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Subs moved to data

parent cdcd8dec
Showing with 2 additions and 3045 deletions
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"text": [
"SPEAKER 1: Before we begin the course, I wanted to cover a",
"few administrative details.",
"First of all, this course does have prerequisites.",
"To do well in the course, you must have a advanced placement",
"or AP-level understanding of electricity and",
"magnetism in physics.",
"And these are at the level of MIT 8.02 course, which you",
"might check out on MIT OpenCourseWare.",
"It's also useful for you to have a basic knowledge of",
"solving simple differential equations.",
"Now, they will cover how to solve some simple equations in",
"this course.",
"But if you come in with a knowledge of solving simple",
"differential equations, that will be extremely helpful.",
"There is a textbook for this course, it is \"Foundations of",
"Analog and Digital Electronic Circuits\" by Agarwal and Lang.",
"You can obtain a copy from Amazon if you like.",
"The book is not required, but certainly useful.",
"We will make available parts of the textbook in an",
"electronic form on our course site as well.",
"I want to draw special attention to some of the",
"underlined readings from this book in your course at a",
"glance handout.",
"This handout tells you what is going to happen",
"weekly in this course.",
"It also tells you week by week what are the readings that we",
"recommend that you do.",
"We really recommend that you at least skim through the",
"material that is assigned as reading.",
"Now, the underlying readings are particularly important, as",
"they stress intuition in how you solve circuits and",
"electronics problems.",
"Now in addition to the various forms of 6.002x material that",
"we will share with you, such as video lectures, interactive",
"exercises, and so on, that we will have several forms of",
"assessment.",
"We will give you weekly homeworks and laboratories.",
"These homeworks and laboratories must be completed",
"by the deadline indicated on the assignment, and we will",
"assign both homeworks and labs each week.",
"Now the video lectures and the exercises and so on are for",
"you to learn the material.",
"Your performance in the course will be assessed",
"using several methods.",
"One is, you will be assessed on homeworks, and those will",
"count for 15% of your grade.",
"And we will have about 10 homeworks.",
"There will be laboratories, again around 10 laboratories,",
"and they also count for 15% of your grade.",
"There will be a mid-term, which will count for 30%, and",
"a final, which will count for 40%.",
"Now, we will give you instructions on how to do the",
"midterm and the final in the course bulletin board that you",
"should be watching constantly.",
"We urge you to collaborate, if you have other friends taking",
"the course, on your lecture videos and on the",
"exercises and so on.",
"And you are also free to, and encouraged to, collaborate in",
"discussing high-level concepts and materials in this course.",
"However, the assessed materials, such as homeworks,",
"labs, midterms and final exams, must be",
"done on your own."
]
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"text": [
"SPEAKER 1: All right.",
"So v1 here is simply the difference between v0 and e1.",
"So v1 is simply v0 minus e1.",
"That's it.",
"What about i1?",
"That is pretty simple, too.",
"i1 is simply v1 divide by r1.",
"And because v1 is v0 minus e1, I can replace v1 by v0 minus",
"e1 and divide by r1.",
"That gives me i1.",
"So in this manner, I can go ahead and find all the vi's",
"and ii's very straightforwardly from the",
"known voltages.",
"So most often when we analyze circuits, we just go ahead and",
"find the e's-- the known voltages--",
"because we know we can very quickly find all the branch",
"voltages and currents.",
"And so, we often stop at the known voltage step."
]
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"text": [
"SPEAKER 1: Well, it turns out that I don't need a variable",
"there because of the trick that I used in picking my",
"ground node.",
"By picking my ground node where it was, notice that the",
"voltage at this node is simply v0, because this node is",
"connected to ground by a voltage source.",
"And so the voltage source would hold the voltage of that",
"node at v0.",
"So I directly have the voltage of that node.",
"So right there I've done my second step.",
"So that's my step two of node analysis.",
"So let's move on and start off with step",
"three of node analysis.",
"All right?",
"Step three would be to write KCL for the nodes-- on each of",
"the nodes-- e1 and e2 here, which are my unknowns.",
"I'm going to write KCL for these nodes, and I am going to",
"substitute device laws and KVL in dividing the current that",
"leaves those nodes.",
"But also remember that as I work with currents, and sum",
"the currents for KCL, I'll simply use my usual",
"convention, which is sum the currents leaving a node always",
"so I don't make mistakes.",
"Now again, for another piece of convenience, I'm going to",
"use conductances.",
"So the variable I have is resistance.",
"1 by that resistance is the conductance, since I would",
"just use that to make my algebra a little simpler.",
"So let's get started.",
"Let's start with node e1.",
"And I'm going to write KCL at node e1.",
"Now, with KCL, notice that I'm going to follow my usual",
"convention to avoid mistakes.",
"I'm going to add up the currents that leave a node so",
"that I don't make mistakes.",
"So let's go ahead and start.",
"Let me start with KCL at e1.",
"So if you look at e1, what is the current that is going up",
"in that direction?",
"I know the node voltage here is e1.",
"I know the voltage of this node is v0.",
"So can you tell me what the current is going up?",
"Let me pause for a second so that you can think about it.",
"And then I'll go back and do it for you."
]
}
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"text": [
"SPEAKER 1: 6.002x is an extraordinarily fun course.",
"This course is the first course in an EE or an EECS",
"curriculum at MIT.",
"This course will help you make the big jump",
"from physics to EECS.",
"You will learn, what, all kinds of fun",
"things in this course.",
"So, for example, you will learn what's behind this.",
"What's behind the iPhone.",
"What are some of the foundational technologies and",
"cool ideas that drive this and many other fun",
"things in our lives?",
"Very useful things in our lives as well, that have",
"really been able to improve the productivity of all of",
"humankind over the past many, many decades.",
"This course also forms the foundations of",
"devices like this.",
"This is a chip photo of Intel's 22",
"nanometer multicore processor.",
"And you will learn about some basic technologies that are",
"used in building devices such as this as well."
]
}
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"text": [
"SPEAKER 1: Our third method is going to be the node method.",
"This method is going to be the most important method that we",
"learn, and you can apply it to all the circuits that you're",
"going to see.",
"This method is going to be a very specific application of",
"the KVL/KCL method.",
"This method has five steps.",
"The first step would be you go and select a reference node--",
"we call that a ground node--",
"represented by an inverted T symbol.",
"And you're going to measure all our voltages with",
"reference to this ground node.",
"The second step.",
"We label all the voltages of the remaining nodes with",
"respect to ground.",
"And these will be our primary unknowns.",
"As a third step, we will write KCL for all the nodes, leading",
"out the ground node.",
"And while writing KCL, we will apply a cool trick.",
"So KCL involves currents.",
"But notice that your primary variables",
"are your node voltages.",
"But KCL involves current, so what we will do is in step",
"three, we will derive the current, in terms of the node",
"voltages, and directly apply the element relationship",
"without actually having to write down",
"any specific current.",
"Then we go and solve for the node",
"voltages as our step four.",
"And finally, we go and back solve for the branch voltages",
"and branch currents.",
"Notice that for circuit analysis, our goal is to find",
"branch voltages and currents, and so to the extent that you",
"need to know all the branch voltages and currents, you can",
"go ahead and find them.",
"The node analysis method is the workhorse of our industry",
"and the workhorse of 6.002x.",
"And so you will be using it all over the place.",
"It's a very, very important method.",
"Let's get started.",
"And for this method, I'm going to use our",
"old faithful circuit.",
"For fun, I'm going to add a extra current source, I1, to",
"our circuit.",
"Notice that we now have seven elements in the circuit.",
"And with seven elements, the number of equations is going",
"to be completely unwieldy.",
"And so you will notice that with the node method, you will",
"be amazed that at the end, we will have to",
"solve only two equations.",
"Watch and see.",
"So as the first step of the node method, I have to select",
"the ground node.",
"Now, in general, you can select any node as the ground,",
"because voltages are always measured with",
"respect to a point.",
"There are differences in potentials between a pair of",
"points, so you can select any node as the ground.",
"But in general, to simplify our lives, I'd recommend using",
"a couple of rules to pick a ground node to",
"simplify the analysis.",
"The first thing to do is to find a node which has the",
"largest number of edges coming to it.",
"And in our circuit here, this node here, which connects R to",
"R5, and the current and voltage sources has the",
"largest number of edges.",
"So that seemed like a good candidate.",
"A second thing you can look at is look for a node that has",
"many of the sources connected to it.",
"And in this case, it does happen that the same node has",
"the voltage source also connected",
"to it with one terminal.",
"So let me go ahead and pick that as my ground node.",
"So let me go ahead and mark that as my ground node.",
"This will be my ground, and I mark it",
"with my ground terminal.",
"So this is step one.",
"Now, let's apply step two.",
"Step two will be label node voltages with respect to the",
"ground node.",
"So what are my nodes?",
"So I have a node here.",
"That's one node.",
"Let me label the node voltage with respect to ground as E1.",
"So if I take this as my ground voltage and",
"take that as a zero--",
"so the voltage at this node here is going to be E1 with",
"respect to the ground.",
"Let me pick this node here as E2 with respect to ground.",
"Finally, I have a third node here.",
"And what can you say about the voltage at that node?",
"Let me pause for a second while you think about it, and",
"then I will continue.",
"So what do you think the voltage is at that node?",
"Do I need a variable there?"
]
}
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"text": [
"SPEAKER 1: OK, so this is case the V-I relationship is V",
"equals capital V. In this is it's a constant and so the",
"relationship is given by this where V is a constant at",
"capital V volts in respect to the current that is flowing",
"through the element.",
"So here are examples of a couple of elements and their",
"I-V relation."
]
}
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"text": [
"PROFESSOR: In the previous segment, we looked at the",
"Thevenin method, which applied to linear circuits.",
"And in that method, I could take an arbitrary network, n,",
"containing a whole bunch of sources and resistors where",
"the current sources are voltage sources.",
"And I could replace that with its Thevenin equivalent, where",
"the Thevenin equivalent pattern was given by a voltage",
"source VTH.",
"in series with the resistance RTH.",
"Now one of the things that I want you to think about in",
"circuits is that whenever you have circuits containing",
"voltages and properties involving voltages, you can",
"immediately think of complimentary properties",
"involving current sources.",
"So much as I was able to replace an arbitrary network n",
"with its Thevenin equivalent, you can think about replacing",
"the arbitrary network n with some pattern involving a",
"current source.",
"And indeed, that method where you replace an arbitrary",
"network with a pattern involving a current source is",
"called the Norton method.",
"So in the Norton method, what we do is we are able to",
"replace an arbitrary network n with its Norton equivalent,",
"where the Norton equivalent contains the current source IN",
"in parallel with the resistance RTH.",
"The current source in parallel with RTH is a Norton pattern,",
"and you should contrast it with the corresponding",
"Thevenin pattern.",
"So a voltage source in series with a resistor is a Thevenin",
"pattern, and a current source in parallel with the",
"resistance is the Norton pattern.",
"So in the case of the Norton pattern, which contains the",
"current source IN and the Norton resistance RN, in the",
"same manner that you defined the Thevenin equivalent, we",
"can derive the Norton equivalent.",
"So to obtain the current IN, what you do is you obtain the",
"short circuit current seen at the port.",
"So recall for the Thevenin method, I open-circuited the",
"port here, and measured the voltage, and that was my VTH.",
"So the Norton method, what I do is I short circuit this",
"port and measure the current I. That current is IN, or the",
"Norton current.",
"And then I can get a Norton resistance RN--",
"oh, I should say RN here-- the Norton resistance RN, which,",
"incidentally, is identical to the Thevenin resistance RTH.",
"I can get that in the same manner as I got RTH, which is",
"I shut off all the independent voltage sources and current",
"sources and simply take the resistance measure at the",
"port, of course, without the short.",
"I go ahead and measure the resistance seen at the port",
"with all the voltages and currents turned off.",
"OK?",
"That would be my Norton resistance, RN.",
"So again, we stated this pattern, a current source IN",
"parallel to a Norton resistance RN, where this",
"corresponds to the Thevenin equivalent, where I have VTH",
"and RTH in series.",
"So the Norton is the dual of the Thevenin.",
"OK?",
"Where the Thevenin is the voltage in series with the",
"resistance, and its dual is the Norton equivalent, which",
"is the current source in parallel with resistance.",
"An immediate question that comes to mind is how are the",
"Thevenin and Norton equivalents",
"related to each other?",
"After all, they are the duals of one another.",
"And so notice the Thevenin equivalent on the left-hand",
"side and the Norton equivalent on the right-hand side.",
"The resistances RTH and the Norton",
"resistance RN are equal.",
"And then we can also relate the Norton current IN and the",
"Thevenin voltage as follows.",
"IN is VTH divided by RTH.",
"And so if you take the Thevenin voltage and divide",
"that by the Thevenin resistance, you get the Norton",
"current, IN.",
"So this very quickly shows you how you can go from the Norton",
"to the Thevenin.",
"One question I am often asked is when do I use the Thevenin",
"method and when do I use the Norton method?",
"Well, you know, that comes from experience.",
"Like you look at circuits in one of our earlier examples",
"where the external network contained a voltage source in",
"series with a resistance, it made sense to take the rest of",
"the network and turn that into Thevenin equivalent.",
"However, if I have a basic circuit containing a current",
"source and a resistance in parallel, then it might be",
"easier to take my external network and convert that into",
"a Norton equivalent.",
"So, really, when you want to get things in",
"parallel, think Norton.",
"When you want to get things in series to simplify analysis,",
"think Thevenin."
]
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"text": [
"SPEAKER 1: So I want to show you a simple circuit that",
"looks like this.",
"And let's go ahead and measure some voltages and currents.",
"In terms of terminology, remember",
"this is called a loop.",
"So if I start from the point C, and I travel through the",
"voltage source, come to the node A, down through R1 and",
"all the way down through R2 back to C, that's a loop.",
"Similarly, this point A is a node where the register R1,",
"the voltage source V0 and R4 are connected.",
"Just make sure your terminology is correct.",
"So what I'll do is let me make some quick measurements for",
"you, and show you that these KVL and KCL are indeed true.",
"So the circuit's up there.",
"So let me take some measurements.",
"And why don't you write down what I measure on the board.",
"Let me borrow another piece of chalk here.",
"What I'll do is focus on this loop here and focus on this",
"node and make some measurements.",
"So you see the circuit up there.",
"[INAUDIBLE]",
"So I get three volts for the voltage from C to A. So why",
"don't you write down three volts.",
"OK, so the next one is minus 1.6.",
"And so that will be I'm doing AB, VAB.",
"And then let me do the last one.",
"And it is minus 1.37.",
"Within the bonds of experimental error, notice",
"that if I add up these three voltages, they",
"nicely sum up to zero.",
"OK, next let me focus on this node here.",
"And at this node, let me go ahead and",
"measure some currents.",
"What I'll do now is change to an AC voltage so that I can go",
"ahead and measure the current without breaking my circuit.",
"This time around, you'll get to see the measurements that",
"I'm taking as well.",
"What I have here is three wires that I have pulled out",
"from D. And this is the node D. So three wires coming into",
"the node D just to make it a little bit easier for me to",
"measure stuff.",
"So everybody keep your fingers crossed so I don't",
"look like a fool here.",
"Hope this works out.",
"So it's about 10 millivolts peak to peak out there.",
"Let's say that if the wave form rises on the left hand",
"side, it's positive.",
"So it's positive 10 millivolts.",
"And another positive 10 millivolts.",
"So that's 20 millivolts.",
"And this time it's a negative, roughly 20, I",
"guess, negative 20.",
"So I'm getting, in terms of currents, I have a positive",
"10, a positive 10 and a negative 20 that adds up to 0.",
"But more interestingly, I can show you the same thing by",
"holding this current measuring probe",
"directly across that node.",
"And notice that the net current that is entering into",
"this node here is zero.",
"So that should just show you that KCL does indeed hold in",
"practice, and it is not just a figment of our imaginations."
]
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"text": [
"All right, this is the sub circuit.",
"And what I've done here is I've have to turn the current",
"source off.",
"So notice that out here, I create an open circuit.",
"And that is the result of my current source",
"being turned off.",
"And this is my usual ground note.",
"And let me call this node voltage, with the voltage",
"source acting alone, as ev. So ev is the partial response of",
"the circuit to the voltage source acting alone.",
"Now how do we go about solving for ev?",
"Notice that we have a known pattern here.",
"We have a voltage source connected to a pair of",
"registers, R1 and R2.",
"And ev is simply the voltage across R2.",
"Now, this is a known pattern.",
"So one thing you should keep in mind is that in circuits,",
"and electronics, we use patterns a lot.",
"Whenever we see a pattern, we can directly go and write down",
"what the output response is going to look like.",
"What I'm going to do is throughout this course, as we",
"see more and more patterns, I'm going to alert you to",
"these patterns.",
"So right here is a voltage divider pattern.",
"So for the voltage divider pattern, I can write down ev.",
"I can write down ev as being some fraction of the source",
"voltage v. And by the divider action, we simply R2 divide by",
"R1 plus R2.",
"So it is simply the voltage across R2, and that is given",
"by R2 divided by R1 plus R2.",
"And this is a known pattern that you'll find very helpful",
"as you analyze circuits very quickly.",
"Next, let's look at I acting alone.",
"Before we do that, what do we have so far?",
"Again, recall, this is the circuit",
"we're trying to analyze.",
"We are trying to get the voltage e.",
"And so far, we have computed the partial voltage ev, due to",
"the voltage source acting alone.",
"As a next step-- again, this is still step one of the",
"superposition method--",
"let's look at the partial response of the circuit due to",
"the current acting alone.",
"To get the response for the current acting alone, I need",
"to build a circuit in which the voltage",
"source is turned off.",
"I'll let you think for a couple of seconds as to what",
"the circuit will look like before I draw it out for you."
]
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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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"text": [
"SPEAKER 1: All right, so to do KCL at e2, let's start with",
"the current leaving this node.",
"Remember, my usual habit is to sum the",
"nodes leaving the node.",
"So the current heading in this direction will be e2 minus e1",
"divided by R3.",
"So current going left from that node will be e2 minus e1",
"divided by R3 or multiplied by G3.",
"Then the current going up will be e2 minus V0 times G4.",
"And the current leaving the node and going down",
"will be e2 times G5.",
"Have I missed anything?",
"Aha, there is a current here that's coming into the node.",
"And so therefore, the current leaving the mode is minus I1.",
"And all of that sums up to zero.",
"There you have it.",
"So I've written KCL for the two nodes.",
"And I've substituted the device laws as I've been",
"writing it so I don't have this",
"intermediate current variable.",
"So just stare at the beauty of this.",
"Notice that I have two equations, one and two, and I",
"have two variables, e1 and e2, two unknowns and two equations",
"and that's it.",
"OK, so let me go on to step four of the node method.",
"The step four of the node method is simply to go ahead",
"and solve for the node voltages, e1 and e2.",
"So I have my two equations which reflect the KCL at node",
"e1 and KCL at e2.",
"So now it's simply juggling it on with some math and trying",
"to collect all the coefficients of e1 and those",
"of e2, collect them all and just write",
"them a little cleanly.",
"So let me move all the constant terms to the",
"right-hand side.",
"And I will move the variables, or the unknowns, to the",
"left-hand hand side.",
"So let me start with e1.",
"So notice that e1, I multiplied by G1, so",
"I write that down.",
"Multiply by G3, so I write that down.",
"And multiply by G2, so I write that down too.",
"So I get e1 times G1 plus G3 plus G2.",
"And then I collect the terms in e2.",
"And there's only one here, which is minus G3.",
"And the constant terms are here, V0 G1.",
"And I'm going to move that to the right-hand side and write",
"that down as V0 G1.",
"For the next set of steps, I go ahead and do e1 for the",
"next equation.",
"I get minus G3.",
"And then for e2, I go ahead and get a G5, and I get a G4,",
"and I get a G3.",
"So it's G3, G4, and a G5.",
"And I can move the constant terms, which is V0 G4, and I",
"want the right-hand side.",
"And in this case, they both become positive as they move",
"to the right.",
"And I get a I1 here.",
"Good, there you go.",
"So I end up with two equations and two unknowns.",
"And notice I have by e1 times something plus e2 times",
"something equals a constant.",
"And then again, that e1 times something plus e2 times",
"something is another constant.",
"So I two equations and two unknowns.",
"And see how remarkably simple this is.",
"This is basic high school math to solve a pair of",
"simultaneous equations in order to get the answer.",
"And just to be a complete here, let me go ahead and",
"complete it for you.",
"So supposing in step four number four you've gone and",
"solved for the node method, and by solving the node method",
"you get the values of e1 and e2.",
"So let's say you've gone and solved the simultaneous",
"equations for step four and you have e1 and e2.",
"Then, to complete your circuit analysis you need to find the",
"branch voltages.",
"And so you can go ahead and find all the v-i's and i-i's.",
"So in this case, one of my branch voltages is v1 i1.",
"So I just do a couple of quick examples just to show you that",
"it's pretty simple.",
"So what is v1 here?",
"Well let me pause and have you do it."
]
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"SPEAKER 1: OK, let's now work on the second method of",
"circuit analysis.",
"This is actually a very simple method.",
"And oftentimes when you're applying some of the more",
"sophisticated methods, it is helpful to apply these methods",
"as some of the partial steps.",
"You can find more about this method and the KVL KCL method",
"in chapter two of the textbook.",
"So this method is very simple.",
"If you have a set of resistors in series, R1 through RN, then",
"you can write up an equivalent resistor whose resistance is",
"equal to the sum of the individual resistances.",
"Now you can also do a complimentary circuit.",
"You can make a set of conductances.",
"Notice that G is our nomenclature for conductance.",
"So G1, for example, is 1 divided by R1 and so on, so",
"G's a conductance.",
"So when I have a set of conductances in parallel, then",
"I can add them all up and replace them with a resulting",
"conductance given by G1 plus G2 plus G3 dot dot dot GN,",
"where G1 equals 1 by RI is a conductance.",
"Another simple thing to remember is when you have two",
"resistances in parallel, let's say R1 and R2, the equivalent",
"resistance is given by R1 R2 divide by R1 plus R2.",
"This is just a special case for two resistors.",
"Let's continue one with element combinations rules.",
"In case C is when I have two voltage sources in parallel.",
"Let's call them V1 and V2.",
"Then I can replace them with a single voltage source whose",
"voltage is given by V1 plus V2.",
"I can get the current based circuit in a similar manner.",
"So let's say I have two current sources in parallel,",
"I1 in parallel with I2.",
"Then I can replace them with a single current source whose",
"current is I1 plus I2.",
"In this example, I would like to use element combination",
"rules to solve for the following situation.",
"So I have a little circuit here with a voltage source of",
"three resistors.",
"And let's say I care about finding the current I through",
"that branch.",
"So how do I go about doing it?",
"So let's start applying element competition rules.",
"As a first step, let me combine these two resistances.",
"And so I get the same voltage source, my resistance R1 here.",
"But in place of R2 and R3, I get the combination of",
"resistors given by R2 R3 3 divide by R2 plus R3.",
"Now as soon as I get that, I now have two resistances in",
"series, so I can sum them up very quickly like so.",
"And I can get a single resistance here, R, which is",
"the sum of R1 plus R2 R3 divide by R2 plus R3.",
"So now notice that this was my current that I needed to find.",
"And I was the current I needed to find.",
"So I brought this down to a very simple pattern.",
"And so I can very quickly write I is simply given by V",
"divided by R.",
"Now the textbook in this particular section gives you a",
"lot more interesting examples of how you can use intuitive",
"analysis to analyze many, many circuits like this.",
"And I would encourage you to go and read that section",
"that's part of section two."
]
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"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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"SPEAKER 1: In this sequence, are going to look at a whole",
"bunch of techniques for analyzing circuits.",
"Think of these as your tool chest. So you are embarking on",
"6.002 and going on to build lots of useful electronic",
"systems.",
"But before we go and build these systems, much like a",
"carpenter who needs to go build a house, much like a",
"carpenter has to go and buy a set of tools from the local",
"store, we need to go and make sure that you have the tools",
"in your tool chest to analyze these circuits.",
"This tool chest will include things like the KVL KCL",
"method, the Node method and so on.",
"But before I begin talking about these techniques for",
"your tool chest, I'd like to do a extremely quick review--",
"as is my usual practice--",
"of what you've covered so far.",
"So remember our EECS playground.",
"We've gotten into this place by promising that we are going",
"to observe the lumped matter discipline.",
"By observing the discipline recall that the complexities",
"of Maxwell's equations and the differential equations that",
"you have to solve-- the partial differential",
"equations-- goes away.",
"And you're left with very simple linear equations.",
"And you will see a lot of that today.",
"As you make the lumped matter discipline, you end up with",
"these lumped elements, like resistors and voltage",
"sources and so on.",
"And what you do with these lumped elements is we can",
"label what are called the branch variables or the",
"terminal variables for these lumped elements, OK?",
"So for example, v is the voltage across the element.",
"And i is the current through the element.",
"The power consumed by the element is given by vi.",
"Continuing with our review, the lumped matter discipline",
"enables us to create the lumped circuit abstraction.",
"So you take these lumped elements and you connect them",
"with ideal wires.",
"So in this case, I have a resistor which is a lumped",
"element, a voltage source.",
"And I connect them with these ideal wires.",
"And what you end up with is called a lumped circuit.",
"But this is your lumped circuit abstraction.",
"Well as we made the transition from physics to EECS by",
"adhering to the lumped matter discipline.",
"I had discussed in the last sequence that Maxwell's",
"equations turn into very simple algebraic equations.",
"And these are captured by Kirchoff's voltage and current",
"laws, called KVL and KCL.",
"So KVL says that for all loops in your circuit, the sum of",
"the voltages around the loops add up to zero.",
"Similarly for all the nodes in the circuit, the currents that",
"enter into a node add up to zero.",
"And in the same matter, if I just summed the currents",
"leaving a node, they also add up to zero.",
"So whether you sum the currents entering the node or",
"currents leaving a node, they would add up to zero by KCL.",
"And the beauty of this was by adhering to lump matter",
"discipline, recall the complexities Maxwell's",
"equations whether an integral form or",
"differential form went away.",
"And we were now left with extremely simple algebraic",
"expressions of the sort.",
"And you will see shortly that you will end up solving",
"extremely simple linear equations",
"as we analyze circuits.",
"So as one example here is a linear circuit.",
"It has one, two, three, four, five, six elements.",
"It's got a voltage source of a voltage v zero.",
"It's got a resistor, r one and so on and so forth.",
"So for this circuit according to our abstraction and the",
"laws of KVL and KCL, the following",
"are going to be true.",
"So for instance if I look at node a, then according to KCL,",
"the currents entering the node must be zero.",
"So in other words, the current here is ica.",
"And I can sum to that the current",
"entering from the d direction.",
"So that would be plus ida.",
"And then there is a current from the ba direction and iba.",
"Those are going to sum to zero.",
"Now I can multiply the whole thing by minus 1.",
"And that would give me the sum of the currents leaving the",
"node are also going to be zero.",
"So that is KCL.",
"Now I can also write KVL in this case for this loop, for",
"instance, here.",
"For this loop I can add up the voltages around the loop.",
"And by KVL they must add up to zero.",
"So for example if I look at the voltage vca, I can add",
"that to the next voltage here.",
"That is to vab and then add that to the",
"final voltage, vbc.",
"And by KCL--",
"so all of those must add up to be zero.",
"Now if you go back to our circuit here that you see on",
"the left hand side, I am going to show you a little demo that",
"will look at these currents, ica, ida, and iba, and also",
"look at the voltages, vcabab and bbc and actually go and",
"look at the circuit, make the measurements, and show that",
"they indeed sum up to zero.",
"Not surprising.",
"KVL and KCL really work.",
"And so the demo should also work.",
"OK.",
"So let's go and do our demo."
]
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"SPEAKER 1: OK, we are ready to begin.",
"So, as I said earlier, 6.002x will represent a big jump from",
"physics to EECS.",
"And let's just dive right into it and take a look at an",
"example of the kind of problems that we",
"might want to solve.",
"So, suppose I have a battery here that supplies the",
"voltage, v. And I connect that to a light bulb.",
"And let's say that I wish to find out the current, I, that",
"will flow through the bulb as a result of connecting the",
"light bulb to the battery.",
"Now, I don't want to find out anything else.",
"All I want to know is, what is the current through the bulb?",
"Oh, I want to remind you that as I go through various parts",
"of the course, I will point to readings in the textbook.",
"And for this material in this set of segments, you will skim",
"chapter one of your textbook.",
"The readings are also indicated in your course at a",
"glance handout.",
"So with the kind of problem we want to solve, with a battery",
"connected to a light bulb, I want to find out what is the",
"current, I, through the bulb.",
"OK.",
"So, here's my problem.",
"Now, I could do it the hard way.",
"As I've said before, we have captured the way nature is",
"through sets of equations.",
"In particular, those that relate to 6002",
"are Maxwell's equations.",
"So I'll parade a bunch of equations in front of you, and",
"don't get scared here.",
"This is the hard way.",
"This is not how we're going to do it in 6.002x.",
"I just want to show you how exciting and fun 6002 is, and",
"how simple things are.",
"But let me start by showing you how we could do it if we",
"were crazy.",
"OK, so I showed you Maxwell's equations in differential form",
"or in integral form.",
"So for example, this is Faraday's equation--",
"del cross E is minus del B by del t.",
"In integral form, it is integral E dot dl is minus del",
"phi B by del t, and so on and so forth.",
"Now I could take Maxwell's equations, and of course, you",
"can go and solve all of them somehow.",
"It would be horrendously hard.",
"But normally this is not what we do in 6002, and not what we",
"do as EECS engineers.",
"Instead, there is a much, much easier way.",
"We are going to make our life extraordinarily simple.",
"So before I show you what that method is, let me help us",
"build some insight.",
"So let's do it by analogy.",
"So supposing I have an object, and suppose I apply some",
"force, F, to the object.",
"And my question to you is, what is the acceleration of",
"the object?",
"OK, so if I ask you this simple question--",
"I have an object, and I apply a force, F, to the object, and",
"I ask you, what is the acceleration of the object?",
"I don't tell you anything else.",
"All right?",
"No more data.",
"I want you to think about how you might solve this problem.",
"What sort of questions would you ask me?",
"How would you answer this problem?",
"Let me pause here for a couple of seconds, and give you some",
"time to think about the answer before I proceed."
]
}
\ No newline at end of file
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