + -ms-box-shadow: none; + -o-box-shadow: none; + box-shadow: none; + background: none; + border: none; + color: #999; + float: right; + text-decoration: underline; + font-weight: normal; } form#wiki_revision input[type="submit"] { margin-top: 20px; } #wiki_edit_instructions { float: left; - width: 31.522%; } + width: 31.522%; + margin-top: 22.652px; + color: #666; } + #wiki_edit_instructions:hover { + color: #333; } #wiki_edit_instructions .markdown-example { - background-color: #dddddd; + background-color: #e3e3e3; + text-shadow: 0 1px 0 #fff; padding-top: 5px; padding-right: 2px; padding-bottom: 5px; padding-left: 5px; - margin-top: 5px; - margin-bottom: 7px; - margin-left: 5px; + margin: 5px 0 7px; line-height: 1.0; } div.wiki-wrapper { @@ -1183,141 +1325,6 @@ section.help.main-content { section.help.main-content dl dt { font-weight: bold; } -body.askbot .secondary-nav { - margin: 0; } - body.askbot .secondary-nav nav { - -webkit-box-sizing: border-box; - -moz-box-sizing: border-box; - -ms-box-sizing: border-box; - -o-box-sizing: border-box; - box-sizing: border-box; - border: 1px solid #eddfaa; - border-top: 0; - margin: 0 auto; - padding: 22.652px; } - body.askbot .secondary-nav nav div { - float: left; } - body.askbot .secondary-nav nav div.question-filter { - font-size: 16px; - margin-top: 4px; - width: 31.984%; } - body.askbot .secondary-nav nav div.question-filter ul { - -webkit-border-radius: 35px; - -moz-border-radius: 35px; - -ms-border-radius: 35px; - -o-border-radius: 35px; - border-radius: 35px; - background: #e4d080; - display: inline; - margin: 0 0 0 10px; - padding: 5.663px 20px; } - body.askbot .secondary-nav nav div.question-filter ul li { - display: inline-block; - list-style: none; - margin-right: 10px; } - body.askbot .secondary-nav nav div.question-filter ul li:last-child { - margin-right: 0; } - body.askbot .secondary-nav nav div.question-filter ul li a { - text-transform: capitalize; - text-shadow: none; - font-size: 14px; } - body.askbot .secondary-nav nav div.question-filter ul li a.on { - font-weight: bold; } - body.askbot .secondary-nav nav div.search-box { - margin-left: 2%; - text-align: right; - width: 65.992%; } - body.askbot .secondary-nav nav div.search-box input[type="text"] { - margin-right: 6px; - width: 22.699%; } -body.askbot section.main-content div.discussion-wrapper div.discussion-content { - -webkit-box-sizing: border-box; - -moz-box-sizing: border-box; - -ms-box-sizing: border-box; - -o-box-sizing: border-box; - box-sizing: border-box; - display: table-cell; - padding: 2.024%; - vertical-align: top; - width: 74.494%; } - body.askbot section.main-content div.discussion-wrapper div.discussion-content div.order-sort { - -webkit-border-radius: 35px; - -moz-border-radius: 35px; - -ms-border-radius: 35px; - -o-border-radius: 35px; - border-radius: 35px; - background-color: #faf7e9; - height: 30px; - float: right; - font-size: 16px; - margin: 3px 0; - padding: 0 20px; } - body.askbot section.main-content div.discussion-wrapper div.discussion-content div.order-sort a { - color: #a88d23; } - body.askbot section.main-content div.discussion-wrapper div.discussion-content div.order-sort a:before { - content: '|'; - color: #eddfaa; - font-size: 22px; } - body.askbot section.main-content div.discussion-wrapper div.discussion-content div.order-sort a:hover { - text-decoration: none; - color: #544611; } - body.askbot section.main-content div.discussion-wrapper div.discussion-content p.tabula-rasa { - -webkit-border-radius: 5px; - -moz-border-radius: 5px; - -ms-border-radius: 5px; - -o-border-radius: 5px; - border-radius: 5px; - background-color: #f6f6f6; - color: #888; - margin: 10px auto; - padding: 20px; - text-align: center; - width: 40.486%; } - body.askbot section.main-content div.discussion-wrapper div.discussion-content p.tabula-rasa:first-child { - margin-top: 70px; } - body.askbot section.main-content div.discussion-wrapper div.discussion-content p.tabula-rasa:last-child { - margin-bottom: 70px; } - body.askbot section.main-content div.discussion-wrapper div.discussion-content p.tabula-rasa a { - text-decoration: none; - color: #888; - font-weight: bold; } -body.askbot section.main-content div.discussion-wrapper aside { - -webkit-box-shadow: inset 1px 0 0 #f6f6f6; - -moz-box-shadow: inset 1px 0 0 #f6f6f6; - -ms-box-shadow: inset 1px 0 0 #f6f6f6; - -o-box-shadow: inset 1px 0 0 #f6f6f6; - box-shadow: inset 1px 0 0 #f6f6f6; - border-left: 1px solid #d3d3d3; - border-right: 1px solid #f6f6f6; - padding: 2.024%; - width: 23.482%; } - body.askbot section.main-content div.discussion-wrapper aside h2 { - font-size: 16px; } - body.askbot section.main-content div.discussion-wrapper aside h3, body.askbot section.main-content div.discussion-wrapper aside div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel body.askbot section.main-content div.discussion-wrapper aside input[type="button"] { - border-bottom: 0; - box-shadow: none; } - body.askbot section.main-content div.discussion-wrapper aside input[type="text"] { - width: 76%; } - body.askbot section.main-content div.discussion-wrapper aside #displayTagFilterControl { - margin-top: 10px; } -body.askbot footer { - margin: 0 auto; - padding: 0; } - body.askbot footer div.footer-wrapper { - -webkit-box-shadow: 0 1px 0 white; - -moz-box-shadow: 0 1px 0 white; - -ms-box-shadow: 0 1px 0 white; - -o-box-shadow: 0 1px 0 white; - box-shadow: 0 1px 0 white; - -webkit-box-sizing: border-box; - -moz-box-sizing: border-box; - -ms-box-sizing: border-box; - -o-box-sizing: border-box; - box-sizing: border-box; - background-color: #000; - border-top: 0; - padding: 1.012%; } - .badges a { color: #763333; text-decoration: underline; } @@ -1700,117 +1707,6 @@ ul#searchTags { float: right; padding-top: 2px; } -.search-tips { - font-size: 16px; - line-height: 17px; - color: #707070; - margin: 5px 0 10px 0; - padding: 0px; - float: left; - font-family: 'Yanone Kaffeesatz',sans-serif; } - .search-tips a { - text-decoration: underline; - color: #1b79bd; } - -#question-list { - float: left; - position: relative; - background-color: #FFF; - padding: 0; - width: 100%; } - -.short-summary { - position: relative; - filter: inherit; - padding: 10px; - border-bottom: 1px solid #DDDBCE; - margin-bottom: 1px; - overflow: hidden; - width: 710px; - float: left; - background: url(../images/summary-background.png) repeat-x; } - .short-summary h2 { - font-size: 24px; - font-weight: normal; - line-height: 26px; - padding-left: 0; - margin-bottom: 6px; - display: block; - font-family: 'Yanone Kaffeesatz',sans-serif; } - .short-summary a { - color: #464646; } - .short-summary .userinfo { - text-align: right; - line-height: 16px; - font-family: Arial; - padding-right: 4px; } - .short-summary .userinfo .relativetime { - font-size: 11px; - clear: both; - font-weight: normal; - color: #555; } - .short-summary span.anonymous { - font-size: 11px; - clear: both; - font-weight: normal; - color: #555; } - .short-summary .userinfo a { - font-weight: bold; - font-size: 11px; } - .short-summary .counts { - float: right; - margin: 4px 0 0 5px; - font-family: 'Yanone Kaffeesatz',sans-serif; } - .short-summary .counts .item-count { - padding: 0px 5px 0px 5px; - font-size: 25px; - font-family: 'Yanone Kaffeesatz',sans-serif; } - .short-summary .counts .votes div, .short-summary .counts .views div, .short-summary .counts .answers div, .short-summary .counts .favorites div { - margin-top: 3px; - font-size: 14px; - line-height: 14px; - color: #646464; } - .short-summary .tags { - margin-top: 0; } - .short-summary .votes, .short-summary .answers, .short-summary .favorites, .short-summary .views { - text-align: center; - margin: 0 3px; - padding: 8px 2px 0px 2px; - width: 51px; - float: right; - height: 44px; - border: #dbdbd4 1px solid; } - .short-summary .votes { - background: url(../images/vote-background.png) repeat-x; } - .short-summary .answers { - background: url(../images/answers-background.png) repeat-x; } - .short-summary .views { - background: url(../images/view-background.png) repeat-x; } - .short-summary .no-votes .item-count { - color: #b1b5b6; } - .short-summary .some-votes .item-count { - color: #4a757f; } - .short-summary .no-answers .item-count { - color: #b1b5b6; } - .short-summary .some-answers .item-count { - color: #eab243; } - .short-summary .no-views .item-count { - color: #b1b5b6; } - .short-summary .some-views .item-count { - color: #d33f00; } - .short-summary .accepted .item-count { - background: url(../images/accept.png) no-repeat top right; - display: block; - text-align: center; - width: 40px; - color: #eab243; } - .short-summary .some-favorites .item-count { - background: #338333; - color: #d0f5a9; } - .short-summary .no-favorites .item-count { - background: #eab243; - color: yellow; } - .pager { margin-top: 10px; margin-bottom: 16px; } @@ -1898,31 +1794,6 @@ ul#searchTags { .tag-size-10 { font-size: 21px; } -ul.tags { - list-style: none; - margin: 0; - padding: 0; - line-height: 170%; - display: block; } - ul.tags.marked-tags { - list-style: none; - margin: 0; - padding: 0; - line-height: 170%; - display: block; } -ul#related-tags { - list-style: none; - margin: 0; - padding: 0; - line-height: 170%; - display: block; } -ul.tags li { - float: left; - display: block; - margin: 0 8px 0 0; - padding: 0; - height: 20px; } - .wildcard-tags { clear: both; } @@ -1946,36 +1817,6 @@ ul#related-tags li { float: left; clear: left; } -.tag-left { - cursor: pointer; - display: block; - float: left; - height: 17px; - margin: 0 5px 0 0; - padding: 0; - -webkit-box-shadow: 0px 0px 5px #d3d6d7; - -moz-box-shadow: 0px 0px 5px #d3d6d7; - box-shadow: 0px 0px 5px #d3d6d7; } - -.tag-right { - background: #f3f6f6; - border: #fff 1px solid; - border-top: #fff 2px solid; - outline: #cfdbdb 1px solid; - display: block; - float: left; - height: 17px; - line-height: 17px; - font-weight: normal; - font-size: 11px; - padding: 0px 8px 0px 8px; - text-decoration: none; - text-align: center; - white-space: nowrap; - vertical-align: middle; - font-family: Arial; - color: #717179; } - .deletable-tag { margin-right: 3px; white-space: nowrap; @@ -2231,443 +2072,6 @@ ul#related-tags li { .edit-question-page .title-desc, #fmedit .title-desc, .wmd-preview .title-desc { margin-bottom: 10px; } -.question-page h1 { - padding-top: 0px; - font-family: 'Yanone Kaffeesatz',sans-serif; } - .question-page h1 a { - color: #464646; - font-size: 30px; - font-weight: normal; - line-height: 1; } -.question-page p.rss { - float: none; - clear: both; - padding: 3px 0 0 23px; - font-size: 15px; - width: 110px; - background-position: center left; - margin-left: 0px !important; } - .question-page p.rss a { - font-family: 'Yanone Kaffeesatz',sans-serif; - vertical-align: top; } -.question-page .question-content { - float: right; - width: 682px; - margin-bottom: 10px; } -.question-page #question-table { - float: left; - border-top: #f0f0f0 1px solid; - margin: 6px 0 6px 0; - border-spacing: 0px; - width: 670px; - padding-right: 10px; } -.question-page .answer-table { - margin: 6px 0 6px 0; - border-spacing: 0px; - width: 670px; - padding-right: 10px; - margin-top: 0px; - border-bottom: 1px solid #D4D4D4; - float: right; } - .question-page .answer-table td { - width: 20px; - vertical-align: top; } -.question-page #question-table td { - width: 20px; - vertical-align: top; } -.question-page .question-body, .question-page .answer-body { - overflow: auto; - margin-top: 10px; - font-family: Arial; - color: #4b4b4b; } -.question-page .question-body p, .question-page .answer-body p { - margin-bottom: 14px; - line-height: 1.4; - font-size: 14px; - padding: 0px 5px 5px 0px; } -.question-page .question-body a, .question-page .answer-body a { - color: #1b79bd; } -.question-page .question-body li, .question-page .answer-body li { - margin-bottom: 7px; } -.question-page .question-body IMG, .question-page .answer-body IMG { - max-width: 600px; } -.question-page .post-update-info-container { - float: right; - width: 175px; } -.question-page .post-update-info { - background: white url(../images/background-user-info.png) repeat-x bottom; - float: right; - font-size: 9px; - font-family: Arial; - width: 158px; - padding: 4px; - margin: 0px 0px 5px 5px; - line-height: 14px; - border-radius: 4px; - -ms-border-radius: 4px; - -moz-border-radius: 4px; - -webkit-border-radius: 4px; - -khtml-border-radius: 4px; - -webkit-box-shadow: 0px 2px 1px #bfbfbf; - -moz-box-shadow: 0px 2px 1px #bfbfbf; - box-shadow: 0px 2px 1px #bfbfbf; } - .question-page .post-update-info p { - line-height: 13px; - font-size: 11px; - margin: 0 0 2px 1px; - padding: 0; } - .question-page .post-update-info a { - color: #444; } - .question-page .post-update-info .gravatar { - float: left; - margin-right: 4px; } - .question-page .post-update-info p.tip { - color: #444; - line-height: 13px; - font-size: 10px; } -.question-page .post-controls { - font-size: 11px; - line-height: 12px; - min-width: 200px; - padding-left: 5px; - text-align: right; - clear: left; - float: right; - margin-top: 10px; - margin-bottom: 8px; } - .question-page .post-controls a { - color: #777; - padding: 0px 3px 3px 22px; - cursor: pointer; - border: none; - font-size: 12px; - font-family: Arial; - text-decoration: none; - height: 18px; - display: block; - float: right; - line-height: 18px; - margin-top: -2px; - margin-left: 4px; } - .question-page .post-controls a:hover { - background-color: #f5f0c9; - border-radius: 3px; - -ms-border-radius: 3px; - -moz-border-radius: 3px; - -webkit-border-radius: 3px; - -khtml-border-radius: 3px; } - .question-page .post-controls .sep { - color: #ccc; - float: right; - height: 18px; - font-size: 18px; } - .question-page .post-controls .question-delete { - background: url(../images/delete.png) no-repeat center left; - padding-left: 16px; } -.question-page .answer-controls .question-delete { - background: url(../images/delete.png) no-repeat center left; - padding-left: 16px; } -.question-page .post-controls .question-flag, .question-page .answer-controls .question-flag { - background: url(../images/flag.png) no-repeat center left; } -.question-page .post-controls .question-edit, .question-page .answer-controls .question-edit { - background: url(../images/edit2.png) no-repeat center left; } -.question-page .post-controls .question-retag, .question-page .answer-controls .question-retag { - background: url(../images/retag.png) no-repeat center left; } -.question-page .post-controls .question-close, .question-page .answer-controls .question-close { - background: url(../images/close.png) no-repeat center left; } -.question-page .post-controls .permant-link, .question-page .answer-controls .permant-link { - background: url(../images/link.png) no-repeat center left; } -.question-page .tabBar { - width: 100%; } -.question-page #questionCount { - float: left; - font-family: 'Yanone Kaffeesatz',sans-serif; - line-height: 15px; } -.question-page .question-img-upvote, .question-page .question-img-downvote, .question-page .answer-img-upvote, .question-page .answer-img-downvote { - width: 25px; - height: 20px; - cursor: pointer; } -.question-page .question-img-upvote, .question-page .answer-img-upvote { - background: url(../images/vote-arrow-up-new.png) no-repeat; } -.question-page .question-img-downvote, .question-page .answer-img-downvote { - background: url(../images/vote-arrow-down-new.png) no-repeat; } -.question-page .question-img-upvote:hover, .question-page .question-img-upvote.on { - background: url(../images/vote-arrow-up-on-new.png) no-repeat; } -.question-page .answer-img-upvote:hover, .question-page .answer-img-upvote.on { - background: url(../images/vote-arrow-up-on-new.png) no-repeat; } -.question-page .question-img-downvote:hover, .question-page .question-img-downvote.on { - background: url(../images/vote-arrow-down-on-new.png) no-repeat; } -.question-page .answer-img-downvote:hover, .question-page .answer-img-downvote.on { - background: url(../images/vote-arrow-down-on-new.png) no-repeat; } -.question-page #fmanswer_button { - margin: 8px 0px; } -.question-page .question-img-favorite:hover { - background: url(../images/vote-favorite-on.png); } -.question-page div.comments { - padding: 0; } -.question-page #comment-title { - font-weight: bold; - font-size: 23px; - color: #7ea9b3; - width: 200px; - float: left; - font-family: 'Yanone Kaffeesatz',sans-serif; } -.question-page .comments { - font-size: 12px; - clear: both; } - .question-page .comments div.controls { - clear: both; - float: left; - width: 100%; - margin: 3px 0 20px 5px; } - .question-page .comments .controls a { - color: #988e4c; - padding: 0 3px 2px 22px; - font-family: Arial; - font-size: 13px; - background: url(../images/comment.png) no-repeat center left; } - .question-page .comments .controls a:hover { - background-color: #f5f0c9; - text-decoration: none; } - .question-page .comments .button, .question-page .comments input[type="submit"], .question-page .comments input[type="button"], .question-page .comments button { - color: #988e4c; - font-size: 11px; - padding: 3px; - cursor: pointer; } - .question-page .comments a { - background-color: inherit; - color: #1b79bd; - padding: 0; } - .question-page .comments form.post-comments { - margin: 3px 26px 0 42px; } - .question-page .comments form.post-comments textarea { - font-size: 13px; - line-height: 1.3; } - .question-page .comments textarea { - height: 42px; - width: 100%; - margin: 7px 0 5px 1px; - font-family: Arial; - outline: none; - overflow: auto; - font-size: 12px; - line-height: 140%; - padding-left: 2px; - padding-top: 3px; - border: #cce6ec 3px solid; } - .question-page .comments input { - margin-left: 10px; - margin-top: 1px; - vertical-align: top; - width: 100px; } - .question-page .comments button { - background: url(../images/small-button-blue.png) repeat-x top; - border: 0; - color: #4a757f; - font-family: Arial; - font-size: 13px; - width: 100px; - font-weight: bold; - height: 27px; - line-height: 25px; - margin-bottom: 5px; - cursor: pointer; - border-radius: 4px; - -ms-border-radius: 4px; - -moz-border-radius: 4px; - -webkit-border-radius: 4px; - -khtml-border-radius: 4px; - text-shadow: 0px 1px 0px #e6f6fa; - -moz-text-shadow: 0px 1px 0px #e6f6fa; - -webkit-text-shadow: 0px 1px 0px #e6f6fa; - -webkit-box-shadow: 1px 1px 2px #808080; - -moz-box-shadow: 1px 1px 2px #808080; - box-shadow: 1px 1px 2px #808080; } - .question-page .comments button:hover { - background: url(../images/small-button-blue.png) bottom repeat-x; - text-shadow: 0px 1px 0px #c6d9dd; - -moz-text-shadow: 0px 1px 0px #c6d9dd; - -webkit-text-shadow: 0px 1px 0px #c6d9dd; } - .question-page .comments .counter { - display: inline-block; - width: 245px; - float: right; - color: #b6a475 !important; - vertical-align: top; - font-family: Arial; - float: right; - text-align: right; } - .question-page .comments .comment { - border-bottom: 1px solid #edeeeb; - clear: both; - margin: 0; - margin-top: 8px; - padding-bottom: 4px; - overflow: auto; - font-family: Arial; - font-size: 11px; - min-height: 25px; - background: white url(../images/comment-background.png) bottom repeat-x; - border-radius: 5px; - -ms-border-radius: 5px; - -moz-border-radius: 5px; - -webkit-border-radius: 5px; - -khtml-border-radius: 5px; } - .question-page .comments div.comment:hover { - background-color: #efefef; } - .question-page .comments a.author { - background-color: inherit; - color: #1b79bd; - padding: 0; } - .question-page .comments a.author:hover { - text-decoration: underline; } - .question-page .comments span.delete-icon { - background: url(../images/close-small.png) no-repeat; - border: 0; - width: 14px; - height: 14px; } - .question-page .comments span.delete-icon:hover { - border: #BC564B 2px solid; - border-radius: 10px; - -ms-border-radius: 10px; - -moz-border-radius: 10px; - -webkit-border-radius: 10px; - -khtml-border-radius: 10px; - margin: -3px 0px 0px -2px; } - .question-page .comments .content, .question-page .comments div.course-wrapper section.course-content, div.course-wrapper .question-page .comments section.course-content, .question-page .comments div.book-wrapper section.book, div.book-wrapper .question-page .comments section.book, .question-page .comments div.wiki-wrapper section.wiki-body, div.wiki-wrapper .question-page .comments section.wiki-body { - margin-bottom: 7px; } - .question-page .comments .comment-votes { - float: left; - width: 37px; - line-height: 130%; - padding: 6px 5px 6px 3px; } - .question-page .comments .comment-body { - line-height: 1.3; - margin: 3px 26px 0 46px; - padding: 5px 3px; - color: #666; - font-size: 13px; } - .question-page .comments .comment-body .edit { - padding-left: 6px; } - .question-page .comments .comment-body p { - font-size: 13px; - line-height: 1.3; - margin-bottom: 3px; - padding: 0; } - .question-page .comments .comment-delete { - float: right; - width: 14px; - line-height: 130%; - padding: 8px 6px; } - .question-page .comments .upvote { - margin: 0px; - padding-right: 17px; - padding-top: 2px; - text-align: right; - height: 20px; - font-size: 13px; - font-weight: bold; - color: #777; } - .question-page .comments .upvote.upvoted { - color: #d64000; } - .question-page .comments .upvote.hover { - background: url(../images/go-up-grey.png) no-repeat; - background-position: right 1px; } - .question-page .comments .upvote:hover { - background: url(../images/go-up-orange.png) no-repeat; - background-position: right 1px; } - .question-page .comments .help-text { - float: right; - text-align: right; - color: gray; - margin-bottom: 0px; - margin-top: 0px; - line-height: 50%; } -.question-page #questionTools { - font-size: 22px; - margin-top: 11px; - text-align: left; } -.question-page .question-status { - margin-top: 10px; - margin-bottom: 15px; - padding: 20px; - background-color: #fef7cc; - text-align: center; - border: #e1c04a 1px solid; } - .question-page .question-status h3, .question-page .question-status div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel .question-page .question-status input[type="button"] { - font-size: 20px; - color: #707070; - font-weight: normal; } -.question-page .vote-buttons { - float: left; - text-align: center; - padding-top: 2px; - margin: 10px 10px 0px 3px; } - .question-page .vote-buttons IMG { - cursor: pointer; } -.question-page .vote-number { - font-family: 'Yanone Kaffeesatz',sans-serif; - padding: 0px 0 5px 0; - font-size: 25px; - font-weight: bold; - color: #777; } -.question-page .vote-buttons .notify-sidebar { - text-align: left; - width: 120px; } - .question-page .vote-buttons .notify-sidebar label { - vertical-align: top; } -.question-page .tabBar-answer { - margin-bottom: 15px; - padding-left: 7px; - width: 723px; - margin-top: 10px; } -.question-page .answer .vote-buttons { - float: left; } -.question-page .accepted-answer { - background-color: #f7fecc; - border-bottom-color: #9BD59B; } - .question-page .accepted-answer .vote-buttons { - width: 27px; - margin-right: 10px; - margin-top: 10px; } -.question-page .answer .post-update-info a { - color: #444444; } -.question-page .answered { - background: #CCC; - color: #999; } -.question-page .answered-accepted { - background: #DCDCDC; - color: #763333; } - .question-page .answered-accepted strong { - color: #E1E818; } -.question-page .answered-by-owner { - background: #F1F1FF; } - .question-page .answered-by-owner .comments { - background-color: #E6ECFF; } - .question-page .answered-by-owner .comments .button, .question-page .answered-by-owner .comments input[type="submit"], .question-page .answered-by-owner .comments input[type="button"], .question-page .answered-by-owner .comments button { - background-color: #E6ECFF; } - .question-page .answered-by-owner .vote-buttons { - margin-right: 10px; } -.question-page .answer-img-accept:hover { - background: url(../images/vote-accepted-on.png); } -.question-page .answer-body a { - color: #1b79bd; } -.question-page .answer-body li { - margin-bottom: 0.7em; } -.question-page #fmanswer { - color: #707070; - line-height: 1.2; - margin-top: 10px; } - .question-page #fmanswer h2 { - font-family: 'Yanone Kaffeesatz',sans-serif; - color: #7ea9b3; - font-size: 24px; } - .question-page #fmanswer label { - font-size: 13px; } -.question-page .message { - padding: 5px; - margin: 0px 0 10px 0; } - @media screen and (-webkit-min-device-pixel-ratio:0) { textarea { padding-left: 3px !important; } } @@ -3560,14 +2964,6 @@ p.signup_p { margin-bottom: 7px; font-size: 14px; } -.search-result-summary { - font-weight: bold; - font-size: 18px; - line-height: 22px; - margin: 0px 0px 0px 0px; - padding: 2px 0 0 0; - float: left; } - .faq-rep-item { text-align: right; padding-right: 5px; } @@ -3674,6 +3070,357 @@ pre.prettyprint { padding: 3px; border: 0px solid #888; } +body.askbot .secondary-nav { + margin: 0; } + body.askbot .secondary-nav nav { + -webkit-box-sizing: border-box; + -moz-box-sizing: border-box; + -ms-box-sizing: border-box; + -o-box-sizing: border-box; + box-sizing: border-box; + border: 1px solid #eddfaa; + border-top: 0; + margin: 0 auto; + padding: 22.652px; } + body.askbot .secondary-nav nav div { + float: left; } + body.askbot .secondary-nav nav div.question-filter { + font-size: 16px; + margin-top: 4px; + width: 31.984%; } + body.askbot .secondary-nav nav div.question-filter ul { + -webkit-border-radius: 35px; + -moz-border-radius: 35px; + -ms-border-radius: 35px; + -o-border-radius: 35px; + border-radius: 35px; + background: #e4d080; + display: inline; + margin: 0 0 0 10px; + padding: 5.663px 20px; } + body.askbot .secondary-nav nav div.question-filter ul li { + display: inline-block; + list-style: none; + margin-right: 10px; } + body.askbot .secondary-nav nav div.question-filter ul li:last-child { + margin-right: 0; } + body.askbot .secondary-nav nav div.question-filter ul li a { + text-transform: capitalize; + text-shadow: none; + font-size: 14px; } + body.askbot .secondary-nav nav div.question-filter ul li a.on { + font-weight: bold; } + body.askbot .secondary-nav nav div.search-box { + margin-left: 2%; + text-align: right; + width: 65.992%; } + body.askbot .secondary-nav nav div.search-box input[type="text"] { + margin-right: 6px; + width: 22.699%; } +body.askbot section.main-content div.discussion-wrapper div.discussion-content { + -webkit-box-sizing: border-box; + -moz-box-sizing: border-box; + -ms-box-sizing: border-box; + -o-box-sizing: border-box; + box-sizing: border-box; + display: table-cell; + padding: 2.024%; + vertical-align: top; + width: 74.494%; } + body.askbot section.main-content div.discussion-wrapper div.discussion-content p.tabula-rasa { + -webkit-border-radius: 5px; + -moz-border-radius: 5px; + -ms-border-radius: 5px; + -o-border-radius: 5px; + border-radius: 5px; + background-color: #f6f6f6; + color: #888; + margin: 10px auto; + padding: 20px; + text-align: center; + width: 40.486%; } + body.askbot section.main-content div.discussion-wrapper div.discussion-content p.tabula-rasa:first-child { + margin-top: 70px; } + body.askbot section.main-content div.discussion-wrapper div.discussion-content p.tabula-rasa:last-child { + margin-bottom: 70px; } + body.askbot section.main-content div.discussion-wrapper div.discussion-content p.tabula-rasa a { + text-decoration: none; + color: #888; + font-weight: bold; } +body.askbot section.main-content div.discussion-wrapper aside { + -webkit-box-shadow: inset 1px 0 0 #f6f6f6; + -moz-box-shadow: inset 1px 0 0 #f6f6f6; + -ms-box-shadow: inset 1px 0 0 #f6f6f6; + -o-box-shadow: inset 1px 0 0 #f6f6f6; + box-shadow: inset 1px 0 0 #f6f6f6; + border-left: 1px solid #d3d3d3; + border-right: 1px solid #f6f6f6; + padding: 2.024%; + width: 23.482%; } + body.askbot section.main-content div.discussion-wrapper aside h2 { + font-size: 16px; } + body.askbot section.main-content div.discussion-wrapper aside h3, body.askbot section.main-content div.discussion-wrapper aside div.wiki-wrapper div#wiki_panel input[type="button"], div.wiki-wrapper div#wiki_panel body.askbot section.main-content div.discussion-wrapper aside input[type="button"] { + border-bottom: 0; + box-shadow: none; } + body.askbot section.main-content div.discussion-wrapper aside input[type="text"] { + width: 76%; } + body.askbot section.main-content div.discussion-wrapper aside #displayTagFilterControl { + margin-top: 10px; } +body.askbot footer { + margin: 0 auto; + padding: 0; } + body.askbot footer div.footer-wrapper { + -webkit-box-shadow: 0 1px 0 white; + -moz-box-shadow: 0 1px 0 white; + -ms-box-shadow: 0 1px 0 white; + -o-box-shadow: 0 1px 0 white; + box-shadow: 0 1px 0 white; + -webkit-box-sizing: border-box; + -moz-box-sizing: border-box; + -ms-box-sizing: border-box; + -o-box-sizing: border-box; + box-sizing: border-box; + background-color: #000; + border-top: 0; + padding: 1.012%; } + +div.question-controls { + display: block; + margin-bottom: 30px; + overflow: hidden; + width: 100%; } + div.question-controls div { + display: inline-block; } + div.question-controls div.question-count { + margin-right: 2.024%; + width: 60.054%; } + div.question-controls div.question-count h1 { + margin-top: 0; } + div.question-controls div.question-sort { + vertical-align: bottom; + width: 37.228%; } + div.question-controls div.question-sort nav { + -webkit-border-radius: 35px; + -moz-border-radius: 35px; + -ms-border-radius: 35px; + -o-border-radius: 35px; + border-radius: 35px; + background-color: #faf7e9; + height: 30px; + float: right; + font-size: 16px; + margin: 3px 0; + padding: 0 20px; } + div.question-controls div.question-sort nav a { + color: #a88d23; } + div.question-controls div.question-sort nav a:before { + content: '|'; + color: #eddfaa; + font-size: 22px; } + div.question-controls div.question-sort nav a:hover { + text-decoration: none; + color: #544611; } + +ul.question-list { + width: 100%; } + ul.question-list li.single-question { + border-top: 1px solid #eee; + list-style: none; + padding: 10px 0; } + ul.question-list li.single-question:hover { + background: #fdfcf6; } + ul.question-list li.single-question div { + display: inline-block; } + ul.question-list li.single-question div.question-body { + -webkit-box-sizing: border-box; + -moz-box-sizing: border-box; + -ms-box-sizing: border-box; + -o-box-sizing: border-box; + box-sizing: border-box; + margin-right: 2.024%; + padding-left: 10px; + width: 60.054%; } + ul.question-list li.single-question div.question-body h2 { + font-size: 16px; + font-weight: normal; + margin: 0px 0 15px 0; + text-transform: none; } + ul.question-list li.single-question div.question-body div.user-info { + display: inline-block; + vertical-align: top; } + ul.question-list li.single-question div.question-body div.user-info span.relative-time { + font-weight: normal; } + ul.question-list li.single-question div.question-body div.user-info a { + color: #993333; } + ul.question-list li.single-question div.question-body ul.tags { + display: inline-block; } + ul.question-list li.single-question div.question-meta { + width: 37.228%; } + ul.question-list li.single-question div.question-meta ul { + text-align: right; } + ul.question-list li.single-question div.question-meta ul li { + -webkit-border-radius: 3px; + -moz-border-radius: 3px; + -ms-border-radius: 3px; + -o-border-radius: 3px; + border-radius: 3px; + display: inline-block; + height: 60px; + margin-right: 10px; + width: 60px; } + ul.question-list li.single-question div.question-meta ul li.views { + background: #faf7e9; } + ul.question-list li.single-question div.question-meta ul li.answers { + background: #F6EFD4; } + ul.question-list li.single-question div.question-meta ul li.votes { + background: #f2e7bf; } + ul.question-list li.single-question div.question-meta ul li span, ul.question-list li.single-question div.question-meta ul li div { + -webkit-box-sizing: border-box; + -moz-box-sizing: border-box; + -ms-box-sizing: border-box; + -o-box-sizing: border-box; + box-sizing: border-box; + color: #7e691a; + display: block; + text-align: center; } + ul.question-list li.single-question div.question-meta ul li span { + font-size: 16px; + font-weight: bold; + height: 35px; + padding-top: 15px; + vertical-align: middle; } + ul.question-list li.single-question div.question-meta ul li div { + height: 25px; + font-size: 12px; } + +div.search-tips { + display: block; } + +div.post-update-info { + -webkit-box-sizing: border-box; + -moz-box-sizing: border-box; + -ms-box-sizing: border-box; + -o-box-sizing: border-box; + box-sizing: border-box; + -webkit-border-radius: 5px; + -moz-border-radius: 5px; + -ms-border-radius: 5px; + -o-border-radius: 5px; + border-radius: 5px; + background: #faf7e9; + padding: 10px; } + div.post-update-info a { + color: #993333; } + div.post-update-info div.change-date { + font-size: 12px; + margin-bottom: 10px; } + div.post-update-info div.avatar { + display: inline-block; + float: left; + margin-right: 3px; } + div.post-update-info div.avatar img.gravatar { + background: white; + border: 1px solid #eddfaa; + margin-right: 5px; + padding: 3px; + vertical-align: bottom; } + div.post-update-info div.user-meta { + display: inline-block; + width: 60%; } + div.post-update-info div.user-meta span.user-badges { + display: block; } + +ul.tags { + list-style: none; } + ul.tags li, ul.tags a { + position: relative; } + ul.tags li { + -webkit-border-radius: 4px; + -moz-border-radius: 4px; + -ms-border-radius: 4px; + -o-border-radius: 4px; + border-radius: 4px; + background: #eee; + color: #555; + display: inline; + font-size: 12px; + margin-left: 15px; + padding: 3px 10px 5px 5px; } + ul.tags li:before { + content: ""; + position: absolute; + top: 0; + left: -11px; + width: 0; + height: 0; + border-color: transparent #eee transparent transparent; + border-style: solid; + border-width: 12px 12px 12px 0; } + +div.question-header div.vote-buttons { + display: inline-block; + float: left; + width: 8.696%; + margin-right: 2.717%; } + div.question-header div.vote-buttons ul li { + background-position: center; + background-repeat: no-repeat; + cursor: pointer; + font-weight: bold; + height: 20px; + list-style: none; + padding: 10px; + text-align: center; + width: 25px; } + div.question-header div.vote-buttons ul li.question-img-upvote, div.question-header div.vote-buttons ul li.answer-img-upvote { + background-image: url(/static/images/askbot/vote-arrow-up-new.png); + background-color: #F6EFD4; } + div.question-header div.vote-buttons ul li.question-img-upvote:hover, div.question-header div.vote-buttons ul li.question-img-upvote.on, div.question-header div.vote-buttons ul li.answer-img-upvote:hover, div.question-header div.vote-buttons ul li.answer-img-upvote.on { + background-image: url(/static/images/askbot/vote-arrow-up-on-new.png); } + div.question-header div.vote-buttons ul li.question-img-downvote, div.question-header div.vote-buttons ul li.answer-img-downvote { + background-image: url(/static/images/askbot/vote-arrow-down-new.png); } + div.question-header div.vote-buttons ul li.question-img-downvote:hover, div.question-header div.vote-buttons ul li.question-img-downvote.on, div.question-header div.vote-buttons ul li.answer-img-downvote:hover, div.question-header div.vote-buttons ul li.answer-img-downvote.on { + background-image: url(/static/images/askbot/vote-arrow-down-on-new.png); } +div.question-header div.question-container { + display: inline-block; + float: left; + width: 88.587%; } + div.question-header div.question-container h1 { + margin-top: 0; } + div.question-header div.question-container div.meta-bar { + border-bottom: 1px solid #eee; + display: block; + margin: 20px 0 10px; + overflow: hidden; + padding-bottom: 15px; } + div.question-header div.question-container div.meta-bar div.tag-list { + display: inline-block; + float: left; + width: 48.466%; + margin-right: 3.067%; } + div.question-header div.question-container div.meta-bar div.question-actions { + display: inline-block; + float: left; + text-align: right; + width: 48.466%; } + div.question-header div.question-container div.meta-bar div.question-actions a { + color: #a88d23; } + div.question-header div.question-container div.meta-bar div.question-actions a.question-delete { + color: #993333; } + div.question-header div.question-container div.meta-bar div.question-actions span.sep { + color: #eddfaa; } + div.question-header div.question-container div.question-content { + overflow: hidden; } + div.question-header div.question-container div.question-content div.question-body { + display: inline-block; + float: left; + margin-right: 3.067%; + width: 76.81%; } + div.question-header div.question-container div.question-content div.post-update-info { + display: inline-block; + float: left; + width: 20.123%; } + /* ---------------------------------------------------------------------------------------- diff --git a/css/marketing.css b/css/marketing.css index f48407a05c..04298414ea 100644 --- a/css/marketing.css +++ b/css/marketing.css @@ -86,29 +86,48 @@ hr { input, select { vertical-align: middle; } +/* Generated by Font Squirrel (http://www.fontsquirrel.com) on January 25, 2012 05:06:34 PM America/New_York */ @font-face { font-family: 'Open Sans'; - font-style: normal; + src: url("/static/fonts/OpenSans-Regular-webfont.eot"); + src: url("/static/fonts/OpenSans-Regular-webfont.eot?#iefix") format("embedded-opentype"), url("/static/fonts/OpenSans-Regular-webfont.woff") format("woff"), url("/static/fonts/OpenSans-Regular-webfont.ttf") format("truetype"), url("/static/fonts/OpenSans-Regular-webfont.svg#OpenSansRegular") format("svg"); + font-weight: 600; + font-style: normal; } + +@font-face { + font-family: 'Open Sans'; + src: url("/static/fonts/OpenSans-Italic-webfont.eot"); + src: url("/static/fonts/OpenSans-Italic-webfont.eot?#iefix") format("embedded-opentype"), url("/static/fonts/OpenSans-Italic-webfont.woff") format("woff"), url("/static/fonts/OpenSans-Italic-webfont.ttf") format("truetype"), url("/static/fonts/OpenSans-Italic-webfont.svg#OpenSansItalic") format("svg"); font-weight: 400; - src: local("Open Sans"), local("OpenSans"), url("http://themes.googleusercontent.com/static/fonts/opensans/v6/cJZKeOuBrn4kERxqtaUH3bO3LdcAZYWl9Si6vvxL-qU.woff") format("woff"); } + font-style: italic; } @font-face { font-family: 'Open Sans'; - font-style: italic; - font-weight: 400; - src: local("Open Sans Italic"), local("OpenSans-Italic"), url("http://themes.googleusercontent.com/static/fonts/opensans/v6/xjAJXh38I15wypJXxuGMBrrIa-7acMAeDBVuclsi6Gc.woff") format("woff"); } + src: url("/static/fonts/OpenSans-Bold-webfont.eot"); + src: url("/static/fonts/OpenSans-Bold-webfont.eot?#iefix") format("embedded-opentype"), url("/static/fonts/OpenSans-Bold-webfont.woff") format("woff"), url("/static/fonts/OpenSans-Bold-webfont.ttf") format("truetype"), url("/static/fonts/OpenSans-Bold-webfont.svg#OpenSansBold") format("svg"); + font-weight: 700; + font-style: normal; } @font-face { font-family: 'Open Sans'; - font-style: normal; + src: url("/static/fonts/OpenSans-BoldItalic-webfont.eot"); + src: url("/static/fonts/OpenSans-BoldItalic-webfont.eot?#iefix") format("embedded-opentype"), url("/static/fonts/OpenSans-BoldItalic-webfont.woff") format("woff"), url("/static/fonts/OpenSans-BoldItalic-webfont.ttf") format("truetype"), url("/static/fonts/OpenSans-BoldItalic-webfont.svg#OpenSansBoldItalic") format("svg"); + font-weight: 700; + font-style: italic; } + +@font-face { + font-family: 'Open Sans'; + src: url("/static/fonts/OpenSans-ExtraBold-webfont.eot"); + src: url("/static/fonts/OpenSans-ExtraBold-webfont.eot?#iefix") format("embedded-opentype"), url("/static/fonts/OpenSans-ExtraBold-webfont.woff") format("woff"), url("/static/fonts/OpenSans-ExtraBold-webfont.ttf") format("truetype"), url("/static/fonts/OpenSans-ExtraBold-webfont.svg#OpenSansExtrabold") format("svg"); font-weight: 800; - src: local("Open Sans Extrabold"), local("OpenSans-Extrabold"), url("http://themes.googleusercontent.com/static/fonts/opensans/v6/EInbV5DfGHOiMmvb1Xr-hqRDOzjiPcYnFooOUGCOsRk.woff") format("woff"); } + font-style: normal; } @font-face { font-family: 'Open Sans'; - font-style: italic; + src: url("/static/fonts/OpenSans-ExtraBoldItalic-webfont.eot"); + src: url("/static/fonts/OpenSans-ExtraBoldItalic-webfont.eot?#iefix") format("embedded-opentype"), url("/static/fonts/OpenSans-ExtraBoldItalic-webfont.woff") format("woff"), url("/static/fonts/OpenSans-ExtraBoldItalic-webfont.ttf") format("truetype"), url("/static/fonts/OpenSans-ExtraBoldItalic-webfont.svg#OpenSansExtraboldItalic") format("svg"); font-weight: 800; - src: local("Open Sans Extrabold Italic"), local("OpenSans-ExtraboldItalic"), url("http://themes.googleusercontent.com/static/fonts/opensans/v6/PRmiXeptR36kaC0GEAetxsBo4hlZyBvkZICS3KpNonM.woff") format("woff"); } + font-style: italic; } .wrapper, .subpage, section.copyright, section.tos, section.privacy-policy, section.honor-code, header.announcement div, section.index-content, footer { -webkit-box-sizing: border-box; @@ -182,7 +201,7 @@ input, select { -ms-transition-delay: 0; -o-transition-delay: 0; transition-delay: 0; - background-color: #990000; + background-color: #993333; color: #fff; margin: 25.888px 0 12.944px; padding: 6.472px 12.944px; @@ -190,7 +209,7 @@ input, select { font-style: normal; -webkit-font-smoothing: antialiased; } .button:hover, header.announcement div section.course section a:hover, section.index-content section.course a:hover, section.index-content section.staff a:hover, section.index-content section.about-course section.cta a.enroll:hover { - background-color: #660000; } + background-color: #732626; } .button span, header.announcement div section.course section a span, section.index-content section.course a span, section.index-content section.staff a span, section.index-content section.about-course section.cta a.enroll span { font-family: Garamond, Baskerville, "Baskerville Old Face", "Hoefler Text", "Times New Roman", serif; font-style: italic; } @@ -208,11 +227,11 @@ body { body em { font-style: italic; } body a { - color: #990000; + color: #993333; font-style: italic; text-decoration: none; } body a:hover, body a:focus { - color: #660000; } + color: #732626; } body input[type="email"], body input[type="number"], body input[type="password"], body input[type="search"], body input[type="tel"], body input[type="text"], body input[type="url"], body input[type="color"], body input[type="date"], body input[type="datetime"], body input[type="datetime-local"], body input[type="month"], body input[type="time"], body input[type="week"], body textarea { -webkit-box-shadow: 0 -1px 0 white; -moz-box-shadow: 0 -1px 0 white; @@ -231,18 +250,23 @@ body { padding: 4px; width: 100%; } body input[type="email"]:focus, body input[type="number"]:focus, body input[type="password"]:focus, body input[type="search"]:focus, body input[type="tel"]:focus, body input[type="text"]:focus, body input[type="url"]:focus, body input[type="color"]:focus, body input[type="date"]:focus, body input[type="datetime"]:focus, body input[type="datetime-local"]:focus, body input[type="month"]:focus, body input[type="time"]:focus, body input[type="week"]:focus, body textarea:focus { - border-color: #990000; } + border-color: #993333; } header.announcement { + -webkit-background-size: cover; + -moz-background-size: cover; + -ms-background-size: cover; + -o-background-size: cover; + background-size: cover; background: #333; border-bottom: 1px solid #000; color: #fff; -webkit-font-smoothing: antialiased; } header.announcement.home { - background: #e3e3e3 url("/static/images/marketing/shot-1-medium.jpg"); } + background: #e3e3e3 url("/static/images/marketing/shot-5-medium.jpg"); } @media screen and (min-width: 1200px) { header.announcement.home { - background: #e3e3e3 url("/static/images/marketing/shot-1-large.jpg"); } } + background: #e3e3e3 url("/static/images/marketing/shot-5-large.jpg"); } } header.announcement.home div { padding: 258.88px 25.888px 77.664px; } header.announcement.home div nav h1 { @@ -304,7 +328,7 @@ header.announcement { zoom: 1; *display: inline; *vertical-align: auto; - background: #990000; + background: #993333; margin-left: 34.171%; padding: 25.888px 38.832px; } header.announcement div section h1 { @@ -339,12 +363,12 @@ header.announcement { margin-left: 0; padding: 0; } header.announcement div section.course section a { - background-color: #330000; + background-color: #4d1919; display: block; padding: 12.944px 25.888px; text-align: center; } header.announcement div section.course section a:hover { - background-color: #660000; } + background-color: #732626; } header.announcement div section.course p { width: 48.092%; line-height: 25.888px; @@ -388,6 +412,8 @@ section.index-content section { letter-spacing: 1px; color: #666; margin-bottom: 25.888px; } + section.index-content section.about section.features h2 span { + text-transform: none; } section.index-content section.about section.features p { width: auto; clear: both; } @@ -395,7 +421,7 @@ section.index-content section { font-family: "Open sans"; font-weight: 800; } section.index-content section.about section.features p a { - color: #990000; + color: #993333; text-decoration: none; -webkit-transition-property: all; -moz-transition-property: all; @@ -418,7 +444,7 @@ section.index-content section { -o-transition-delay: 0; transition-delay: 0; } section.index-content section.about section.features p a:hover, section.index-content section.about section.features p a:focus { - color: #4d0000; } + color: #602020; } section.index-content section.about section.features ul { margin-bottom: 0; } section.index-content section.about section.features ul li { @@ -472,7 +498,7 @@ section.index-content section { margin-right: 3.817%; } section.index-content section.about-course section.requirements { clear: both; - width: auto; + width: 100%; border-top: 1px solid #E5E5E5; padding-top: 25.888px; margin-bottom: 0; } @@ -637,55 +663,55 @@ div.leanModal_box { color: #666; font-size: 14px; float: none; } - div.leanModal_box form input[type="button"] { - border: 1px solid #520000; + div.leanModal_box form input[type="button"], div.leanModal_box form input[type="submit"] { + border: 1px solid #691b1b; -webkit-border-radius: 3px; -moz-border-radius: 3px; -ms-border-radius: 3px; -o-border-radius: 3px; border-radius: 3px; - -webkit-box-shadow: inset 0 1px 0 0 #dc0909; - -moz-box-shadow: inset 0 1px 0 0 #dc0909; - -ms-box-shadow: inset 0 1px 0 0 #dc0909; - -o-box-shadow: inset 0 1px 0 0 #dc0909; - box-shadow: inset 0 1px 0 0 #dc0909; + -webkit-box-shadow: inset 0 1px 0 0 #bc5c5c; + -moz-box-shadow: inset 0 1px 0 0 #bc5c5c; + -ms-box-shadow: inset 0 1px 0 0 #bc5c5c; + -o-box-shadow: inset 0 1px 0 0 #bc5c5c; + box-shadow: inset 0 1px 0 0 #bc5c5c; color: white; display: inline; font-size: 11px; font-weight: bold; - background-color: #990000; - background-image: -webkit-gradient(linear, left top, left bottom, color-stop(0%, #990000), color-stop(100%, #610000)); - background-image: -webkit-linear-gradient(top, #990000, #610000); - background-image: -moz-linear-gradient(top, #990000, #610000); - background-image: -ms-linear-gradient(top, #990000, #610000); - background-image: -o-linear-gradient(top, #990000, #610000); - background-image: linear-gradient(top, #990000, #610000); + background-color: #993333; + background-image: -webkit-gradient(linear, left top, left bottom, color-stop(0%, #993333), color-stop(100%, #761e1e)); + background-image: -webkit-linear-gradient(top, #993333, #761e1e); + background-image: -moz-linear-gradient(top, #993333, #761e1e); + background-image: -ms-linear-gradient(top, #993333, #761e1e); + background-image: -o-linear-gradient(top, #993333, #761e1e); + background-image: linear-gradient(top, #993333, #761e1e); padding: 6px 18px 7px; - text-shadow: 0 1px 0 #3d0000; + text-shadow: 0 1px 0 #5d1414; -webkit-background-clip: padding-box; font-size: 18px; padding: 12.944px; } - div.leanModal_box form input[type="button"]:hover { - -webkit-box-shadow: inset 0 1px 0 0 #ac0606; - -moz-box-shadow: inset 0 1px 0 0 #ac0606; - -ms-box-shadow: inset 0 1px 0 0 #ac0606; - -o-box-shadow: inset 0 1px 0 0 #ac0606; - box-shadow: inset 0 1px 0 0 #ac0606; + div.leanModal_box form input[type="button"]:hover, div.leanModal_box form input[type="submit"]:hover { + -webkit-box-shadow: inset 0 1px 0 0 #a44141; + -moz-box-shadow: inset 0 1px 0 0 #a44141; + -ms-box-shadow: inset 0 1px 0 0 #a44141; + -o-box-shadow: inset 0 1px 0 0 #a44141; + box-shadow: inset 0 1px 0 0 #a44141; cursor: pointer; - background-color: #7d0303; - background-image: -webkit-gradient(linear, left top, left bottom, color-stop(0%, #7d0303), color-stop(100%, #520000)); - background-image: -webkit-linear-gradient(top, #7d0303, #520000); - background-image: -moz-linear-gradient(top, #7d0303, #520000); - background-image: -ms-linear-gradient(top, #7d0303, #520000); - background-image: -o-linear-gradient(top, #7d0303, #520000); - background-image: linear-gradient(top, #7d0303, #520000); } - div.leanModal_box form input[type="button"]:active { - border: 1px solid #520000; - -webkit-box-shadow: inset 0 0 8px 4px #420000, inset 0 0 8px 4px #420000, 0 1px 1px 0 #eeeeee; - -moz-box-shadow: inset 0 0 8px 4px #420000, inset 0 0 8px 4px #420000, 0 1px 1px 0 #eeeeee; - -ms-box-shadow: inset 0 0 8px 4px #420000, inset 0 0 8px 4px #420000, 0 1px 1px 0 #eeeeee; - -o-box-shadow: inset 0 0 8px 4px #420000, inset 0 0 8px 4px #420000, 0 1px 1px 0 #eeeeee; - box-shadow: inset 0 0 8px 4px #420000, inset 0 0 8px 4px #420000, 0 1px 1px 0 #eeeeee; } + background-color: #823030; + background-image: -webkit-gradient(linear, left top, left bottom, color-stop(0%, #823030), color-stop(100%, #691c1c)); + background-image: -webkit-linear-gradient(top, #823030, #691c1c); + background-image: -moz-linear-gradient(top, #823030, #691c1c); + background-image: -ms-linear-gradient(top, #823030, #691c1c); + background-image: -o-linear-gradient(top, #823030, #691c1c); + background-image: linear-gradient(top, #823030, #691c1c); } + div.leanModal_box form input[type="button"]:active, div.leanModal_box form input[type="submit"]:active { + border: 1px solid #691b1b; + -webkit-box-shadow: inset 0 0 8px 4px #5c1919, inset 0 0 8px 4px #5c1919, 0 1px 1px 0 #eeeeee; + -moz-box-shadow: inset 0 0 8px 4px #5c1919, inset 0 0 8px 4px #5c1919, 0 1px 1px 0 #eeeeee; + -ms-box-shadow: inset 0 0 8px 4px #5c1919, inset 0 0 8px 4px #5c1919, 0 1px 1px 0 #eeeeee; + -o-box-shadow: inset 0 0 8px 4px #5c1919, inset 0 0 8px 4px #5c1919, 0 1px 1px 0 #eeeeee; + box-shadow: inset 0 0 8px 4px #5c1919, inset 0 0 8px 4px #5c1919, 0 1px 1px 0 #eeeeee; } div#login { min-width: 400px; } From fe3a6bd7bc187c0deeada8adf5ff96b115094475 Mon Sep 17 00:00:00 2001 From: Ernie Park Date: Wed, 1 Feb 2012 13:25:07 -0500 Subject: [PATCH 4/4] add leanmodal minified and original --- js/jquery.leanModal.js | 75 ++++++++++++++++++++++++++++++++++++++ js/jquery.leanModal.min.js | 1 + 2 files changed, 76 insertions(+) create mode 100644 js/jquery.leanModal.js create mode 100644 js/jquery.leanModal.min.js diff --git a/js/jquery.leanModal.js b/js/jquery.leanModal.js new file mode 100644 index 0000000000..e6974d1520 --- /dev/null +++ b/js/jquery.leanModal.js @@ -0,0 +1,75 @@ +(function($){ + + $.fn.extend({ + + leanModal: function(options) { + + var defaults = { + top: 100, + overlay: 0.5 + } + + options = $.extend(defaults, options); + + return this.each(function() { + + var o = options; + + $(this).click(function(e) { + + var overlay = $("
"); + + var modal_id = $(this).attr("href"); + + $(".leanModal_box").css({ 'display' : 'none' }); + + $("body").append(overlay); + + $("#lean_overlay").click(function() { + close_modal(modal_id); + }); + + var modal_height = $(modal_id).outerHeight(); + var modal_width = $(modal_id).outerWidth(); + + $('#lean_overlay').css({ 'display' : 'block', opacity : 0 }); + + $('#lean_overlay').fadeTo(200,o.overlay); + + $(modal_id).css({ + + 'display' : 'block', + 'position' : 'fixed', + 'opacity' : 0, + 'z-index': 11000, + 'left' : 50 + '%', + 'margin-left' : -(modal_width/2) + "px", + 'top' : o.top + "px" + }); + + var top_position = $(modal_id).offset().top + "px"; + $(modal_id).css({ + 'position' : 'absolute', + 'top': top_position + }); + + $(modal_id).fadeTo(200,1); + + e.preventDefault(); + + }); + + }); + + function close_modal(modal_id){ + + $("#lean_overlay").fadeOut(200); + + $(modal_id).css({ 'display' : 'none' }); + + } + + } + }); + +})(jQuery); diff --git a/js/jquery.leanModal.min.js b/js/jquery.leanModal.min.js new file mode 100644 index 0000000000..a40020e91c --- /dev/null +++ b/js/jquery.leanModal.min.js @@ -0,0 +1 @@ +(function(a){a.fn.extend({leanModal:function(b){function d(b){a("#lean_overlay").fadeOut(200);a(b).css({display:"none"})}var c={top:100,overlay:.5};b=a.extend(c,b);return this.each(function(){var c=b;a(this).click(function(b){var e=a("
");var f=a(this).attr("href");a(".leanModal_box").css({display:"none"});a("body").append(e);a("#lean_overlay").click(function(){d(f)});var g=a(f).outerHeight();var h=a(f).outerWidth();a("#lean_overlay").css({display:"block",opacity:0});a("#lean_overlay").fadeTo(200,c.overlay);a(f).css({display:"block",position:"fixed",opacity:0,"z-index":11e3,left:50+"%","margin-left":-(h/2)+"px",top:c.top+"px"});var i=a(f).offset().top+"px";a(f).css({position:"absolute",top:i});a(f).fadeTo(200,1);b.preventDefault()})})}})})(jQuery)