Материал готовится,

пожалуйста, возвращайтесь позднее

пожалуйста, возвращайтесь позднее

We have put some of the quiz stats here. The mean was about 75%. And I must tell you that that is very impressive. I guess MIT undergrads never cease to amaze me. And this was not an easy quiz. This was a relatively hard quiz.

And that average implies that you guys did well on a relatively hard quiz. Good. Let's get back to our final lecture on amplifiers and small signal circuits. And as always let me start with a review.

Very quickly — — we came up with a notation to represent small signals. And our notation looked like this. Our total variable was small and capital, and this was a DC bias and this was a small signal.

This is also called the operating point. And the small signal is also called the incremental signal. In general, if you have some function, some variable of interest in the circuit, say a total variable V out, let's say it relates to some input variable as F of VI.

So mathematically we can find out V out by simply finding the slope of this function at the operating point and then multiplying it by the incremental change in the input. Gold standard math. So we do the slope of this function and evaluate it at the operating point.

So this would give us the slope of the function. And multiply that by small VI, which is incremental change. This is standard math. What this will tell you is given a small change in VI this function gives you, this expression gives you the small change in V out.

And in lecture we have pretty much used this method so far, used the math to get to where we wanted it to be. And then the way we provided biasing and so on was for our amplifier in particular we had a bias voltage, some small signal value, VS.

And this was output which was also given to be some output operating point plus a small change, which was a change in the output voltage. So what we have done here is mathematically computed small V out.

And what I am showing you here is to get the same effect in a circuit is you build your circuit and replace what used to be a total variable with a DC bias plus a small change. And then you will get your output here.

And this output will relate to this input using this expression. So this is more review. To continue on with the math review, for our amplifier VO was given to be VS-K/2(vI-VT)^2 RL. So this was the output versus input relationship for the amplifier.

And mathematically I could get the small change in the output VO by simply differentiating this function with respect to VI, evaluating that function, at capital VI and multiplying by the small change in the input.

And the resulting expression that we got for small VO — — was simply minus K, this was our DC value, and RL times small VI. So we derived all of this the last time. So nothing new so far. So my small signal output was some function given by K(VI-VT)RL times small vi.

And notice that this is how VI relates to VO. And this is a constant with respect to VI. V capital I is a DC bias, so this is a constant. So therefore this is the linear relationship that we had set out to get.

This term here, for reasons we will see today, this term here K(VI-VT) is called gm. Transconductance. We will look at it in more detail a little later. Even more review. So I can draw the transfer function and plot VO versus VI.

Another way to graphically view what is going on is by plotting the load line curve for this circuit, so this is VI. And I said we draw that by first plotting the — These were our MOSFET curves.

And that average implies that you guys did well on a relatively hard quiz. Good. Let's get back to our final lecture on amplifiers and small signal circuits. And as always let me start with a review.

Very quickly — — we came up with a notation to represent small signals. And our notation looked like this. Our total variable was small and capital, and this was a DC bias and this was a small signal.

This is also called the operating point. And the small signal is also called the incremental signal. In general, if you have some function, some variable of interest in the circuit, say a total variable V out, let's say it relates to some input variable as F of VI.

So mathematically we can find out V out by simply finding the slope of this function at the operating point and then multiplying it by the incremental change in the input. Gold standard math. So we do the slope of this function and evaluate it at the operating point.

So this would give us the slope of the function. And multiply that by small VI, which is incremental change. This is standard math. What this will tell you is given a small change in VI this function gives you, this expression gives you the small change in V out.

And in lecture we have pretty much used this method so far, used the math to get to where we wanted it to be. And then the way we provided biasing and so on was for our amplifier in particular we had a bias voltage, some small signal value, VS.

And this was output which was also given to be some output operating point plus a small change, which was a change in the output voltage. So what we have done here is mathematically computed small V out.

And what I am showing you here is to get the same effect in a circuit is you build your circuit and replace what used to be a total variable with a DC bias plus a small change. And then you will get your output here.

And this output will relate to this input using this expression. So this is more review. To continue on with the math review, for our amplifier VO was given to be VS-K/2(vI-VT)^2 RL. So this was the output versus input relationship for the amplifier.

And mathematically I could get the small change in the output VO by simply differentiating this function with respect to VI, evaluating that function, at capital VI and multiplying by the small change in the input.

And the resulting expression that we got for small VO — — was simply minus K, this was our DC value, and RL times small VI. So we derived all of this the last time. So nothing new so far. So my small signal output was some function given by K(VI-VT)RL times small vi.

And notice that this is how VI relates to VO. And this is a constant with respect to VI. V capital I is a DC bias, so this is a constant. So therefore this is the linear relationship that we had set out to get.

This term here, for reasons we will see today, this term here K(VI-VT) is called gm. Transconductance. We will look at it in more detail a little later. Even more review. So I can draw the transfer function and plot VO versus VI.

Another way to graphically view what is going on is by plotting the load line curve for this circuit, so this is VI. And I said we draw that by first plotting the — These were our MOSFET curves.

Загрузка...

Выбрать следующее задание

Ты добавил

Выбрать следующее задание

Ты добавил