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This commit is contained in:
Kyle Fiedler
2012-01-12 17:06:10 -05:00
parent 202d42e772 ce607db8db
commit b62bb4401d
63 changed files with 3928 additions and 1405 deletions
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45
js/video_player.js
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@@ -102,9 +102,9 @@ function caption_index(now) {
function format_time(t)
{
seconds = Math.round(t);
minutes = Math.round(seconds / 60);
hours = Math.round(minutes / 60);
seconds = Math.floor(t);
minutes = Math.floor(seconds / 60);
hours = Math.floor(minutes / 60);
seconds = seconds % 60;
minutes = minutes % 60;
return hours+":"+((minutes < 10)?"0":"")+minutes+":"+((seconds < 10)?"0":"")+(seconds%60);
@@ -141,6 +141,7 @@ function setytplayerState(newState) {
// IMPORTANT TODO: Load test
// POSSIBLE FIX: Move to unload() event and similar
var ajax_video=function(){};
var ytplayer;
function onYouTubePlayerReady(playerId) {
ytplayer = document.getElementById("myytplayer");
@@ -152,15 +153,49 @@ function onYouTubePlayerReady(playerId) {
var id=load_id;
loadNewVideo(id, 0);
}
}
/* HTML5 YouTube iFrame API Specific */
function onYouTubePlayerAPIReady() {
ytplayer = new YT.Player('html5_player', {
events: {
'onReady': onPlayerReady,
'onStateChange': onPlayerStateChange
}
});
updateytplayerInfoInterval = setInterval(updateytplayerInfo, 500);
ajax_videoInterval = setInterval(ajax_video, 5000);
}
// Need this function to call the API ready callback when we switch to a tab with AJAX that has a video
// That callback is not being fired when we switch tabs.
function loadHTML5Video() {
if (!ytplayer && switched_tab){
onYouTubePlayerAPIReady();
}
}
function onPlayerReady(event) {
// alert("ready");
event.target.playVideo();
}
function onPlayerStateChange(event) {
if (event.data == YT.PlayerState.PLAYING) {
}
}
/* End HTML5 Specific */
var switched_tab = false; // switch to true when we destroy so we know to call onYouTubePlayerAPIReady()
// clear pings to video status when we switch to a different sequence tab with ajax
function videoDestroy() {
load_id = 0;
clearInterval(updateytplayerInfoInterval);
clearInterval(ajax_videoInterval);
ytplayer = false;
switched_tab = true;
}
function log_event(e, d) {
@@ -233,7 +268,7 @@ function updateytplayerInfo() {
update_captions(getCurrentTime());
}
// updateHTML("videoduration", getDuration());
// updateHTML("videoduration", getDuration());
// updateHTML("videotime", getCurrentTime());
// updateHTML("startbytes", getStartBytes());
// updateHTML("volume", getVolume());

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"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."
]
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"text": [
"",
"All right. 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 --",
@@ -1341,7 +1320,6 @@
"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",
@@ -1514,7 +1492,6 @@
"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.",
@@ -1725,7 +1702,6 @@
"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",
@@ -1745,7 +1721,6 @@
"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",
@@ -1797,10 +1772,8 @@
"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.",

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"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",
@@ -1406,11 +1395,9 @@
"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.",
@@ -1829,7 +1816,6 @@
"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.",
@@ -1923,7 +1909,6 @@
"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",

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"",
"OK. Good morning.",
"Let's get going. As always, I will start with a",
"review. And today we embark on another",
@@ -2051,7 +2042,6 @@
"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?",
@@ -2079,7 +2069,6 @@
"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",
@@ -2328,7 +2317,6 @@
"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,",

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"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",
@@ -1359,12 +1322,9 @@
"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",
@@ -1446,7 +1406,6 @@
"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.",
@@ -1553,7 +1512,6 @@
"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,",
@@ -1592,7 +1550,6 @@
"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",
@@ -1713,7 +1670,6 @@
"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",
@@ -1753,7 +1709,6 @@
"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",
@@ -1787,28 +1742,23 @@
"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",
@@ -1838,7 +1788,6 @@
"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",
@@ -1861,11 +1810,9 @@
"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",
@@ -1944,7 +1891,6 @@
"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,",

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"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."
]
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"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",
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@@ -1809,7 +1804,6 @@
"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.",

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"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",
@@ -1353,21 +1322,17 @@
"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,",
@@ -1405,7 +1370,6 @@
"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.",
@@ -1546,7 +1510,6 @@
"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.",
@@ -1666,14 +1629,11 @@
"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,",
@@ -1730,7 +1690,6 @@
"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",
@@ -1781,7 +1740,6 @@
"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",
@@ -1820,7 +1778,6 @@
"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,",
@@ -1831,7 +1788,6 @@
"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",
@@ -1872,7 +1828,6 @@
"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",

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"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."
]
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"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.",

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"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",
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"it's variously called small signal analysis,",
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"small signal discipline, whatever you want.",
"",
"OK, this simply says that by boosting and shrinking my",
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"little bit longer, switch to page five of your",
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"",
"OK, so what I have here, this is my offset VD,",
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"and the total signal is called V capital D.",
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"total signal I capital D. OK, so that's the small signal",
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"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.",
@@ -1810,7 +1790,6 @@
"good old Taylor's series stuff. OK, the first term is the first",
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"",
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"current ID. And similarly,",
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"F of --",
"",
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"Expo Dweeb, and let me just plug in the values.",
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"",
"OK, and so that is given by a e to the BVD, oops,",
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"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."
]
}

72
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"text": [
"",
"Good morning.",
"",
"All right. 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",
@@ -1268,14 +1218,12 @@
"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",
@@ -1317,7 +1265,6 @@
"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",
@@ -1327,11 +1274,9 @@
"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.",
@@ -1345,7 +1290,6 @@
"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",
@@ -1418,7 +1362,6 @@
"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",
@@ -1495,11 +1438,9 @@
"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.",
@@ -1517,7 +1458,6 @@
"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.",
@@ -1536,7 +1476,6 @@
"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",
@@ -1546,13 +1485,11 @@
"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.",
@@ -1568,7 +1505,6 @@
"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",
@@ -1576,7 +1512,6 @@
"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",
@@ -1604,7 +1539,6 @@
"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",
@@ -1656,17 +1590,14 @@
"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",
@@ -1741,9 +1672,7 @@
"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.",
@@ -1784,7 +1713,6 @@
"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.",

78
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"text": [
"",
"All right. Let's get started.",
"I guess this watch is a couple minutes fast.",
"First a quick announcement. In case you have forgotten,",
@@ -1305,11 +1252,9 @@
"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",
@@ -1329,7 +1274,6 @@
"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,",
@@ -1356,15 +1300,12 @@
"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",
@@ -1379,7 +1320,6 @@
"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,",
@@ -1412,7 +1352,6 @@
"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",
@@ -1453,7 +1392,6 @@
"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",
@@ -1481,16 +1419,13 @@
"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",
@@ -1500,7 +1435,6 @@
"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",
@@ -1587,7 +1521,6 @@
"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,",
@@ -1597,7 +1530,6 @@
"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",
@@ -1628,7 +1560,6 @@
"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",
@@ -1646,12 +1577,10 @@
"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",
@@ -1661,7 +1590,6 @@
"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",
@@ -1727,7 +1655,6 @@
"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",
@@ -1735,7 +1662,6 @@
"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.",
@@ -1818,7 +1744,6 @@
"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,",
@@ -1828,7 +1753,6 @@
"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",
@@ -1890,7 +1814,6 @@
"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,",
@@ -1912,7 +1835,6 @@
"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",

87
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"that stuff hopefully next time. 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",
@@ -1299,12 +1240,10 @@
"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",
@@ -1351,7 +1290,6 @@
"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",
@@ -1362,9 +1300,7 @@
"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.",
@@ -1375,7 +1311,6 @@
"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,",
@@ -1539,7 +1474,6 @@
"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.",
@@ -1555,11 +1489,9 @@
"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.",
@@ -1584,22 +1516,16 @@
"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.",
@@ -1609,7 +1535,6 @@
"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",
@@ -1625,10 +1550,8 @@
"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,",
@@ -1645,7 +1568,6 @@
"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.",
@@ -1688,7 +1610,6 @@
"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",
@@ -1696,7 +1617,6 @@
"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",
@@ -1766,7 +1686,6 @@
"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,",
@@ -1777,7 +1696,6 @@
"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.",
@@ -1792,7 +1710,6 @@
"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.",
@@ -1800,11 +1717,9 @@
"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?",
@@ -1814,7 +1729,6 @@
"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,",
@@ -1825,7 +1739,6 @@
"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.",

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"",
"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",
@@ -1277,12 +1220,10 @@
"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",
@@ -1313,7 +1254,6 @@
"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",
@@ -1323,7 +1263,6 @@
"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.",
@@ -1337,14 +1276,11 @@
"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",
@@ -1386,7 +1322,6 @@
"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",
@@ -1443,9 +1378,7 @@
"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.",
@@ -1499,7 +1432,6 @@
"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",
@@ -1521,16 +1453,13 @@
"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,",
@@ -1545,9 +1474,7 @@
"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",
@@ -1557,7 +1484,6 @@
"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.",
@@ -1588,7 +1514,6 @@
"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.",
@@ -1651,7 +1576,6 @@
"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.",
@@ -1720,7 +1644,6 @@
"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.",
@@ -1739,7 +1662,6 @@
"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.",
@@ -1770,7 +1692,6 @@
"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",
@@ -1780,7 +1701,6 @@
"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",
@@ -1802,7 +1722,6 @@
"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",
@@ -1822,11 +1741,9 @@
"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",
@@ -1885,7 +1802,6 @@
"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",

57
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"Let's get started.",
"",
"Can you hear me back there? Loud and clear.",
"OK. Let's get started.",
"Before I begin, just a couple of announcements.",
@@ -1423,7 +1384,6 @@
"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",
@@ -1457,7 +1417,6 @@
"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",
@@ -1529,7 +1488,6 @@
"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,",
@@ -1608,7 +1566,6 @@
"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",
@@ -1618,7 +1575,6 @@
"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.",
@@ -1628,7 +1584,6 @@
"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.",
@@ -1644,7 +1599,6 @@
"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",
@@ -1663,7 +1617,6 @@
"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",
@@ -1719,7 +1672,6 @@
"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",
@@ -1733,7 +1685,6 @@
"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",
@@ -1757,11 +1708,9 @@
"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",
@@ -1863,7 +1812,6 @@
"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.",
@@ -1884,7 +1832,6 @@
"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",
@@ -1895,7 +1842,6 @@
"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",
@@ -1915,14 +1861,12 @@
"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.",
@@ -1944,7 +1888,6 @@
"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.",

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"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."
]
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"",
"OK. 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",
@@ -1645,7 +1615,6 @@
"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",
@@ -1681,7 +1650,6 @@
"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,",
@@ -1695,7 +1663,6 @@
"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.",
@@ -1769,7 +1736,6 @@
"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",
@@ -1783,7 +1749,6 @@
"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?",
@@ -1811,7 +1776,6 @@
"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",
@@ -1899,7 +1863,6 @@
"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",
@@ -1943,7 +1906,6 @@
"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.",
@@ -2025,7 +1987,6 @@
"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.",
@@ -2045,7 +2006,6 @@
"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,",
@@ -2083,7 +2043,6 @@
"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.",
@@ -2094,7 +2053,6 @@
"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.",

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"",
"All right. 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",
@@ -1514,10 +1484,8 @@
"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.",
@@ -1542,9 +1510,7 @@
"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,",
@@ -1867,7 +1833,6 @@
"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.",
@@ -1883,7 +1848,6 @@
"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",
@@ -1902,7 +1866,6 @@
"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",
@@ -1938,7 +1901,6 @@
"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.",
@@ -1986,7 +1948,6 @@
"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.",
@@ -2050,7 +2011,6 @@
"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,",
@@ -2065,7 +2025,6 @@
"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",
@@ -2086,7 +2045,6 @@
"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,",

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"",
"All right. 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",
@@ -1293,7 +1257,6 @@
"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",
@@ -1326,7 +1289,6 @@
"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.",
@@ -1506,7 +1468,6 @@
"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,",
@@ -1568,10 +1529,8 @@
"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",
@@ -1596,7 +1555,6 @@
"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",
@@ -1606,7 +1564,6 @@
"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",
@@ -1619,7 +1576,6 @@
"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",
@@ -1672,7 +1628,6 @@
"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",
@@ -1762,7 +1717,6 @@
"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",
@@ -1788,7 +1742,6 @@
"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.",
@@ -1840,7 +1793,6 @@
"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.",
@@ -1877,16 +1829,13 @@
"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."
]
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"",
"I will be replacing Professor Agarwal today because he is",
"away. I am one of the recitation",
"instructors for those of you who have not seen me.",
@@ -1108,19 +1061,16 @@
"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.",
@@ -1162,7 +1112,6 @@
"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.",
@@ -1204,7 +1153,6 @@
"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.",
@@ -1223,7 +1171,6 @@
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"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",
@@ -1238,7 +1185,6 @@
"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",
@@ -1254,18 +1200,14 @@
"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.",
@@ -1285,7 +1227,6 @@
"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.",
@@ -1293,7 +1234,6 @@
"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.",
@@ -1303,7 +1243,6 @@
"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.",
@@ -1414,7 +1353,6 @@
"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",
@@ -1463,7 +1401,6 @@
"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.",
@@ -1475,13 +1412,11 @@
"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",
@@ -1490,11 +1425,8 @@
"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",
@@ -1508,7 +1440,6 @@
"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",

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"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,",
@@ -1457,7 +1450,6 @@
"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,",
@@ -1512,7 +1504,6 @@
"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",

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"",
"SPEAKER 1: OK, in the previous segment, we",
"looked at a linear circuit.",
"And you saw that the equations that governed the behavior of",
@@ -363,14 +310,11 @@
"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",
@@ -378,33 +322,27 @@
"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",
@@ -417,7 +355,6 @@
"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.",
@@ -431,13 +368,11 @@
"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",
@@ -446,9 +381,7 @@
"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",
@@ -459,21 +392,16 @@
"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",
@@ -488,26 +416,22 @@
"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.",
@@ -519,7 +443,6 @@
"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.",
@@ -527,7 +450,6 @@
"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.",
""
"with the application of the load method."
]
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"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."
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"text": [
"All right. 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.",
@@ -1408,14 +1389,11 @@
"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",
@@ -1433,7 +1411,6 @@
"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",
@@ -1592,7 +1569,6 @@
"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",
@@ -1622,7 +1598,6 @@
"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",
@@ -1716,7 +1691,6 @@
"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+,",
@@ -1825,7 +1799,6 @@
"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?",

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"",
"All right. 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",
@@ -1397,7 +1345,6 @@
"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",
@@ -1450,22 +1397,18 @@
"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",
@@ -1540,7 +1483,6 @@
"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.",
@@ -1577,9 +1519,7 @@
"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?",
@@ -1616,7 +1556,6 @@
"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",
@@ -1635,7 +1574,6 @@
"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.",
@@ -1675,7 +1613,6 @@
"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",
@@ -1727,7 +1664,6 @@
"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",
@@ -1795,7 +1731,6 @@
"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.",
@@ -1803,7 +1738,6 @@
"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.",
@@ -1825,7 +1759,6 @@
"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?",
@@ -1839,9 +1772,7 @@
"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",
@@ -1864,7 +1795,6 @@
"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.",
@@ -1932,7 +1862,6 @@
"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",
@@ -1953,7 +1882,6 @@
"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.",
@@ -1987,11 +1915,9 @@
"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.",
@@ -2009,7 +1935,6 @@
"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",

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"text": [
"Good morning. 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,",
@@ -1464,11 +1429,9 @@
"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",
@@ -1521,7 +1484,6 @@
"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",
@@ -1658,9 +1620,7 @@
"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",
@@ -1673,7 +1633,6 @@
"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",
@@ -1927,7 +1886,6 @@
"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.",
@@ -1961,7 +1919,6 @@
"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.",
@@ -1984,10 +1941,8 @@
"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.",
@@ -2008,7 +1963,6 @@
"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.",
@@ -2040,7 +1994,6 @@
"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.",
@@ -2064,7 +2017,6 @@
"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",
@@ -2073,7 +2025,6 @@
"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",
@@ -2086,7 +2037,6 @@
"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.",
@@ -2137,7 +2087,6 @@
"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",

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"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."
]
}

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"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.",
@@ -1466,7 +1451,6 @@
"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",
@@ -1490,7 +1474,6 @@
"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.",
@@ -1926,7 +1909,6 @@
"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",
@@ -1984,7 +1966,6 @@
"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,",
@@ -2019,10 +2000,8 @@
"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,",

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"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."
]
}

395
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"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",
@@ -437,9 +405,7 @@
"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.",
@@ -450,20 +416,15 @@
"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,",
@@ -496,13 +457,11 @@
"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.",
@@ -522,12 +481,10 @@
"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",
@@ -551,7 +508,6 @@
"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.",
@@ -566,7 +522,6 @@
"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.",
""
"combination of the various source voltages."
]
}