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fischerl
2012-01-20 16:18:57 -05:00
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"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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"ANANT AGARWAL: So let me give you an example of a bunch of",
"interesting lumped elements and then show you a couple of",
"really nasty lumped elements.",
"LORENZO: I'm going to switch to the other one.",
"I made a mistake.",
"ANANT AGARWAL: So what you see out here, so we characterize",
"lumped elements by the vi characteristics, OK?",
"You apply a voltage, measure the current, So what I can do",
"is I can plot i here and v here and see",
"what it looks like.",
"I can characterize elements by their vi relationship, and",
"there are a bunch of elements that I can create based on the",
"vi relationship.",
"So let me show you a few examples.",
"So for the resistor, since v is directly proportional to i,",
"and r is the constant, I get a straight line.",
"That's the i-axis, the v-axis, and this is a resistor.",
"What I actually have is a variable resistor, so I'm",
"going to change the resistance value r, and the curve will",
"also change slope.",
"I change the value r because it's a variable resistor, and",
"it changes slope because my r is different.",
"Next, let me go to--",
"LORENZO: Fixed.",
"ANANT AGARWAL: --a fixed resistor, and this guy here on",
"the screen to your left, I guess, is a fixed resistor.",
"And you see that its iv characteristic is a line of a",
"given slope, 1 by r, and that's it.",
"I can't change it.",
"Number three, I have another lumped element, called a Zener",
"diode, that you will see in the fourth week of this class.",
"And the characteristics for the Zener",
"diode look like this--",
"i, v. If my voltage goes across, that Zener diode goes",
"up slightly, the current shoots up.",
"But if the voltage becomes negative, I don't have any",
"current flowing through it until the voltage passes some",
"threshold, at which point my current begins to build up.",
"So you can increase voltage a little bit, and you can show",
"that the current starts building up again.",
"So that's another interesting lumped element",
"called a Zener diode.",
"Let's switch to the next one called a diode.",
"So a diode looks like this--",
"i, v. If the voltage across the diode becomes positive,",
"around 0.6 volts or thereabout, the current begins",
"to shoot up.",
"But if the voltage is below that threshold of 0.6, then my",
"current is almost zero.",
"It's another lumped element called a diode.",
"And you will begin using these elements in your 002 lives to",
"build interesting systems.",
"Next example is a thermistor.",
"A thermistor is a resistor whose resistance varies with",
"temperature, OK?",
"So this is a very expensive little drier, hair drier.",
"And what I'm going to do is blow some hot air at my",
"resistor, and you're going to see that its value is going to",
"change depending on how much I heat it.",
"As it cools down--",
"let me cool it down.",
"So you can see it's coming down.",
"I can zap it again.",
"[TURNS ON DRYER]",
"ANANT AGARWAL: I could do this all day.",
"This is so much fun.",
"[LAUGHTER]",
"ANANT AGARWAL: OK, so that's a another",
"interesting lumped element.",
"As the temperature rises, its resistance changes.",
"LORENZO: Photo.",
"ANANT AGARWAL: Next thing is called a photoresistor.",
"It's a resistor.",
"It used to be a resistor, Lorenzo?",
"LORENZO: Yeah.",
"OK, that's fine.",
"ANANT AGARWAL: So this is a photoresistor.",
"And notice that it almost behaves like an open circuit.",
"Well, what I'm going to do is shine some light on it.",
"When I shine light on it, it begins to conduct and becomes",
"a resistor of some value.",
"There you go, OK?",
"So that's a photoresistor.",
"LORENZO: Now, we go to the--",
"ANANT AGARWAL: So now I'm going to show you a battery.",
"Notice, we didn't talk about batteries before.",
"I'll show you a battery.",
"So before we show a battery, just think in your own minds,",
"what should the iv characteristic of a",
"battery look like?",
"i, v, a battery supplies a constant voltage.",
"You know, your little cell, your double A",
"battery, 1.5 volts?",
"So think about what the iv characteristic of a battery",
"should look like for three seconds before",
"I show it to you.",
"And so I show it, Lorenzo.",
"It's a straight line.",
"This is a good battery.",
"It's a straight vertical line, which says that the voltage is",
"1.5 volts or thereabouts no matter",
"what current it supplies.",
"As an ideal voltage source, it as a fixed voltage v no matter",
"what the current going through it is.",
"Now I'll show you a dud, a bad battery.",
"And this is what the bad battery looks like.",
"So many of you had a your car batteries die on you, and when",
"you go to the store, they check your batteries.",
"They use exactly this principle, that dead batteries",
"have resistance.",
"Whenever you see slopes here, you're thinking of resistance,",
"They can use this property to figure out that",
"your battery is dead.",
"So that's a dead battery.",
"And finally, let me show you a bulb.",
"We started with a bulb, and so I need to end--",
"OK.",
"We started with a bulb, so we need to end with a bulb.",
"And what you'll see is that a bulb is simply--",
"behaves like a resistor.",
"It's iv curve is going to look like this.",
"OK, notice, this is my bulb, and guess what?",
"It behaves like a resistor.",
"It's a very interesting kind of resistor.",
"So I won't go into details for now, but notice its iv",
"characteristic behaves like a resistor, OK?",
"So those are some pretty standard lumped elements.",
"You'll deal with a lot more set of lumped elements--",
"switches, MOFETs, capacitors, inductors, a bunch",
"of other fun stuff.",
"But before we do that, what I wanted to tell you is that",
"don't go berserk on this abstraction binge, OK?",
"Too much of anything is bad for you.",
"So what I'm going to show you is abstractions or models are",
"only valid provided you work within a set of constraints.",
"Notice, we've already had this tacit handshake, which said",
"that we'll follow the discipline, OK?",
"Even after we follow the discipline, there are ranges",
"to how well physical elements can behave like",
"ideal lumped elements.",
"For example, what I'm going to do is show you as a resistor.",
"And it's going to look like a resistor, and I'm going to",
"keep the voltage around it.",
"What's going to happen at some point?",
"I just keep doing that.",
"If it's an ideal element, if you're a theorist, you'll say,",
"oh yeah, the curve will keep extending",
"until I reach infinity.",
"But this is a practical resistor, so, you know.",
"The people out here, you're going to have to cover your",
"eyes or something.",
"So your abstraction can predict that.",
"It says the current is an amp.",
"It can predict the heat, light, or the smell.",
"Because in the laboratory, when you get the smell, you",
"know what somebody has just done.",
"They blown the resistor.",
"So that's one example of a lumped",
"abstraction breaking down.",
"So if I really believe in my own BS, anything's a lumped",
"element, so here's a pickle.",
"[LAUGHTER]",
"ANANT AGARWAL: A pickle's a lumped element.",
"I can treat it as a lumped resistor.",
"But this is a very interesting lumped resistor.",
"[LAUGHTER]",
"ANANT AGARWAL: Don't try this at home.",
"This is a standard pickle into which we are",
"pumping 110 volts AC.",
"[LAUGHTER]",
"ANANT AGARWAL: I promise you, this is a standard pickle.",
"So as you can tell, it has a fixed resistance, but your",
"lumped abstraction cannot predict the nice light and",
"sound effect.",
"[LAUGHTER]"
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"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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"SPEAKER 1: OK.",
"So let me proceed here.",
"I've applied a force, F. And I have asked you the question,",
"what is the acceleration?",
"OK?",
"Now, the answer here is pretty simple.",
"What you would do, given that you've taken physics,",
"mechanics, and so on, you would very quickly ask me what",
"is the mass of the object, m.",
"And I would very quickly tell you the mass of",
"the object is m.",
"And then, you would very quickly respond that the",
"acceleration is given by the force divided by the mass of",
"the object.",
"Gives you the acceleration.",
"So that was pretty simple.",
"So you asked me for m.",
"I tell you what m is.",
"You respond a equals F divided by m.",
"And you are done.",
"OK?",
"That was pretty simple.",
"It wasn't hard at all.",
"Now, why wasn't that hard?",
"It wasn't hard because, in trying to figure out the",
"acceleration of the object, you just asked me for the",
"mass, m, of the object.",
"You ignored a whole bunch of other",
"properties of the object.",
"You ignore its shape, its temperature, its color, where",
"did I apply the force, how it smelled, and",
"so on and so forth.",
"This kind of simplification where you took an object and",
"you assumed that the object had a mass acting at that",
"point and the force was applied at that point is",
"called point-mass discretization or point-mass",
"simplification.",
"And by making the point-mass simplification, you were able",
"to tremendously simplify how you solved the problem.",
"And in doing so, you were able to get the acceleration very,",
"very quickly.",
"OK.",
"So with this little piece of insight, let us go back to our",
"light bulb example and see how we can find the current",
"through the light bulb through the filament and by an",
"application of a [? voltage read ?]",
"and somehow take inspiration from the point-mass",
"discretization that we did in physics.",
"So let's data the bulb for a second here.",
"In this bulb, we really don't care about exactly how the",
"current flows inside the filament.",
"We don't care about its temperature, its shape, its",
"orientation.",
"We just don't get about a lot of things.",
"All I care about is what is the current through the bulb.",
"So to do so, much like we did the point-mass discretization,",
"what we're going to do is replace the bulb with a",
"discrete resistor.",
"We will replace the bulb with a discrete resistor for the",
"simple purpose of calculating the current.",
"And using this very simple model, this very simple",
"simplification, I'm not going to be able to tell you what",
"its temperature is or what its shape is and so on, but I will",
"be able to tell you what its current is.",
"So let's proceed with this simplification and continue",
"down the easy path.",
"So as I said, we'll replace the bulb with a discrete",
"resistor for the purpose of computing the current.",
"And so, let me draw a little picture.",
"So here's my representation for the battery.",
"And what I'm going to do is here are my two points, A and",
"B, representing the two terminals of the bulb.",
"And I'm going to replace the bulb and model it as a",
"resistor with resistance, R. There's going to be some",
"voltage, V, across the resistor.",
"And my goal, as I said earlier, was to figure out the",
"current, I.",
"So what I've done is I've replaced the bulb here with a",
"resistor, where the resistor is serving as a",
"model for the bulb.",
"It's a discrete element called the resistor.",
"And by doing so, now I can very quickly compute the",
"current through the bulb using Ohm's Law, as the current, I,",
"is simply V divided by R. Now, wasn't that simple?",
"OK?",
"Show me where the differential equations are.",
"They're all gone.",
"By making an extremely simple model, by making the",
"simplification and replacing all of the properties of the",
"bulb with the simple resistor with resistance, R, I was able",
"to compute the current, I.",
"Let me continue.",
"And in EE what we are going to be doing is we're going to be",
"doing things the simple way.",
"And in this particular situation, to find the",
"current, I, through the bulb, I replace the bulb with a",
"resistor with resistance, R. And I very quickly was able to",
"find the current.",
"So this is going to be a constant, constant point that",
"we make in 6002X, which is that, in EECS, as engineers,",
"we do things the easy way.",
"In fact, this is true of all engineering.",
"Here in engineering, our goal is to build useful systems",
"that help humanity.",
"And our goal will be to try to do it in the simplest manner",
"possible, unlike like science where, in science, you have to",
"learn what is.",
"But in engineering, we're going to take the easiest path",
"possible in order to build useful systems and possibly",
"make as many simplifications as we want, as long as we get",
"to our goal",
"So in this particular situation with our resistance,",
"R, represents the only property of interest for us,",
"in terms of computing the current, I, for the filament",
"of the bulb.",
"So this is very much like the point-mass simplification",
"where we replaced placed objects with their mass, m, in",
"order to find the acceleration, a equals F",
"divided by m.",
"So I really hope that you see this relationship between the",
"simplifications we made in physics to the simplifications",
"we make in EECS.",
"And as we go on, I'm going to show you some really, really",
"extraordinary results that we get by making some of these",
"some simplifications.",
"So as I said, the R represents the key property of interest",
"for the bulb and enables us to compute the current.",
"What R has done is that it relates the voltage across the",
"resistor to its current.",
"So R relates the voltage and current",
"related to the element.",
"R relates the V and I of the element to each other by the",
"expression I is given by V divided by R.",
"So this relation, I equals V divided by R, is called the",
"element v-i relationship.",
"So obey these elements, and we will define a v-i relationship",
"for those elements that's going to capture the voltage",
"and current relationships for each element that you will see",
"in this course.",
"So this lumped element, R, that we've created to replace",
"the bulb for the purpose of computing the current through",
"the bulb is a lumped element abstraction for the bulb.",
"You've abstracted out all the properties of the bulb into",
"this element, R, for the purpose of computing the",
"current through the bulb.",
"It's important for me to point out this word that you see",
"here, abstraction.",
"This is probably the single most common word that you will",
"hear in an EECS curriculum.",
"A large part of what we do in engineering is we build",
"abstractions.",
"We make things simple and represent them with some",
"abstract properties.",
"OK?",
"Many of you have probably done computer programming.",
"And in computer programming, you are very used to writing",
"programs with a set of lines of code.",
"And what you might do is if you have a function, f, with",
"some arguments, then you might replace the properties and the",
"actions of a bunch of lines of code with this abstract",
"function, f.",
"So that's another example of abstraction where f replaces a",
"set of lines of code that will perform the same function.",
"So it's so much easier to use f.",
"f can replace a set of lines of code.",
"The same manner, our element, R, will replace a large set of",
"differential equations and properties that would",
"characterize the bulb.",
"So you will see this concept of abstraction again and again",
"and again in all of electrical engineering and computer",
"science as you do more and more courses in this area.",
"And if there's one word that describes our entire field of",
"EECS, it is this word abstraction.",
"OK.",
"Enough on abstraction.",
"As you can see, I love the concept of abstraction.",
"And let's pretty quickly summarize what",
"we've seen so far.",
"We build lumped elements.",
"And lumped elements are",
"characterized by their vi relation.",
"So for example, I could have a lumped element",
"that looks like this.",
"And I can define a voltage across a lumped element.",
"And I can define a current through the lumped element.",
"And in this case, when I define the voltage and the",
"current going in through the positive terminal of the",
"element, the power consumed by the element is given by the i.",
"So remember this.",
"You will see this again and again as well that I take an",
"element, and I define a voltage, v, across the",
"element, and I define a current going in to the",
"positive terminal of the element.",
"And in that case, the power consumed by the element is",
"going to be vi.",
"I want you to be careful whenever you define power as",
"whether the power was consumed by the element or power is",
"supplied by the element OK?",
"In this case, the power consumed by the element is vi.",
"So to continue with the resistor, my resistor is a",
"lumped element.",
"And I can describe it with a voltage, v, and a current, i.",
"And I can also plot the values.",
"So for the resistor, the vi relation is given by i equals",
"V divided by R, where R is the resistance",
"property of this resistor.",
"So this element is characterized by its iv",
"relation. i equals V divided R.",
"One interesting computation you can make is, how do you",
"plot this element relationship on an iv curve?",
"Then I show you a pair of axes here.",
"So let me pause for a couple of seconds while you think",
"about what this relationship might look like."
]
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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."
]
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"SPEAKER 1: OK, let me go ahead and give you the answer.",
"In this case, I equals V divided by R is a linear",
"relationship.",
"And notice that the I here and this V here, it's linear",
"relationship.",
"And the slope of the straight line is given by 1 divided by",
"R.",
"So the resistor is one element.",
"And we have enumerable elements in EECS.",
"And another element is a voltage source.",
"A voltage source is an idealistic model of a battery.",
"Again, you can see that there's a voltage, V, and",
"current, I, that I've defined for the element.",
"And the voltage, V, the capital V written inside the",
"element, that is the voltage supplied by the element itself",
"for a typical battery.",
"It might be, for example, 1.5 volts.",
"But the properties of the element are described by its",
"V-I relation, and so this is given by capital V.",
"So notice the small v in this equation here is related to",
"the V-I for the element, while capital V, which could be one",
"1.5 volts, is the voltage supplied by the element.",
"So just make sure to distinguish between what I",
"call up variable V and I that describe through an I-V",
"relation, the element behavior with the element's internal",
"properties, such as the resistance or the voltage.",
"Much like we did with the resistor, we could also plot",
"V-I relation for the voltage source.",
"And before I show it, let me pause for a couple of seconds",
"so you could think about what it might look like before I",
"give you the answer."
]
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