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