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parent b92ca002
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subs/02jk2f2qWCc.srt.sjson 0 → 100644
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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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"text": [
"PROFESSOR: OK, so i1 is very quickly calculated by taking",
"the difference of V and VTH and dividing that by the sum",
"of the two resistances.",
"So the current i1, flowing in this direction, is given by V",
"minus VTH divided by R1 plus RTH.",
"And there I have it.",
"Notice that by converting the arbitrary network N into the",
"Thevenin equivalent, I turn this into a really trivial",
"problem where I could write down i1 simply by inspection.",
"Finally, before we move off the topic of the Thevenin",
"network and the Thevenin method, it is worthwhile",
"staring at this pattern here comprising the voltage source",
"in series with the resistance and the equation v equals vTH",
"plus RTHi that governs the vi of the Thevenin pattern.",
"So it's worthwhile looking at this graphically as well.",
"So I'm going to show you a little graph here and plot the",
"iv relation for this Thevenin pattern.",
"And usually the way you draw these iv relations is you try",
"to find out an open-circuit voltage.",
"In other words, try to find out of the voltage when the",
"current is 0, so open-circuit voltage when i is 0.",
"So in this case, when i is set to 0 and there's no current,",
"then the open-circuit voltage here is simply",
"vTH so v equals vTH.",
"So in other words, when the current is 0,",
"my voltage is vTH.",
"So I found one point on the iv relation for the Thevenin",
"equivalent pattern.",
"Next, let me find out the short-circuit current.",
"And for the short circuit, v is set to 0.",
"So in this case, I apply a short circuit here, and I'm",
"going to measure the current.",
"So the current in this case, i is given by minus",
"vTH divided by RTH.",
"Notice that because vTH is positive here, the current",
"flows down in this direction and is given by vTH divided by",
"RTH, and that is in a direction opposite to i.",
"And so therefore, I get the minus sign.",
"So my current is given by minus vTH divided by RTH.",
"And so for 0 volts, I get some current here, and that is",
"given by vTH divided by RTH.",
"And so this voltage here is my open-circuit voltage, and this",
"current here is my short-circuit current, OK?",
"So this is my short-circuit current, and that's my",
"open-circuit voltage, and my iv relation is drawn by simply",
"connecting the two points.",
"And the slope of this curve is given by 1 divided by RTH.",
"So here again, to very quickly summarize, I've drawn the iv",
"relation for this definite pattern, which has a vTH in",
"series with an RTH and found two points on the iv relation.",
"One is on the voltage axis, and one is on the current axis",
"by measuring the open-circuit voltage and the short-circuit",
"current, and then drawing a line through them."
]
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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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