[User] Please transcribe this text

[Assistant] There are different ways to do that, some of them are better than the others, but let's try one.


[User] Please transcribe this text

[Assistant] Right, so you don't want to make it basic, because then we'd be solving a second order problem at the expense of a first order.


[User] Please transcribe this text

[Assistant] Problem. But, so, we don't want to make the bass physically larger.


[User] Please transcribe this text

[Assistant] We just want to make sure that most of the variation of the depletion region happens on, not in the base site, on the collector site.


[User] Please transcribe this text

[Assistant] So yeah, so if the, most of the depletion region is on the collector side, most of its variation would also be on the collector side. So how do you make sure that it's larger, there's more depletion region on the collector side? The doping of the collector will have to be smaller than the doping of the base.


[User] Please transcribe this text

[Assistant] So let's say n, or let's say it was n minus, what's the other problem that it introduces? Yes, it solves the early effect problem, but if I just do that, I've introduced a first order problem.


[User] Please transcribe this text

[Assistant] What would it do? What, what's an N minus? N minus is lightly dope. What's the conductivity or resistivity of an N minus?


[User] Please transcribe this text

[Assistant] Low conductivity, low high resistivity. So now you have a large resistor in series with your collector, which is your output terminal. So that's terrible. So what do we do?


[User] Please transcribe this text

[Assistant] Well, you need the depletion region only when the depletion region, the distop low concentration only where the depletion region exists, right? You don't need it down here.


[User] Please transcribe this text

[Assistant] Transisting action, or the action of the transistor is happening, is already happened by this time. This is just a connection.


[User] Please transcribe this text

[Assistant] Other effects that we haven't talked about. And again, this is not a device physics class, so we're not going to be talking about those. Anyway, so there are a couple other quick things that we want to kind of, yes?


[User] Please transcribe this text

[Assistant] Correct. So the question is, can you just have an intrinsic region? Right? And you could.


[User] Please transcribe this text

[Assistant] Right? The resistivity of an extreme, eh, eh, eh, intrinsic region is going to be very high.


[User] Please transcribe this text

[Assistant] Which basically means that you don't have that much control over the range of this voltage.


[User] Please transcribe this text

[Assistant] Correct. Basically, if you had a real intrinsic region, your depletion region would go to infinity, right? It would become very very large. Because there are no


[User] Please transcribe this text

[Assistant] So you can't really do it that way. I can say it's very lightly doped.


[User] Please transcribe this text

[Assistant] What we are doing is essentially the same thing, we are just like using a lo- low enough concentration that would


[User] Please transcribe this text

[Assistant] If this connects, it's possible to do other things with these two PN. You have two PN junctions, so there are four combinations. You can have both of them forward, both of them reverse, or one forward and one reverse, right? So you have like four different combinations. So what are these regions and what happens in them?


[User] Please transcribe this text

[Assistant] But here's the thing. Let me ask you this question. What if I switch the emitter and the collector? This is also a common problem if you don't use the transistor correctly. You can somehow connect the transistor backwards and this will happen. So what kind of transistor do we have if we have it backward? If it's connected backward?


[User] Please transcribe this text

[Assistant] Think about it. First start with this emitter injection efficiency business. What is the emitter injection efficiency if I connect the transistor backward? It's horrible, right?


[User] Please transcribe this text

[Assistant] Because I have more concentration, less concentration in my emitter than my, so I have a whole lot more holes than electrons. So the emitter injection efficiency is going to be less than half. Which means that base transport factor is going to be low. Means that beta is going to be horrible. Right? So that's one thing. How about your early voltage?


[User] Please transcribe this text

[Assistant] And we don't use it often. I mean, there are some really kind of like niche circuits that use it in reverse active, uhm, and we are not going to talk about it. And they are not used today. They were used like 40 years ago. 30 years ago. But anyway, most of the times we don't use them. Now, the other thing is, what if both of them are reverse biased? What happens in that case?


[User] Please transcribe this text

[Assistant] Nothing that exciting, you have two capacitances, two depletion capacitances, and that's it. Now what if both of them are forward biased?


[User] Please transcribe this text

[Assistant] So that is a little bit more interesting because it can happen.


[User] Please transcribe this text

[Assistant] And the question is, what's, what would happen? So now, if you think about this model, we should modify this model slightly, because we do have two back-to-back diagonals. Right?


[User] Please transcribe this text

[Assistant] We do have the two back-to-back dies, and we have that current source. But for the transistor in the reverse,


[User] Please transcribe this text

[Assistant] We also have, let's call this, another current source with its own alpha reverse.


[User] Please transcribe this text

[Assistant] And basically we call this IR and IF. So we can call this IF.


[User] Please transcribe this text

[Assistant] I forward, and we call this I reverse, and this is alpha reverse, I reverse, this is alpha forward, I forward. This is called Ebers-Moll model. Name up to two people to, okay, Ebers-Moll model.


[User] Please transcribe this text

[Assistant] And this is the full model for the transistor. So it captures all of them, all of the effects. Uhm, now,


[User] Please transcribe this text

[Assistant] Now if both of these diodes are forward biased, you have just two forward biased diodes, right? So you have a diode that looks like this, right?


[User] Please transcribe this text

[Assistant] And a diode, you know, a silicon diode typically, you know, the on voltage we talked about roughly is 0.7 volts or something. And as soon as you start forward biasing it, you're basically forward biasing this diode, which basically means that you have about like at least 0.5 or 0.6 volts to turn it on.


[User] Please transcribe this text

[Assistant] The voltage between your collector and emitter is going to be roughly around .1, .2 volts.


[User] Please transcribe this text

[Assistant] So this is called the v-saturation. So in that situation, a very simplified, highly simplified model for the transistor is like a 0.7 volt battery, or voltage source, fixed voltage here, and a 0.1 or 0.2 volt here. So this is the trans-model and the saturation.


[User] Please transcribe this text

[Assistant] Which is basically when both of these junctions are forward biased.


[User] Please transcribe this text

[Assistant] And it's a very simplified model just to understand how the general behavior of this thing looks like. Any questions on this?


[User] Please transcribe this text

[Assistant] Okay, so, alright, so if there are no questions on that, let's start talking about one more thing.


[User] Please transcribe this text

[Assistant] Moved over. Any questions? You don't look very convinced. You look very skeptical. No, behind you.


[User] Please transcribe this text

[Assistant] Obviously this is not an equilibrium picture, because there's current flowing, but it's a steady state picture.


[User] Please transcribe this text

[Assistant] So now the question is that what happens when you go away from steady state, when you have changes in this thing, when it starts changing, the current goes up, you turn the transistor on, you turn the transistor off. What happens? Well, how does it behave? Well, the key to all of that is this stored charge in the base. This charge that we discussed, there's this minority charge carrier.


[User] Please transcribe this text

[Assistant] Now QF really had two components. It's that charge and there's a little bit of a charge on this side. So it's QB plus this Q, the QE. But let's just forget about this for a second. Or forever. Uhm, and


[User] Please transcribe this text

[Assistant] Just deal with this. I mean, we can take that into account and it's gonna be a minor modification to that.


[User] Please transcribe this text

[Assistant] Over time, due to the thermal energy, they will make it to the collector, and then they will form the collector current. In steady state, let's say for now.


[User] Please transcribe this text

[Assistant] If I told you that the average, at the time it takes an average electron to get from the edge of this depletion region to the edge of that depletion region was tau f, a parameter, call it tau f.


[User] Please transcribe this text

[Assistant] Can you tell me what the average current is in terms of Qf and Tau f? What's the collective current in terms of those? Qf over Tau f, right?


[User] Please transcribe this text

[Assistant] That's the total charge. It takes an average electron tau f to get across from here to there. So,


[User] Please transcribe this text

[Assistant] It should not be surprising to say that IC is gonna be QF over tau F.


[User] Please transcribe this text

[Assistant] Where tau f is the time it takes an average electron to get from the edge of one depletion region to the edge of the next depletion.


[User] Please transcribe this text

[Assistant] So, if that's the IC, that's, so I know that. Right?


[User] Please transcribe this text

[Assistant] What are the mechanisms? So, there are a couple of things happening here.


[User] Please transcribe this text

[Assistant] It's replenishing some of these losses, right? But let's think about this for a second. If I look at this QF,


[User] Please transcribe this text

[Assistant] So what makes it larger? What, what are the things that increase it? It increases at the rate of the, if the emitter charge injection was the only thing, it would go up and this would be the case, right? So this is the emitter charge. That's the, the charge that comes out of, from the emitter is added to it.


[User] Please transcribe this text

[Assistant] So it goes up at the rate, at that rate. The charge increases at that rate. Now,


[User] Please transcribe this text

[Assistant] What is it? Recombination, right? So, the recombination is proportional to what? The rate of recombination. How many recombine


[User] Please transcribe this text

[Assistant] There's a probability, there's a time constant associated with it, right? That's called a tau b. But, it's also proportional to something simple.


[User] Please transcribe this text

[Assistant] It's proportional, how many, how many electrons are combined per second is proportional to what?


[User] Please transcribe this text

[Assistant] If there are no electrons, there will be no, I mean, if the probability even is one, if there are no electrons, there is no electrons. So it is, you lose them at the rate of Qf, which is the number of electrons, divided by tau b. The time constant associated with this loss. So this is the differential equation describing the dynamics of the thing. But there's something simple in there.


[User] Please transcribe this text

[Assistant] Then it's a lump device, which basically means that the three currents have to add up at any instant in time.


[User] Please transcribe this text

[Assistant] The IC plus IB should be IE at all times. And these transistors are pretty small. And even at highest frequencies you are considering, they're still much smaller than the wavelength.


[User] Please transcribe this text

[Assistant] For the moment, I mean there may be some special cases, but almost all of them exist. So, I can strike this as what?


[User] Please transcribe this text

[Assistant] IB. So the differential equation I end up with is this.


[User] Please transcribe this text

[Assistant] But this is how IV comes to be. It's IE minus IC. It's the ones that are injected minus the ones that have left. So this is the differential equation governing the behavior of


[User] Please transcribe this text

[Assistant] That's one thing. Now, the other thing that you can think about is, uhm, so, okay, so if I know this, what do I, what else do I know? What else do I know about


[User] Please transcribe this text

[Assistant] So how about in steady state? What does this equation tell me? So this equation is valid in all cases, including steady state, right? In steady state, what can you say about the left hand side? It's zero by definition, right? So then in steady state,


[User] Please transcribe this text

[Assistant] What you have is that IB is equal to QF divided by Tau B. Now contrast this with that. But we also know one more thing in steady state. What do we know? We know that IC over IB is what?


[User] Please transcribe this text

[Assistant] So beta is that, so if you divide this by that, then you cancel Qf.


[User] Please transcribe this text

[Assistant] So which basically means that beta is tau b over tau f.


[User] Please transcribe this text

[Assistant] Or in other words, tau b is beta tau f.


[User] Please transcribe this text

[Assistant] So you don't need to know both Tau F and Tau B.


[User] Please transcribe this text

[Assistant] If you know tau f and if you know beta, you can calculate tau b. So,


[User] Please transcribe this text

[Assistant] If I have a BJT, if I have a bipolar junction transistor that I want to work with, what are some of the parameters that I need to know if I want to work with it?


[User] Please transcribe this text

[Assistant] Beta is a good thing to know, although it turns out, if you design properly, you don't need to know it as long as it's large. And that's the thing. You say, well, as long as I know it's large, enough.


[User] Please transcribe this text

[Assistant] It's gonna be okay, but again, I need to know what beta is, but I need to know what order of magnitude beta is. So if you know beta, it's good. What else do we need to know?


[User] Please transcribe this text

[Assistant] Tao F. If I wanted to look at this dynamics I need to know it's Tao F. Now what else? The early voltage, VA.


[User] Please transcribe this text

[Assistant] And if I, if I'm designing, doing certain kinds of design, then I need to know what IS is. The saturation current. So those would be some of the key parameters of this thing. Now,


[User] Please transcribe this text

[Assistant] This leads to a certain value of, so, so, this, this is a useful thing, you will do problem sets where you actually use this differential equation to find the response of a transistor to a certain kind of input, and, and that's fine. Now the other thing that you could get out of this, this kind of discussion is that if you think about it, there's this charge stored in the base, right? So there is a capacitance there.


[User] Please transcribe this text

[Assistant] So the junction, so remember these two depletion regions have junction capacitances that we calculated last time, right? We did this calculation of the junction capacitance, you remember? We did that calculation, we looked at it, we calculated the width, et cetera, et cetera, so we have the junction capacitance. But in addition to the junction capacitance, we also have this additional charge storage in the channel.


[User] Please transcribe this text

[Assistant] Which we'll see next time, it's gonna be gm tau f. gm is the transconductance which we haven't defined yet, it's its small signal parameter, and times tau f.


[User] Please transcribe this text

[Assistant] So that capacitance in conjunction with these two junction capacitances form the three main capacitances in the, in the transistor, in the BJT, which determine its general behavior in terms of high frequency behavior.


[User] Please transcribe this text

[Assistant] If you think about, very briefly talk about this, is that in saturation, what happens to this charge?


[User] Please transcribe this text

[Assistant] Now we didn't talk about it, and we are not going to extensively go into it. I mean, this model we developed for saturation is probably okay for a lot of things that we want to do. But, what happens to this QF?


[User] Please transcribe this text

[Assistant] If the transistor is in saturation. What was the definition of saturation? When both junctions are forward biased. So, what happens to QF?


[User] Please transcribe this text

[Assistant] So you have all the charge that's being injected by the emitter into the base. But now this guy is forward bias, this junction is forward bias too. Right?


[User] Please transcribe this text

[Assistant] And if you have a lot of charge stored in the device, what does it tell you about


[User] Please transcribe this text

[Assistant] In that state, what does it tell you about how quickly you can remove the charge or replenish it? It would take longer, right?


[User] Please transcribe this text

[Assistant] And what does that tell you about the speed of the transistor and saturation? Slower, right? Because you have a lot more charge stored there.


[User] Please transcribe this text

[Assistant] So, to get it into the saturation, you need to store all the charge, and then you, to, to slow it, to basically remove, go away from the saturation, you have to take this charge out. Now, if you have a mechanism to take this charge out quickly, maybe okay.


[User] Please transcribe this text

[Assistant] Turning a transistor and putting it into saturation is not that slow, because you have a source of charge, but turning it off, if you just let it on its own,


[User] Please transcribe this text

[Assistant] We'll take a long time, because all that charge needs to recombine. Put a lot of charge in there, it needs to be absorbed and recombined in the base, and it just takes a while.


[User] Please transcribe this text

[Assistant] That's why transistor and saturation are pretty slow, and you try to avoid that if you can. So it's not a mode of operation we typically shoot for, it's a mode of operation that we try to avoid in most of the circuits. Now, in the old days, there were some digital circuits that were designed based on saturation, but they were slow.


[User] Please transcribe this text

[Assistant] He was teaching his students one day and saw that scorpion creeping toward him. He tried to move it away, but it stung him. The pain was horrible. He told his guards to capture the scorpion, but it escaped to earth.


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[Assistant] What's to guarantee that my conscience will be the same as your conscience?


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[Assistant] Journey to the West, Chapter 71, Money.


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[Assistant] Bajie moaned. His stomach grumbled loudly.


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[Assistant] They had continued for another hour when the pig complained again.


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[Assistant] Wokong! Pride the Tang Monk, hanging on tightly.


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[Assistant] When the horse finally stopped running, the monk was far ahead of his companions.


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[Assistant] Said a man with an axe. The Tang monk shook with fear. Wukong was already running over.


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[Assistant] He pulled out his iron bar which quickly drew to the height of a person. The men looked nervous. The monkey stood the bar on the ground.


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[Assistant] Go ahead and try, said Wukong. The man put down the axe.


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[Assistant] He grasped the bar with his hands and tried to lift it.


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[Assistant] Said the man. He tried to lift the bar again.


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[Assistant] He lifted the bar over his head and twirled it around.


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[Assistant] Wukong could see that the monk wasn't going to change his mind.


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[Assistant] With tears in his eyes, the monkey leaped into the air and was gone.


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[Assistant] Journey to the West, Chapter 68, The Woman in the Crowd.


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[Assistant] The monkey leaped onto a cloud and soared toward the west.


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[Assistant] He arrived at the Thunder Clap Monastery. A guard at the gate stopped him.


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[Assistant] When Wukong arrived at Laozi's house, the sage frowned.


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[Assistant] The door flew open and one horned buffalo stepped outside. His face fell when he saw Lousa.


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[Assistant] Lousa raised the fan and brought it down fast.


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[Assistant] The sage caught it and brought the fan down once more.


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[Assistant] Lousa tucked the fan and the ring into his robe.


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[Assistant] Then he climbed onto the buffalo and rode up into the sky.


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[Assistant] Wukong went into the cave, and the warrior and two gods followed.


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[Assistant] Suddenly, a young woman rushed out of the crowd.


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[Assistant] The tag monk! She cried. She threw her arms around the monk.


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[Assistant] And I'm just finishing my first year of design school.


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[Assistant] A form of ritual torture for design students where they make you take everything you made over the course of the year and lay it out on a table.


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[Assistant] And stand next to it while a bunch of professors, most of whom you've never seen before, give you their unfiltered opinions of it.


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[Assistant] So it's my turn, and I'm standing next to my table, everything neatly lined up.


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[Assistant] And I'm just hoping that my professors can see


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[Assistant] And I'm starting to get really nervous because for a long time, no one says anything. It's just completely silent.


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[Assistant] And then one of the professors starts to speak and he says, your work gives me a feeling of joy. Joy?


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[Assistant] I wanted to be a designer because I wanted to solve real problems. Joy is nice, I guess, but it's kind of light, not substantial.


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[Assistant] I asked the professors, how do things make us feel joy? How do tangible things make us feel intangible joy?


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[Assistant] They hemmed and hawed and gestured a lot with their hands. They just do, they said.


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[Assistant] This launched a journey, one that I didn't know at the time would take me 10 years to understand the relationship between the physical world and the mysterious, quixotic emotion we call joy. And what I discovered is that


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[Assistant] Not only are they linked, but that the physical world can be a powerful resource to us in creating happier, healthier lives.


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[Assistant] Even scientists don't always agree and they sometimes use the words joy and happiness and positivity more or less interchangeably.


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[Assistant] But broadly speaking, when psychologists use the word joy, what they mean is an intense, momentary experience of positive emotion, one that makes us smile and laugh and feel like we want to jump up and down.


[User] Please transcribe this text

[Assistant] I started asking everyone I knew and even people I just met on the street about the things that brought them joy.


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[Assistant] And ice cream cones, especially the ones with the sprinkles.


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[Assistant] I mean, if you think about it, we all stop and turn our heads to the sky when the multicolored arc of a rainbow streaks across it. And fireworks.


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[Assistant] We don't even need to know what they're for, and we feel like we're celebrating too.


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[Assistant] These things aren't joyful for just a few people. They're joyful for nearly everyone. They're universally joyful. And seeing them all together,


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[Assistant] It gave me this indescribably hopeful feeling.


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[Assistant] Feels so vast as to be insurmountable. And yet underneath it all, there's a part of each of us that finds joy in the same things.


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[Assistant] And though we're often told that these are just passing pleasures, in fact, they're really important because they remind us of the shared humanity we find in our common experience of the physical world.


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[Assistant] I had pictures of them up on my studio wall, and every day I would come in and try to make sense of it. And then one day, something just clicked. I saw all these patterns, round things, pops of bright color, symmetrical shapes, a sense of abundance and multiplicity.


[User] Please transcribe this text

[Assistant] We can access it through tangible physical attributes, or what designers call aesthetics.


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[Assistant] A word that comes from the same root as the Greek word, isenomai, which means, I feel, I sense, I perceive.


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[Assistant] And since these patterns were telling me that joy begins with the senses,


[User] Please transcribe this text

[Assistant] Now that I knew what to look for, I was seeing it everywhere. It was like these little moments of joy were hidden in plain sight.


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[Assistant] And at the same time, I had another realization that if these are the things that bring us joy, then why does so much of the world look like this?


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[Assistant] Why do we go to work here? Why do we send our kids to schools that look like this? Why do our cities look like this?


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[Assistant] And this is most acute for the places that house the people that are most vulnerable among us. Nursing homes, hospitals, homeless shelters, housing projects.


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[Assistant] How did we end up in a world that looks like this? We all start out joyful,


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[Assistant] As we get older, being colorful or exuberant opens us up to judgment.


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[Assistant] I spent the last two years scouring the planet, looking for different ways that people have answered this question.


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[Assistant] It's a real place, just outside Tokyo. I spent a night there, and it's a lot.


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[Assistant] The floors undulate, so you don't end up walking around, so much as kind of bouncing around the apartment, and there are bright colors in every direction. I'm not sure I left any younger, but it says if ...


[User] Please transcribe this text

[Assistant] It made me wonder, what about the rest of us? How do we bring these ideas back into the real world? So I started finding people who were doing just that.


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[Assistant] Are these schools transformed by the non-profit public color?


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[Assistant] What's interesting is that Publicolor has heard from school administrators who say that attendance improves, graffiti disappears, and kids actually say they feel safer in these painted schools.


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[Assistant] And this aligns with research conducted in four countries, which shows that people working in more colorful offices are actually more alert, more confident and friendlier than those working in drab spaces.


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[Assistant] Why would this be the case? Well, as I started to trace back our love of color I found that some researchers see a connection to our evolution.


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[Assistant] Color, in a very primal way, is a sign of life, a sign of energy.


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[Assistant] Isn't very joyful, but multiply it and you have a handful of one of the most joyful substances on the planet.


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[Assistant] The architect Emmanuelle Moreau uses this idea in her work a lot. This is a nursing home she designed where she uses these multicolored spheres to create a feeling of abundance. And what about all those round things I noticed?


[User] Please transcribe this text

[Assistant] Well, it turns out neuroscientists have studied this too. They put people into fMRI machines and they showed them pictures of angular objects and round ones.


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[Assistant] And what they found is that the amygdala, part of the brain associated in part with fear and anxiety, lit up when people looked at angular objects, but not when they looked at the round ones. They speculate that because


[User] Please transcribe this text

[Assistant] After the mass shooting there in 2012, the architects, Vigals plus partners knew that they needed to create a building that was secure, but they wanted to create one that was joyful. And so they filled it with curves. There are waves running along the side of the building and these squiggly canopies over the entryway, and the whole building bends toward the entrance in a welcoming gesture.


[User] Please transcribe this text

[Assistant] Each moment of joy is small, but over time they add up to more than the sum of their parts.


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[Assistant] Deep within us, we all have this impulse to seek out joy in our surroundings. And we have it for a reason.


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[Assistant] It's directly connected to our fundamental instinct for survival. On the most basic level, the drive toward joy.


[User] Please transcribe this text

[Assistant] Is the drive toward life. Thank you.


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[Assistant] Journey to the West, Chapter 74, Curious Ear.


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[Assistant] Said one Wukong. He pointed at the other.


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[Assistant] He tried to strike the other Wukong but that one dodged the blow and swung back.


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[Assistant] The two monkeys were still fighting when they arrived at the southern gate of heaven.


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[Assistant] Spirits and gods bled as the two Wukongs fought all over heaven. The monkeys knocked over statues and trees.


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[Assistant] When the Jade Emperor saw them, he was furious.


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[Assistant] The two Wukong stood still as the Jade Emperor looked carefully at them. Finally, the Emperor shrugged.


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[Assistant] He turned the pages of the giant book reading carefully. Finally, he closed it.


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[Assistant] The beast stared hard at the two Wukongs. Finally, it spoke.


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[Assistant] Tire Town School Episode 18 Flat Tire


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[Assistant] I don't care, said Poppy.


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[Assistant] Come here, Poppy. Called Ms. Fender. You need a new tire.


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[Assistant] Thump, thump, thump, thump.


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[Assistant] Listen to Ms. Fender, said Eddie. You need a new tire. Nah, said Poppy. I'm fine. Poppy drove forward. She drove backward. Thump, thump, thump. See, said Poppy. I can still drive. Let's keep playing tag.


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[Assistant] Ms. Fender frowned. Poppy tried to tag Eddie. But Eddie drove away. Then?


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[Assistant] But I do not design buildings or computer systems. Rather, I build body parts.


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[Assistant] Bionic legs that augment human walking and running.


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[Assistant] In 1982, I was in a mountain climbing accident and both of my legs had to be amputated due to tissue damage from frostbite. Here you can see my legs. Twenty-four sensors.


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[Assistant] Six microprocessors and muscle tendon-like actuators. I'm basically a bunch of nuts and bolts from the knee down.


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[Assistant] Neural signals from my central nervous system pass through my nerves and activate muscles within my residual limbs.


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[Assistant] Artificial electrodes sense these signals, and small computers on the bionic limb decode my nerve pulses into my intended movement patterns.


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[Assistant] When I touch and move my synthetic limbs, I do not experience normal touch and movement sensations. If I were a cyborg and could feel my legs,


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[Assistant] Via small computers inputting information into my nervous system, it would fundamentally change, I believe, my relationship to my synthetic body. Today, I can't feel my legs.


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[Assistant] I believe that if I were a cyborg and could feel my legs, they would become part of me, part of self.


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[Assistant] At MIT, we're thinking about neural and body design. In this design process,


[User] Please transcribe this text

[Assistant] The designer designs human flesh and bone, the biological body itself, along with synthetics.


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[Assistant] To enhance the bi-directional communication between the nervous system and the built world.


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[Assistant] Neuron body design is a methodology to create cyborg function.


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[Assistant] Contemplate a future in which technology no longer comprises separate lifeless tools from our minds and our bodies.


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[Assistant] A future in which technology has been carefully integrated within our nature.


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[Assistant] A world in which what is biological and what is not, what is human and what is not, what is nature and what is not, will be forever blurred.


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[Assistant] Neural and body design will extend our nervous systems into the synthetic world, and the synthetic world into us, fundamentally changing who we are.


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[Assistant] Extending human capability beyond innate physiological levels, cognitively, emotionally and physically.


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[Assistant] From the biomolecular to the scale of tissues and organs. Today I want to talk about one area of neural and body design in which the body's tissues are manipulated and sculpted using surgical and regenerative processes.


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[Assistant] The current amputation paradigm hasn't changed fundamentally since the US Civil War and has grown obsolete in light of dramatic advancements in actuators, control systems and neural interfacing technologies.


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[Assistant] A major deficiency is the lack of dynamic muscle interactions for control and proprioception. What is proprioception?


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[Assistant] When you flex your ankle, muscles in front of your leg contract, simultaneously stretching muscles in the back of your leg. The opposite happens when you extend your ankle.


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[Assistant] When these muscles flex and extend, biological sensors within the muscle tendons send information through nerves to the brain. This is how we're able to feel where our feet are, without seeing them with our eyes.


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[Assistant] The current amputation paradigm breaks these dynamic muscle relationships, and in so doing, eliminates normal proprioceptive sensations.


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[Assistant] Consequently, a standard artificial limb cannot feed back information into the nervous system about where the prosthesis is in space. The patient, therefore, cannot sense and feel the positions and movements of the prosthetic joint without seeing it with their eyes.


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[Assistant] I can feel my feet, I can feel them right now, as a phantom awareness. But when I try to move them, I cannot. It feels like they're stuck inside rigid ski boots.


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[Assistant] To solve these problems at MIT, we invented the agonist-antagonist mild neural interface, or AMI for short.


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[Assistant] The AMI is a method to connect nerves within the residuum to an external bionic prosthesis. How is the AMI designed, and how does it work?


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[Assistant] The emmy comprises two muscles that are surgically connected, an agonist linked to an antagonist.


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[Assistant] When the agonist contracts upon electrical activation, it stretches the antagonist. This muscle-dynamic interaction causes biological sensors within the muscle tendon to send information through the nerve to the central nervous system, relating information on the muscle tendon's length, speed and force.


[User] Please transcribe this text

[Assistant] Can feel and sense the positions, movements and forces on our limbs.


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[Assistant] When a limb is amputated, the surgeon connects these opposing muscles within the residuum to create an amy. Now, multiple amy constructs can be created


[User] Please transcribe this text

[Assistant] For the control and sensation of multiple prosthetic joints.


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[Assistant] Artificial electrodes are then placed on each amy muscle, and small computers within the bionic limb decode those signals to control powerful motors on the bionic limb. When the bionic limb moves,


[User] Please transcribe this text

[Assistant] The amy muscles move back and forth, sending signals through the nerve to the brain, enabling a person wearing the prosthesis


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[Assistant] To experience natural sensations of positions and movements of the prosthesis.


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[Assistant] Can these tissue design principles be used in an actual human being?


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[Assistant] Jim was in a terrible climbing accident. He fell 50 feet in the Cayman Islands when his rope failed to catch him hitting the ground surface.


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[Assistant] He suffered many, many injuries, punctured lungs and many broken bones.


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[Assistant] After his accident, he dreamed of returning to his chosen sport of mountain climbing. But how might this be possible?


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[Assistant] A team of surgeons, scientists and engineers assembled at MIT to rebuild Jim back to his former climbing prowess.


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[Assistant] Team member Dr. Matthew Cardy amputated Jim's badly damaged leg at Brigham Women's Hospital in Boston using the AME surgical procedure.


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[Assistant] Tendon pulleys were created and attached to Jim's tibia bone to reconnect the opposing muscles.


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[Assistant] The AMI procedure reestablished the neural link between Jim's ankle foot muscles and his brain. When Jim moves his phantom limb,


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[Assistant] The reconnected muscles move in dynamic pairs, causing signals to pass through nerves of proprioception to the brain.


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[Assistant] So Jim experiences normal sensations of ankle foot positions and movements even when blindfolded.


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[Assistant] Here's Jim at the MIT laboratory after his surgeries.


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[Assistant] We electrically linked Jim's amy muscles via the electrodes to a bony limb, and Jim quickly learned how to move the bony limb in four distinct ankle-foot movement directions.


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[Assistant] As an involuntary reflexive action. All the intricacies of foot placement. Thank you. During stair ascent.


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[Assistant] It knows exactly how to control the synthetic limb in a natural way. Now Jim,


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[Assistant] Moves and behaves as if the synthetic limb is part of him.


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[Assistant] For example, one day in lab, he accidentally stepped on a roll of electrical tape.


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[Assistant] Now what do you do when something's stuck to your shoe? You don't reach down like this, it's way too awkward. Instead, you shake it off, and that's exactly what Jim did after being narrowly connected to the limb for just a few hours.


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[Assistant] What was most interesting to me is what Jim was telling us he was experiencing. He said, the robot became part of me.


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[Assistant] By connecting Jim's nervous system bidirectionally to his synthetic limb, neurological embodiment was achieved.


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[Assistant] I hypothesize that because Jim can think and move his synthetic limb,


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[Assistant] And because he can feel those movements within his nervous system.


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[Assistant] The prosthesis is no longer a separate tool, but an integral part of Jim, an integral part of his body.


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[Assistant] Because of this neurological embodiment, Jim doesn't feel like a cyborg.


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[Assistant] Now I'm often asked when I'm going to be narrowly linked to my synthetic limbs bidirectionally, when I'm going to become a cyborg. The truth is, I'm hesitant to become a cyborg.


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[Assistant] Before my legs were amputated, I was a terrible student. I got Ds and often Fs in school. And then after my limbs were amputated, I suddenly became an MIT professor.


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[Assistant] That once I'm neurally connected to my limbs, once again, my brain will remap back to its not-so-bright self.


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[Assistant] I believe the reach of neuron-body design will extend far beyond limb replacement and will carry humanity into realms that fundamentally redefine human potential.


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[Assistant] In this 21st century, designers will extend the nervous system into powerfully strong exoskeletons that humans can control and feel with their minds.


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[Assistant] Muscles within the body can be reconfigured for the control of powerful motors.


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[Assistant] In this 21st century, I believe humans will become superheroes.


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[Assistant] Humans may also extend their bodies into non-anthropomorphic structures, such as wings.


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[Assistant] During the twilight years of this century, I believe humans will be unrecognizable in morphology and dynamics from what we are today. Humanity will take flight and soar.


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[Assistant] Jim Ewing fell to earth and was badly broken, but his eyes turned skyward where he always longed to return.


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[Assistant] After his accident, he not only dreamed to walk again, but also to return to his chosen sport of mountain climbing.


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[Assistant] At MIT, Team Cyborg built Jim a specialized limb for the vertical world. A brain-controlled leg with full position and movement sensations.


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[Assistant] Using this technology, Jim returned to the Cayman Islands, the site of his accident.


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[Assistant] Rebuilt as a cyborg to climb skyward once again.


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[Assistant] Tire Town School, Episode 20, Out of Gas.


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[Assistant] Yes, we all know about that, Wukong. But this is different. The Tang Monk is with us. We must keep him safe.


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[Assistant] Everybody has that one friend. You know, the single-minded one. The one who, no matter what the question is, always finds a way to make the answer whatever it is she's single-minded about. I'm that friend.


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[Assistant] And the thing that I'm single-minded about is racism.


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[Assistant] If someone were to ask me, so Janet, got any plans for the 4th of July? I'm subject to answer, yea, I'm going to binge watch Roots.


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[Assistant] Or if they said, Janet, I got a joke for you. Why the chicken crossed the road? Uh, was it a black chicken? Probably gentrification.


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[Assistant] But for me, single-mindedness is not just caring about something. It's caring about something enough to do something about it.


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[Assistant] It's not just praying, it is moving your feet.


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[Assistant] And the reason I'm single-minded about racism is because I know single-mindedness can destroy it. I learned that many, many years ago.


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[Assistant] Back in 1984, I was a junior at Davidson College in Davidson, North Carolina.


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[Assistant] Now, Davidson is a little bitty town, southern town, split by railroad tracks. White Davidson on one side, black Davidson on the other side. And as black students living on the white side of the tracks, we got used to being stopped in downtown and asked for ID.


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[Assistant] Until the police memorized our faces. But fortunately that didn't take too long because out of 1,200 students, only 52 of us were black. There was one black professor, one black assistant dean. Things were a lot better on campus.


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[Assistant] Well, I wasn't okay with this. And so I started writing things. And then I started yelling things. And after about three years of that, I got tired. So I decided to write one more thing. And I wrote something called Project 87.


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[Assistant] Project 87 was really just a challenge to Davidson. In three years, by 1987, enroll 100 black students, hire 10 black professors,


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[Assistant] Create five black studies classes and hire one black dean. Didn't seem particularly revolutionary.


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[Assistant] But what was different about it was, we also challenged Davidson to say that if you don't do this, we will question your commitment to diversity. It was a real problem, we put some real numbers to it, we gave them some real consequences. Well, campus went absolutely nuts.


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[Assistant] But fortunately, in the middle of this, Davidson got a new president. And that president was single-minded about racism, too. And so he created a task force.


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[Assistant] To address the issues in Project 87. And several months after that, we produced a 77-page report. That report was the foundation for all the change that came after it.


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[Assistant] However, the change did happen. And today, there are 185 black students. There are 16 black or multiracial professors. There are four black deans, and there's an entire degree-granting Africana Studies department.


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[Assistant] Project 87 changed Davidson, but it also changed me because what it taught me was there's a lot of power in single-mindedness.


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[Assistant] It's a profession that is 92 percent white and predominantly male, which makes me a little bit of a unicorn, but I'm a single-minded unicorn.


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[Assistant] So the thing about speech writing is it's very personal. So I spend a lot of time in deep conversation with the CEO and senior executives, and a lot of times those conversations turn to diversity and inclusion, which of course I'm always happy to talk about.


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[Assistant] But after quite a few of these conversations, I've come to a conclusion.


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[Assistant] I believe that business is in a position to do something that no other entity can do. Business can dismantle racism.


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[Assistant] Now colleges can't do it. There aren't but 5,000 of them in the United States and only 20 million students enrolled.


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[Assistant] Church can't do it either. Only 35 percent of us go on a regular basis. And when we do, 11 o'clock Sunday morning is the most segregated hour in America. But business?


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[Assistant] There are 162 million people in the US workforce alone. People of all races, united in the spirit of wanting a paycheck and having to show up to get it.


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[Assistant] Now I'm aware that diversity is bigger than race, and racism is bigger than America, but racial discrimination is the most prominent form, and lord knows, America is the absolute best at it. So, what if though, what if,


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[Assistant] We worked in diverse and inclusive environments that we had something to do something with.


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[Assistant] And since we spent one third of our lives at work, what if we did that with people who didn't look like us? I think the world would be a totally different place outside of work. That can happen.


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[Assistant] Diversity is not really a problem for business, yet. I mean, it's a nice thing to have. It's the right thing to do. But for decades, we've been trying to make the case that diversity fuels innovation and customer insight.


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[Assistant] I mean, at this point, it's kind of a no-brainer. A little bit like hearing a smoke alarm going off and standing there with your hand on the hot door waiting for some data to tell you that your house is on fire. Because the data is already there.


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[Assistant] Ethnically diverse companies perform 33 percent better than the norm.


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[Assistant] And there are only three black CEOs in the Fortune 500. And if your name is Molly or Connor, you got a 14 percent better chance of getting a call back on your resume than if your name is Shanice or Deshawn.


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[Assistant] The business case for diversity as it stands today doesn't really speak to any problem.


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[Assistant] And the only way business is going to get single-minded about racial diversity is if it has a problem that is urgent and relative to somebody other than people of color.


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[Assistant] I got one. How about employees and customers? Because no matter what business you're in, you're going to need those, right? Well, let's talk about some real numbers.


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[Assistant] If you have employees and customers, wouldn't it make sense if they looked a little bit like the people


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[Assistant] Companies can mandate diversity, but they have to cultivate inclusion.


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[Assistant] And if inclusion is what you're after, you got to calculate some slightly different numbers. How about 30 percent?


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[Assistant] Because that's the point that research shows, at which the voices of minorities actually begin to be heard.


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[Assistant] If you want a real problem, you're going to need real numbers to fix it. And if you're not willing to set real numbers, then maybe you're not real serious about diversity and inclusion. That brings me to my third point. Real consequences. Think about this. When salespeople


[User] Please transcribe this text

[Assistant] We give them a little time, maybe we give them some training, but then if they don't hit those numbers eventually, we fire them.


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[Assistant] However, when you start talking about diversity and inclusion, we use terms like accountability.


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[Assistant] And maybe we scold, and maybe we hold back an incentive or two. But you know what the best incentive is? A job. And you know what the best disincentive is? Losing it. So.


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[Assistant] If companies really want accountability, they should assume that that is a given. Consequences are what happen when you don't do what you're accountable for. Imagine this.


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[Assistant] Where those people feel safe, indeed expected, to bring their unassimilated, authentic selves to work every day. Because the difference that they bring is both recognized and respected.


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[Assistant] And imagine a place where the lessons we learn about diversity at work.


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[Assistant] Actually transform the things we do, think and say outside of work.


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[Assistant] That is what happens if we all work together to fix what's broken.


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[Assistant] Tire Town School, Episode 23, The Slippery Racetrack.


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[Assistant] Zippy drove toward the tree. He slammed on his brakes.


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[Assistant] But the racetrack was slippery. Zippy slid.


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[Assistant] He tried to turn. Oh no! Cried Zippy. I'm going to hit the- BAM!


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[Assistant] Ouch, said Zippy. I got a bad dent. Eddie drove slowly. He went around the tree.


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[Assistant] You were going too fast. Zippy frowned.


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[Assistant] Zoom. Zippy shot past Eddie. Water splashed on Eddie.


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[Assistant] He went left. He went right. Zippy spun in circles. Woah! He cried. Oh no! Said Eddie. He saw Zippy spin. Then Zippy flew off the track.


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[Assistant] Before the break, what we did, we looked at a parallel treatment of the MOSFET and bipolar BJTs and MOSFETs of


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[Assistant] The small signal model. And we saw that small signal model is really a way of looking at a nonlinear behavior and looking at the perturbation around an operation point in that nonlinear point. And we saw that for BJTs, for example, the most important part of the operation is the transistor part. The transisting part of the transistor, quote unquote, is the transconductance. GM, or one over RN.


[User] Please transcribe this text

[Assistant] Essentially the gate overdrive in a non-velocity saturated device would determine the GM in a MOSFET and the collector current would determine the GM in a bipolar transistor. So, now if you think about that, if you start with that and then try to create a model


[User] Please transcribe this text

[Assistant] Is going to be essentially the gm. So now what we mean by gm, we saw that gm was the derivative of the collector current with respect to the base emitter voltage. So it is fair to think about it, there are two different models that we'll discuss, but so this is the so called hybrid pi model.


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[Assistant] In that, if you think about the three terminals, and now we show in this model, we show these three terminals with lowercase letters.


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[Assistant] To emphasize, so when we show these terminals with lowercase letters, we are really trying to emphasize the fact that this is the model of the perturbation.


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[Assistant] On top of the operation point. Now, that model is a linear model. And basically, this, there's a current, voltage dependent current source, V pi, and it's shown here. You can also show it as VBE, lowercase VBE, which is equal to V pi. You can say,


[User] Please transcribe this text

[Assistant] If my VBE, I fluctuate the VBE as you see in that upper picture,


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[Assistant] Down here, a fluctuation in the VBE, that red fluctuation, produces a fluctuation in the current, in the IC. So, this is really, these fluctuations, the red ones, are the IC.


[User] Please transcribe this text

[Assistant] And it's basically saying that the collector current is modulated by the base emitter voltage.


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[Assistant] Good part of the transistor. Now, the same thing for the MOSFET, right? We can do a similar, we can draw a similar model for the MOSFET. And again, since it's the ratio of similar terminals, this is the drain.


[User] Please transcribe this text

[Assistant] And this is the source. Now, with the MOSFET, we have to be careful because we know that we have a fourth terminal, the bulk, which we haven't talked about yet. And we'll see how it comes into play soon.


[User] Please transcribe this text

[Assistant] But, so far we've drawn these three terminals. And then we have the good part of the transistor, the useful part of the transistor, which is this transconductance. Let's do it in green. Differentiate it.


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[Assistant] So this is gm. Now, you could call it vpi, or we could call it vgs. Now, interestingly,


[User] Please transcribe this text

[Assistant] It's more common to call this VGS in a MOSFET and not call it VPI and call it VPI in bipolar transistors and not call it VGS. But as far as I'm concerned, they are the same thing.


[User] Please transcribe this text

[Assistant] These models were done for different people as, you know, one of them. So, so, you know, the reason that there are these differences.


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[Assistant] In the way they're drawn, in the way they're modeled, and things of that sort. People develop that reasonable model first. And we'll see.


[User] Please transcribe this text

[Assistant] Uhm, examples of that. And then some other people tried to differentiate their work from other people, they gave them different names, they drew them differently, they did these different things, they just say, okay, no, we are different, this is the new method. Okay?


[User] Please transcribe this text

[Assistant] Now, and that's why I'm always a fan of going back to the original work and saying, okay, what were they thinking originally?


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[Assistant] If that still makes sense, I would use it. And we'll see that actually even, I think, as we'll see in 80% of circuit design that we deal with, the Pi model is not the best model to use.


[User] Please transcribe this text

[Assistant] Which was the original use. And everyone now use it because the original books that were written on this subject


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[Assistant] Analysis in many cases, 80% of the cases. There are times that it's useful, so we'll introduce both models.


[User] Please transcribe this text

[Assistant] But anyway, let's start with the Pi model and we'll get to the T model in a few, few minutes.


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[Assistant] There are different ways to think about it. The easiest way is that there's some base current. If I apply voltage here, I draw a current.


[User] Please transcribe this text

[Assistant] I increase the voltage, the current increases. I decrease the current, the current decreases. So incrementally, there is some resistance.


[User] Please transcribe this text

[Assistant] So as an incremental perturbation perspective, there should be a resistance here. Right? So this resistance,


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[Assistant] Let's call this r-pi, because it's sitting in parallel with the v-pi. Now r-pi


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[Assistant] By definition, if it's an incremental resistance, it's gonna be DIB to DVBE inverse, right?


[User] Please transcribe this text

[Assistant] It's the ratio, the ratio of the change in the current versus voltage, that's the conductance, so 1 over that would be the resistance. So, now, this quantity though, is not that hard to calculate because, I mean, there's a relationship between IB and IC.


[User] Please transcribe this text

[Assistant] So if you plug that in, it becomes clear that this is beta times DIC over DVBE.


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[Assistant] We have already calculated it on the upper whiteboard. What is that in purple? It's the transconductance. It's GM. So this is beta over GM or beta RM. So at one milliamp,


[User] Please transcribe this text

[Assistant] And let's say if beta were 100, you're looking at 2.5 kiloohms. Not too high, not too low. Right?


[User] Please transcribe this text

[Assistant] And of course, as you increase GM or RM, this changes its resistance. Another way to see this is that if you remember earlier, we developed this equivalent nonlinear model, right? We had a diode here, and


[User] Please transcribe this text

[Assistant] Transistor here, so we said this was beta IB and this current IB


[User] Please transcribe this text

[Assistant] Was IS over beta B to the VBE over VT. So this was the model we had developed. And you can see we're going from this to that.


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[Assistant] So we are, another way to think about all of this is that we are linearizing this nonlinear Pi model.


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[Assistant] Okay, so that's, that's one element that's quite important. There's another element. Now, in this picture, if you change the v...


[User] Please transcribe this text

[Assistant] Collector emitter voltage, there should be no change in the collector current. See, no dependence on the collector current, of the collector current, on the voltage it's experiencing. But we know this is not true, right? We know, we've seen these pictures before. We've seen these pictures of ID versus VCE, right?


[User] Please transcribe this text

[Assistant] So if you look at VCE and IC, sorry not ID, versus different VBEs,


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[Assistant] So what happens is that there is another, so there must, so how can we model that? Because a current source will not change, it's current. Versus changing the voltage, right?


[User] Please transcribe this text

[Assistant] We call it the RO, because this is usually the output resistance, this is the output resistance. So what is RO?


[User] Please transcribe this text

[Assistant] So RO is gonna be DIC, DVCE inverse. One over that, right? But we also know from the definition of the early voltage,


[User] Please transcribe this text

[Assistant] So if you bring that in and write it in there, you clearly see that this is going to be VA over IC.


[User] Please transcribe this text

[Assistant] Now, early voltage for a PNP can be anywhere between like, let's say, 50 to 100. Typical PNP is 50 to 100 volts. So, for 1 milliamp, this is gonna be what? Let's say it's 100, VA is 100 volts.


[User] Please transcribe this text

[Assistant] Just to get a feel for these resistors. Because then you will sometimes say, well this resistor really doesn't matter. So for example, if this guy was in parallel with that guy, most of the times it doesn't matter. It's just the R pi.


[User] Please transcribe this text

[Assistant] Or if that was a series with some small resistance, that would also not work. So remember, there are three resistances we are talking about. Rm, rpi, and ro.


[User] Please transcribe this text

[Assistant] An ro is on the order of hundreds of kilo ohms. So they are all about like an order of magnitude of parts. A couple, two orders of magnitude of parts. So it's a ro, rm to rr, rm to rpi.


[User] Please transcribe this text

[Assistant] Couple orders of magnitude, and r pi to r o, another couple orders of magnitude.


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[Assistant] Let's talk about the MOSFET. So let's go and do these things. What is, is there an r-pi in the MOSFET equivalent? Should there be one?


[User] Please transcribe this text

[Assistant] No, right? Because that current, at least in the classical model, if there's no gate current, there's no tunneling current, that would be zero. That current, since it's zero, its derivative is also zero, so it's gonna be, not gonna be perturbed, so that resist, there's no resistance here, really, in this classical model. Now, how about an RO?


[User] Please transcribe this text

[Assistant] We have this, so you can write it as


[User] Please transcribe this text

[Assistant] That one is VA. So overall, what you will get in something like that is that your RO is proportional to your L. The channel A. Now, this is a knob


[User] Please transcribe this text

[Assistant] That you have in the design with MOSFET. That's another advantage of a MOSFET, because you have really control over the W and L. And what this knob does, it allows you to control the RO. While in a bipolar, your RO is really controlled by an intrinsic parameter, or built-in parameter, VA, the device parameter for that given device, and the current.


[User] Please transcribe this text

[Assistant] It means that if I really need to increase my output resistance, and there are cases that you need to increase your output resistance, especially if you want to get gain, you have this knob to turn.


[User] Please transcribe this text

[Assistant] In a MOSFET though, it's a design parameter because you can draw it wider or you can draw it narrower. You can make the L increase, increase the L, decrease the L, reduce the W.


[User] Please transcribe this text

[Assistant] So, and as such, that's another reason for popularity of MOSFET, because it's a more versatile device. You have more knobs to turn. Engineers love knobs, right?


[User] Please transcribe this text

[Assistant] We like to have more controlling parameters. And that's basically one of the advantages of a MOSFET over a bipolar.


[User] Please transcribe this text

[Assistant] It appears that MOSFET has a simpler model, right? Yes? No? Maybe? Have we forgotten something that MOSFET has and bipolar doesn't?


[User] Please transcribe this text

[Assistant] The bulk, yeah, the bulk, yeah. To differentiate it from, I mean, it logically makes sense to call it base, but we, to differentiate it from the bipolar, we call it the bulk, or the substrate. So, MOSFET really has a fourth terminal. Alright, it's here.


[User] Please transcribe this text

[Assistant] That depletion region and all those things can be controlling that stuff. So there's a second transistor, a JFET, that shares its drain and source with the MOSFET.


[User] Please transcribe this text

[Assistant] So there are really two transistors that are in parallel, which have two different gates.


[User] Please transcribe this text

[Assistant] It's not here in the equations that you gave me in either one of these. Where is that voltage? Where is that bulk voltage?


[User] Please transcribe this text

[Assistant] How is it influencing the drain current? Why are you telling me that I have to worry about that? It's not there. Where is it?


[User] Please transcribe this text

[Assistant] In the threshold voltage, exactly, right? This, remember, was a function of VSV. What was the functionality?


[User] Please transcribe this text

[Assistant] So I can define, we can define a uhm,


[User] Please transcribe this text

[Assistant] Transconductance associated with that. What would that transconductance be? How would we define it? Well, the definition, let's call it GMB for bulk or body effect.


[User] Please transcribe this text

[Assistant] The only part that's a function of VVBS is this guy.


[User] Please transcribe this text

[Assistant] So it will be the derivative of this, so it would basically, this comes, cancels that guy, so you're left with a gm, this, a term like this, plus, or times, the derivative of vt with respect to vbs.


[User] Please transcribe this text

[Assistant] So we have to calculate the derivative of that, which basically is gonna be gamma over 2 square root of 2 phi f plus Vsp.


[User] Please transcribe this text

[Assistant] Now, chi is defined as this, but very interestingly, chi


[User] Please transcribe this text

[Assistant] Actually happens to be the ratio of the junction capacitance of the substrate, only that substrate, that half of it, that comes to the channel, because they have one sided junction.


[User] Please transcribe this text

[Assistant] That's only the lower part of it. It doesn't have the opposite side because the other side is balanced by the capacitance of the, uh, gate over the gate oxide capacitance.


[User] Please transcribe this text

[Assistant] Now, if you think about this expression, this is an insightful expression. This last form. What is the insight? Remember, chi is simply the ratio


[User] Please transcribe this text

[Assistant] Of GMB to GM. It's the ratio of the strength.


[User] Please transcribe this text

[Assistant] of that back transistor, that JFET or back gate transistor to the front transistor, to the main transistor, right?


[User] Please transcribe this text

[Assistant] And it says that ratio is exactly the same as the ratio of the two capacitances. Because this is a field effect transistor.


[User] Please transcribe this text

[Assistant] Right? You induce the channel, you modulate the channel through the field. So the capacitance that's larger


[User] Please transcribe this text

[Assistant] One side of both of these capacitors is the channel in the middle. One is coming from behind, one is coming from the bottom, one is coming from the top. Right?


[User] Please transcribe this text

[Assistant] So it's the ratio of strength of these two capacitances that determines the ratio of the strength of these two transistors really.


[User] Please transcribe this text

[Assistant] So now, now we have a decision to make. Very important one. Should we use green or blue? To show this.


[User] Please transcribe this text

[Assistant] Current source. Where is that current source? Again, it's modulating the drain, drain source current. Remember, this transistor is in parallel. It shares the same drain and source. So it would be in parallel with this guy. So should I use a blue or a green in your mind? This is completely subjective, right? But no, not completely. Practically. So, what do you think? Green or blue? Green? Green, green. Any votes for blue?


[User] Please transcribe this text

[Assistant] Both of you could be correct. I mean, as I said, this is subjective. I personally would use blue.


[User] Please transcribe this text

[Assistant] Because it's more of a nuisance most of the time. There are some scenarios, there are some topologies where this is useful, but in most, more, more scenarios than not, it is a nuisance.


[User] Please transcribe this text

[Assistant] And we'll see when it's useful and when it's not, when we do a different topology. So Elliot doesn't agree with me, but that's okay. We can use agree, we can use turquoise or teal. Alright, anyway, so let's pick one.


[User] Please transcribe this text

[Assistant] Desire to think about this as a potentially positive thing, can do this.


[User] Please transcribe this text

[Assistant] Anyway, so that's the basic low-frequency model of a MOSFET. It's a Pi model. But we are not done yet.


[User] Please transcribe this text

[Assistant] Or the Pi model. But I just said a few minutes ago that this is really practically not the best model in my opinion for most of the transistor analysis.


[User] Please transcribe this text

[Assistant] Because, for a variety of reasons, and we'll get to see them as we go. The model that's more physical


[User] Please transcribe this text

[Assistant] And the more realistic, and it actually happens to be more useful for analysis, in many cases, not always, is the T model. So we'll use both of them.


[User] Please transcribe this text

[Assistant] So it's important to be familiar with that. But, now we can convert this to T-model. There are different ways to do this. You can do a direct conversion, or you can use the original T-model, the large signal T-model that you developed. Now if you want to do a direct conversion,


[User] Please transcribe this text

[Assistant] What you can do is that you can use the source transformation, uh, transportation.


[User] Please transcribe this text

[Assistant] So introduce two new current sources. I'm just going to temporarily show them with pink, and then I'm going to remove them, because I want to keep this model.


[User] Please transcribe this text

[Assistant] So if I make a GMVPi from here and a GMVPi from here,


[User] Please transcribe this text

[Assistant] Okay, and remove this, that would be equivalent, right? Because there's the same amount of current still leaving this node, there's the same amount of current entering this node, and there's no net current entering this node. Because you're taking out the same thing that you're putting in.


[User] Please transcribe this text

[Assistant] So these two should be equivalent. If I remove the green and replace it with the two, with the pink. But here's the question.


[User] Please transcribe this text

[Assistant] What is the name of the current source whose current is proportional to its own voltage? It's called a resistor.


[User] Please transcribe this text

[Assistant] And its resistance is 1 over gm, or its conductance is gm. So now you have a gm, or rm, in parallel with beta rm.


[User] Please transcribe this text

[Assistant] So you have Rm in parallel with beta Rm. What is that parallel combination?


[User] Please transcribe this text

[Assistant] Alpha was defined, beta, I'm sorry, beta was defined as alpha over one minus alpha.


[User] Please transcribe this text

[Assistant] And if you solve for that, you will see that alpha is beta over one plus beta.


[User] Please transcribe this text

[Assistant] And when you put them in parallel, so this becomes alpha RM. So the new model, or the transistor, the T model,


[User] Please transcribe this text

[Assistant] Which is the original model, in fact, that people used and generally produced. Looks like this. You have alpha RM, and now this current is IE.


[User] Please transcribe this text

[Assistant] What is this current, if that is IE? This is the collector current. How is the collector current related to the emitter current?


[User] Please transcribe this text

[Assistant] So this is the base, this is the collector, this is the emitter. Now, this model is more realistic, it's more physical because you can actually see the NPN junction in it.


[User] Please transcribe this text

[Assistant] You can see that it's this current mostly flowing, so it is the emitter current that's mostly appearing across the collector.


[User] Please transcribe this text

[Assistant] And the difference of them is the base card. The difference between IE and alpha IE.


[User] Please transcribe this text

[Assistant] Is the base current. This current is 1 minus alpha IE.


[User] Please transcribe this text

[Assistant] So, this shows what's happening in the transistor, and it happens to be actually a pretty useful model in terms of analysis. And of course the RO is sitting here.


[User] Please transcribe this text

[Assistant] Well, I didn't, I messed up my color convention, but it's okay.


[User] Please transcribe this text

[Assistant] And similarly here, so let's see what happens here. Now by the way,


[User] Please transcribe this text

[Assistant] If I want to convert this model to that model, to a T model, how would I do that? Well, I need to do the same thing, same operation with both of these sources. For this guy, I take it from here to there and from there to there.


[User] Please transcribe this text

[Assistant] Right? The same thing that we did with the bipolar. And what do we get? So in this case, you will get


[User] Please transcribe this text

[Assistant] Now, what is gonna be, what is this resistance gonna be? The one that's left when you have this current source going from the gate to the source.


[User] Please transcribe this text

[Assistant] It's RM, right? And there's no r-pi for it to be parallel. So there is no alpha. It is just gonna be RM.


[User] Please transcribe this text

[Assistant] Right? And what is this current gonna be? Again.


[User] Please transcribe this text

[Assistant] It is gonna be the same current, so it's gonna be, if this is, let's call it IS1, this is gonna be IS1. And what does that make this current? The gate current. Zero.


[User] Please transcribe this text

[Assistant] Right? So this is going to be the drain, this is going to be the source, and that's the gain. Now, the RO is sitting here, so that's for the main transistor, the MOSFET. How about the JFET? Where is the JFET?


[User] Please transcribe this text

[Assistant] Or that back gate transistor. How do we model that?


[User] Please transcribe this text

[Assistant] How do we turn it into something that's similar to this? What do we need to do with this current source? Where do we need to take it? To and back. Which node?


[User] Please transcribe this text

[Assistant] You want to go get to a node that at least for one of those two current sources, it would be a current source whose current depends on its own voltage. What is this in own voltage? Vbs. So I need to take this from here.


[User] Please transcribe this text

[Assistant] So if I remove this guy and replace it with these two of the same value, it would do the same thing, right? Because the net current injected in this node is zero.


[User] Please transcribe this text

[Assistant] The net current taken out of this node is the same, if I remove this and replace it with that. The net current injected into this node is the same.


[User] Please transcribe this text

[Assistant] And then, that other current source is simply there. So what you have, this is your bulk, terminal. This is RMB.


[User] Please transcribe this text

[Assistant] And this is the same current, so let's call it IS2. This is gonna be IS2.


[User] Please transcribe this text

[Assistant] Now, and this way you can even more clearly see the two parallel transistors.


[User] Please transcribe this text

[Assistant] This is the gate. This current, all of the current goes through the channel. There's no gate channel. There's no current. There's no gate channel, uh, gate current, sorry. There's no gate current. And there's no bulk current.


[User] Please transcribe this text

[Assistant] So everything we've done so far, as far as our models are concerned, are static. Or DC, low frequency stuff. Now how about high frequency stuff?


[User] Please transcribe this text

[Assistant] You have to think what else do we need to add here. So I'm going to remove this pink stuff from the hybrid pi model now that we've derived them. But now you know this is how it's generated.


[User] Please transcribe this text

[Assistant] So let's find out what they are. What kind of capacitors do we have in a BJT? If you think about the BJT, you bring the BJT back and think about it, say this guy.


[User] Please transcribe this text

[Assistant] The capacitors. Well, the capacitors are where charge can be stored. Right?


[User] Please transcribe this text

[Assistant] So what kind of capacitances do we have? What do you see here? Do you see anything that produces a capacitance, with capacitance we've calculated before? The junctions, right? You have the 2PN junctions.


[User] Please transcribe this text

[Assistant] So we need to take them into account. So that's one thing we need to take into account. What else do we need to take into account? So let's start taking them into account. The junction capacitors are actually pretty...


[User] Please transcribe this text

[Assistant] More straightforward to take into account, in the sense that you can say, well there are two junctions, there's a CJE, the base emitter junction, capacitance associated with that,


[User] Please transcribe this text

[Assistant] So both of these guys have a CJ, we know that the junction capacitance can be written, we did this before, right? And some sort of a junction capacitance 0, 1 plus, so in this case it would be VBE.


[User] Please transcribe this text

[Assistant] Or v, yeaah, or it would be eb really, over some psi 1, to the power of some m, some coefficient.


[User] Please transcribe this text

[Assistant] We saw that it's a nonlinear capacitance, we derived the junction capacitance expression, and then we have the CjC0 over 1 plus some VcB Psi2 to the power of m2, that is m1.


[User] Please transcribe this text

[Assistant] So we know that this coefficient, this exponent, depends on what? What determines this exponent? You've done a problem set on this already.


[User] Please transcribe this text

[Assistant] The profile of the doping, right? This is the built-in potential.


[User] Please transcribe this text

[Assistant] And this is the junction capacitance value at zero bias, when there's zero bias. So this is the built-in capacitance.


[User] Please transcribe this text

[Assistant] So those are the junction capacitances, fine. Is there anything else?


[User] Please transcribe this text

[Assistant] Any other junction capacitance before we get to the other capacitances? Is there any other junction that you can recognize? Well, not in this picture, right?


[User] Please transcribe this text

[Assistant] But how about this picture if I draw the bottom part of it?


[User] Please transcribe this text

[Assistant] To create isolation, if you have more than one transistor, this probably has to be a p-type for it to be reverse biased. So there's another junction here. There's another diode that's reverse biased here. A substrate. We call this Cj.


[User] Please transcribe this text

[Assistant] Which would have a similar expression, so cj is 0 over 1 plus, now this is basically the junction, the collector substrate voltage, um, psi 3 and M3.


[User] Please transcribe this text

[Assistant] So there are three junction capacitances, where do we put them on the model?


[User] Please transcribe this text

[Assistant] So, where are they? The first one, CJB. Yes, question.


[User] Please transcribe this text

[Assistant] Okay, good question. So she's asking, why does the substrate need to be p-doped?


[User] Please transcribe this text

[Assistant] The collectors are shorted, right? Because they're connected through n-type material.


[User] Please transcribe this text

[Assistant] So if you make it intri-, well, if you make it intrinsic, still the depletion region, then the depletion region extends very quickly. So you have a depletion region, if you have an intrinsic level, truly intrinsic level, the depletion region goes to infinity, right? So the depletion region of these two will start touching each other. So they will not be electrically isolated. There's no potential barrier between them. Good thinking,


[User] Please transcribe this text

[Assistant] So, so, I like the way you're thinking about it. But you need to kind of like practically you need to make a p-type and have a reverse bias junction to isolate them. There's a, this is not the only way by the way. There's another way. You can actually make these what we call the deep trench isolation. You can actually make an insulator trench and separate them by that.


[User] Please transcribe this text

[Assistant] Typically this is the most vanilla kind of transistor.


[User] Please transcribe this text

[Assistant] And that's the way they are. So there is that jumper. Now if it's not there, it's not there, right? So you just need to, don't worry about it. So where are these capacitors though? Where is C, J, E? That's between the base and the emitter, right? So there is a capacitance here, we call it C, J, B. I'm sorry, C, J, E.


[User] Please transcribe this text

[Assistant] Because your bulk is generally connected to some fixed potential ground, which is AC ground.


[User] Please transcribe this text

[Assistant] DC potentials, fixed DC potentials are AC ground in the small signal model, right? In the perturbation model. It's a constant whose derivative would be zero.


[User] Please transcribe this text

[Assistant] So anything that's connected to a fixed DC voltage is considered zero in the AC small signal model, because there's no perturbation on.


[User] Please transcribe this text

[Assistant] That's source charge. We talked about this, this briefly before.


[User] Please transcribe this text

[Assistant] Right? When we developed the dynamic model for the transistor, we saw that there's this minority charge storage in the base.


[User] Please transcribe this text

[Assistant] Was what? So we knew that basically Ic was qf over tau f. The collector current was determined by that charge anyway.


[User] Please transcribe this text

[Assistant] So, now if I wanted to find a capacitance associated with that chart, it makes sense for that capacitance to be defined as dqf


[User] Please transcribe this text

[Assistant] So what is dqf dvb? Well, we know what qf is. So it's gotta be d...


[User] Please transcribe this text

[Assistant] Versus VBE, it doesn't depend on VBE at least. Uhm, then you get this. But this is a known quantity.


[User] Please transcribe this text

[Assistant] Fractional changes in the collector current versus VBE. This was the first thing we derived. This is a transconductance. This is GM. So this is GM tau f. So there's a, there's another capacitance here.


[User] Please transcribe this text

[Assistant] And it's associated, it's because of the charge that's stored inside the base.


[User] Please transcribe this text

[Assistant] So the total capacitance, we sometimes call this combination, these two together, c pi, and we call this capacitance sometimes c mu.


[User] Please transcribe this text

[Assistant] What are the capacitors for the MOSFETs?


[User] Please transcribe this text

[Assistant] If you have a MOSFET, if you think about the structure of a MOSFET, you have a gate and two drains. So you have a gate oxide and then you have a gate.


[User] Please transcribe this text

[Assistant] Now you have some overlap and some fringe fields here. So there's some classic capacitance between the gate and these devices and the drain and source. Right? We call these two capacitances, uhm,


[User] Please transcribe this text

[Assistant] C, uh, G, D, and C, G, S. Let's call them C overlap for now. Because it's because of the overlap of the field. C overlap. So that's part of the capacitance. You also have these junctions to ground.


[User] Please transcribe this text

[Assistant] Because of the backset, so let's say if this was n-type, n-type, you have two p-n junctions.


[User] Please transcribe this text

[Assistant] In the Pinchoff region, which is the region we are mostly interested in, was what? Do you remember?


[User] Please transcribe this text

[Assistant] So, there's a wlcox element to it, and there's a vgs-vt.


[User] Please transcribe this text

[Assistant] Which is the inversion charge. But there was a factor of two thirds when we did that integration. You remember?


[User] Please transcribe this text

[Assistant] So that was what it was. So if I define now a capacitance, so c channel, which I define it as dq


[User] Please transcribe this text

[Assistant] I know that my VGS, so this is the only part that depends on VGS, so I simply get two thirds of WLCOX.


[User] Please transcribe this text

[Assistant] You have a capacitance between here, c, b, uh, b, did I say b?


[User] Please transcribe this text

[Assistant] Yeah, Sb or Bs. And then you have another capacitance through here. C, D, B.


[User] Please transcribe this text

[Assistant] And again, you can combine these two and call it CPi, or in MOSFET more commonly they call it CGS.


[User] Please transcribe this text

[Assistant] And look at that and call it CGD or CMU.


[User] Please transcribe this text

[Assistant] When does the transistor stop being used? Now, this parameter can be tricky because, as we'll see later, there are some subtleties that will allow it to be used even above these frequencies. But in


[User] Please transcribe this text

[Assistant] A simplistic perspective for a bipolar transistor, let's say, if you're thinking about it as having a gain of beta.


[User] Please transcribe this text

[Assistant] Right? You put a collector co- base current into it, and then you get a collector current out.


[User] Please transcribe this text

[Assistant] In other words, the question is, when does a wire perform better than your transistor? In terms of amplifying the current.


[User] Please transcribe this text

[Assistant] When that current regain, the ratio of the IC to IB, becomes what? One.


[User] Please transcribe this text

[Assistant] Right? So that's what we call the cutoff frequency of the transistor. And the way you actually practically would measure it is by applying some bias to the transistor.


[User] Please transcribe this text

[Assistant] So you have some VCC, you're monitoring the IC, and you're putting some IB while you have some fixed VBE. So you have on top of that, you have some sort of a current source.


[User] Please transcribe this text

[Assistant] That, well, that doesn't work really. So you have to put a voltage source here to induce this IB. And that's what it is. So now from a small signal perspective, if you look at this, for example, the Pi model,


[User] Please transcribe this text

[Assistant] What this looks like is that all the DC stuff go away, right? All the DC voltage sources become short and all the DC current sources become open. So you can think about this as some IB going into the transistor. So you have the R pi.


[User] Please transcribe this text

[Assistant] Sorry, you have the CPi, you have the RPi, and then you have the CMu, then you have the GM,


[User] Please transcribe this text

[Assistant] V pi. And then you have, where should I connect the collector? If it's connected to, in the small signal model, if it's connected to VCC directly. What does it connect to in the small signal model perspective? The ground, right? Because it's zero.


[User] Please transcribe this text

[Assistant] So this is IC that I'm trying to calculate, and this is the IB that's going in. So the question is, what is the transfer function of this thing? And it's relatively easy to calculate, and we'll talk about how do we calculate these things straightforward, and it's in your handouts too, but the short answer of it is that this thing, you can define the ratio of this as beta of S, is going to be beta zero, right, divided by


[User] Please transcribe this text

[Assistant] Any kind of basic KVLKCL calculation or uhm,


[User] Please transcribe this text

[Assistant] You know, nodal analysis that we'll discuss later. Anyway, so that's, that's what, so if you actually plot this versus frequency, versus log of omega,


[User] Please transcribe this text

[Assistant] What you will see is that it's going down like this. But the question is that when does it become, become one?


[User] Please transcribe this text

[Assistant] Well, you can easily see that for this to become 1, roughly this thing has to become equal to that. Right? So if these betas cancel, you can clearly see that Ft gonna be 1 over 2 pi gm


[User] Please transcribe this text

[Assistant] Over c pi plus c mu, which is, this is the f t, this is the frequency, or omega t, with 2 pi f t.


[User] Please transcribe this text

[Assistant] So now let's look at that expression and see how it changes with the current, for example. So if you look at this expression, and let's see what our capacitances look like. So, what is gm in terms of the current? We have derived an expression for gm, right? Ic over Vt.


[User] Please transcribe this text

[Assistant] So it's proportional to IC, so this is IC over VT. What is, and there's a 1 over 2 pi, that doesn't really matter.


[User] Please transcribe this text

[Assistant] And then, what is CPI? What does CPI consist of? It has two parts, right?


[User] Please transcribe this text

[Assistant] It has a junction capacitance part and a charge storage, base charge storage, CB.


[User] Please transcribe this text

[Assistant] And C mu is purely junction, so there's some junction capacitance total.


[User] Please transcribe this text

[Assistant] From both the base and the, from the emitter and the collector side. Plus that, plus this guy.


[User] Please transcribe this text

[Assistant] You can actually write it again as GM tau f, or you can write it as IC over VT tau f.


[User] Please transcribe this text

[Assistant] So the key question for you is, how does, if I wanted to plot,


[User] Please transcribe this text

[Assistant] So the denominator, if I see small is dominated by the junction capacitance, right?


[User] Please transcribe this text

[Assistant] So it would be low, but it would increase proportionately with IC.


[User] Please transcribe this text

[Assistant] At some point this becomes comparable, and at some point this becomes larger than that, and when it becomes larger than that sufficiently, you can see that the ICs cancel, and you're basically getting 1 over tau f. So it flattens, according to this model.


[User] Please transcribe this text

[Assistant] Practically, what happens is this.


[User] Please transcribe this text

[Assistant] Now why does that happen? It's a device physics question.


[User] Please transcribe this text

[Assistant] Because what happens is that remember, the electrons are going from the emitter to the collector. Right?


[User] Please transcribe this text

[Assistant] But at some point, if your current is large enough, there's so many electrons here, that their actual electrostatic charge will repel the electrons that are behind them. It's called the space charge effect. Kirk effect.


[User] Please transcribe this text

[Assistant] So what happens is that you, this, this region becomes so negatively charged at any point in time that these electrons have a slight preference not to go that way and going this way.


[User] Please transcribe this text

[Assistant] So it takes them longer to go across, so your tau f is actually increasing for an average electron to cross.


[User] Please transcribe this text

[Assistant] Would be 1 over 2 pi, exactly simi- since the models are similar, c pi, we can call it cgs plus cgd.


[User] Please transcribe this text

[Assistant] And now the question is what is the dependence of these parameters on the voltages or currents? Now, at low, if you have no velocity saturation,


[User] Please transcribe this text

[Assistant] Let's write this as 1 over 2 pi, you have some C overlap, plus what? Plus this expression, 2 3rd WLC ox, which can be dominant.


[User] Please transcribe this text

[Assistant] But you get an L squared in the denominator. So this becomes inversely proportional to L squared.


[User] Please transcribe this text

[Assistant] And then what you have here in the numerator is vgs minus vt. And then of course you have the mu n and c ox.


[User] Please transcribe this text

[Assistant] So it tells you, if you might want to make the device faster, what is the parameter that gives you the most return? First. In a non-velocity saturated device. What parameter makes this number larger? Decreasing L.


[User] Please transcribe this text

[Assistant] So that, you remember when we said the scaling helped a lot? You get an L squared. Why are you getting an L squared? You get one enhancement in the GM as you shrink your L, and you reduce your capacitance too.


[User] Please transcribe this text

[Assistant] Then ft is gonna be same expression, but gm is gonna have a different expression. So now you have 1 over 2pi.


[User] Please transcribe this text

[Assistant] Divided by, let's say, two-thirds, let's ignore the overlap for now. Wl cox. So, the cox is cancelled.


[User] Please transcribe this text

[Assistant] And the w's cancel. We have some constants. And then you have mu n E sat divided by L.


[User] Please transcribe this text

[Assistant] Now of course this reduction will go away if the second term, that's the overlap,


[User] Please transcribe this text

[Assistant] It becomes dominant. At some point, if this becomes dominant, then this improvement will completely go away. You have no dependence with it. But if before that happens, you will have an improvement.


[User] Please transcribe this text

[Assistant] Of course mobility is there. If you can get better semiconductor material, that's always good. Or strain the silicon to do some stuff with that. And ESAT.


[User] Please transcribe this text

[Assistant] And you cannot, you may not be able to improve the cutoff frequency significantly by just scaling it down. So you have to do some other, play some other tricks for that.