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added subs for current course.xml

parent 7167950c
Showing with 44 additions and 685 deletions
subs/2SwT6JnfCq8.srt.sjson
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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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"text": [
"",
"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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"and I'm going to show you a similar simple process to do the",
"problem with the light bulb. OK, so take my light bulb",
"again,",
"",
"And I focus on the filament of the light bulb.",
"OK, all I care about is the current flowing through the",
"light bulb. OK, I don't care about whether",
......@@ -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",
......
subs/JB2HgohNHYQ.srt.sjson
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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",
"picture out there, you see the region of the",
"transfer curve that's being articulated.",
......@@ -1700,14 +1683,12 @@
"it's variously called small signal analysis,",
"incremental analysis, small signal method,",
"small signal discipline, whatever you want.",
"",
"OK, this simply says that by boosting and shrinking my",
"signal, I get a response that's more or less linear even when I",
"have a nonlinear device. And this technique is called",
"the small signal approach. So, just to focus on that a",
"little bit longer, switch to page five of your",
"notes and let me draw something out for you.",
"",
"OK, so what I have here, this is my offset VD,",
"and from the VD offset I have my little signal V small d,",
"and the total signal is called V capital D.",
......@@ -1732,7 +1713,6 @@
"total signal I capital D. OK, so that's the small signal",
"method. So, let me summarize that for",
"you.",
"",
"There are three steps to the method.",
"So, first of all, operate at some DC offset.",
"This is also called DC bias, and in that example it's VDID.",
......@@ -1810,7 +1790,6 @@
"good old Taylor's series stuff. OK, the first term is the first",
"derivative of the function times the change.",
"And then, the second one is second derivative.",
"",
"OK, and then I get higher order terms.",
"So this is nothing new here. This is good old Taylor series",
"expansion, and again, let me tell you where I'm",
......@@ -1838,7 +1817,6 @@
"conditions, I can ignore second higher order terms,",
"in which case I am left with this expression here.",
"So let me rewrite this. Let me rewrite this down here.",
"",
"OK, I've just copied this turnout, I've ignored all these",
"terms here, and so I have a more or less equal to sign that",
"remains. So what I'm going to do is when",
......@@ -1871,7 +1849,6 @@
"current ID. And similarly,",
"ID is equal to that component. Delta ID is equal to D,",
"F of --",
"",
"OK, so my incremental change in the output is the first",
"derivative multiplied by the small change in the current.",
"OK, so I'm pretty much done. So, therefore,",
......@@ -1927,7 +1904,6 @@
"Expo Dweeb, and let me just plug in the values.",
"So, ID plus small id. Notice, I'm just shuttling back",
"and forth between the notation delta VD, and small v small d.",
"",
"OK, and so that is given by a e to the BVD, oops,",
"plus, I'm just writing that equation up there.",
"Let me call this equation X. And so, I get the second term",
......
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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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"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",
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......@@ -1457,7 +1450,6 @@
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......@@ -1512,7 +1504,6 @@
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"",
"So at Vo I'm getting this funny behavior.",
"OK, so does anybody want to take the next piece of clues",
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......
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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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"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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"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": [
"",
"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."
]
}
\ No newline at end of file
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