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All right, good morning. So today, we are going to talk about what is both a basic device in itself, the amplifier, and it also serves as a real key example of both nonlinear analysis and small signal analysis.

So, today, dependent sources and amplifiers. So, let me first spend a few seconds just pointing out to you some of the key points from our previous lectures. I also want to point out that each chapter in the course notes has a summary at the end of it.

And if you take a quick scan of the summary at the end of each chapter, it highlights the major takeaway points from each chapter. It stresses what's important, and if you have to remember a few things, what are those things to remember? So, to quickly review, we talked about a few primitive elements: resistors, voltage sources, and so on.

And by now, you should have the facility to play around with these device elements. And then we talked about the Node method, and this is kind of the workhorse of 6.002. When in doubt, use the Node method.

OK, and this will work both for linear circuits and nonlinear circuits. OK, so if you see a problem, or if you see a situation in real life that requires analysis, then as a first step, you should try to think of whether you could apply some of the key intuitive shortcut methods, superposition.

One of my favorites, the Thevenin method, the Norton method, or the method that involves composition, that is very quickly analyzing circuits that have resistors in series and parallel. OK, so if you can apply one of these quick, intuitive, shortcut methods, go do so.

If you can't, then usually you can resort to the Node method irrespective of whether the circuit is linear or nonlinear. So the last week was focused on the nonlinear method or nonlinear circuits, and we spent the first lecture talking about a straightforward application of the Node method, which gave us a bunch of nonlinear equations that we had to solve.

In the last lecture, we talked about the small signal trick. What we said is if you look at the whole space of nonlinear circuits, then within that space, if we focus on small variations, small perturbations about an operating point, then even the behavior of nonlinear circuits in that small regime would be linear.

So small signal method. And as an example, I showed you how I could take a highly nonlinear device like the garage door opener LED, and using that, build a pretty nice transmitter that would transmit music.

And as long as we kept the signal small, and operated the device in a region where its transfer curve was relatively smooth, and I biased, or set the operating point appropriately, I would get a linear, small signal response.

OK. So today, we're going to do a couple things. We're going to look at dependent sources. And the reading for this is section 2.6 of your course notes. And, the dependent source will be a new element in your tool chest.

We will also do amplifiers, and amplifiers are in section 7.1 and section 7.2 of your course notes. So, before I begin with dependent sources, I'm just a huge believer in motivating things with real world examples.

OK, so let me start by motivating: why we need an amplifier? Why do we need to do things like this? Or why do we even bother? And, spend a few minutes really getting you to appreciate that amplification is fundamental.

OK, it's as foundational to life as high fat potato chips and stuff like that. So, let's do some basic examples here. So first, let me talk about, why do we need to amplify signals.

So, today, dependent sources and amplifiers. So, let me first spend a few seconds just pointing out to you some of the key points from our previous lectures. I also want to point out that each chapter in the course notes has a summary at the end of it.

And if you take a quick scan of the summary at the end of each chapter, it highlights the major takeaway points from each chapter. It stresses what's important, and if you have to remember a few things, what are those things to remember? So, to quickly review, we talked about a few primitive elements: resistors, voltage sources, and so on.

And by now, you should have the facility to play around with these device elements. And then we talked about the Node method, and this is kind of the workhorse of 6.002. When in doubt, use the Node method.

OK, and this will work both for linear circuits and nonlinear circuits. OK, so if you see a problem, or if you see a situation in real life that requires analysis, then as a first step, you should try to think of whether you could apply some of the key intuitive shortcut methods, superposition.

One of my favorites, the Thevenin method, the Norton method, or the method that involves composition, that is very quickly analyzing circuits that have resistors in series and parallel. OK, so if you can apply one of these quick, intuitive, shortcut methods, go do so.

If you can't, then usually you can resort to the Node method irrespective of whether the circuit is linear or nonlinear. So the last week was focused on the nonlinear method or nonlinear circuits, and we spent the first lecture talking about a straightforward application of the Node method, which gave us a bunch of nonlinear equations that we had to solve.

In the last lecture, we talked about the small signal trick. What we said is if you look at the whole space of nonlinear circuits, then within that space, if we focus on small variations, small perturbations about an operating point, then even the behavior of nonlinear circuits in that small regime would be linear.

So small signal method. And as an example, I showed you how I could take a highly nonlinear device like the garage door opener LED, and using that, build a pretty nice transmitter that would transmit music.

And as long as we kept the signal small, and operated the device in a region where its transfer curve was relatively smooth, and I biased, or set the operating point appropriately, I would get a linear, small signal response.

OK. So today, we're going to do a couple things. We're going to look at dependent sources. And the reading for this is section 2.6 of your course notes. And, the dependent source will be a new element in your tool chest.

We will also do amplifiers, and amplifiers are in section 7.1 and section 7.2 of your course notes. So, before I begin with dependent sources, I'm just a huge believer in motivating things with real world examples.

OK, so let me start by motivating: why we need an amplifier? Why do we need to do things like this? Or why do we even bother? And, spend a few minutes really getting you to appreciate that amplification is fundamental.

OK, it's as foundational to life as high fat potato chips and stuff like that. So, let's do some basic examples here. So first, let me talk about, why do we need to amplify signals.

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