Lecture 08 : Module 02

Now, we will come back, we just now saw that starting from first principles and some assumptions, some incremental assumptions, some exact, some assumptions which we just drew out of a hat, we could come up with a desirable IV characteristics of a 2 port network which can give us amplification of power right. So, now as it turns out, as it turns out, there are, there are 2 port network, there are devices right which can be, which can be arranged in this form of 2 port networks which have characteristics similar to whatever we just plotted right. A case in point is a device called MOSFET right. So, so as it turns out, if we, inside this 2 port network, we assume that we have a MOSFET and we can further assume that one terminal of the MOSFET is shared between the input and the output and we denote this terminal as V 2, denote this terminal as V 1 and denote this current as I 1 and denote this current as I 2 right. Do not bother about the particular symbol as of now, but if we simply denote these currents and voltages as I 1, I 2, V 1, V 2 as shown here, as it turns out, as it turns out, the I 1, V 1 characteristics. So, even if before sketching the I 1, V 1 characteristics, let me simply write that I 1 is equal to 0 for all V 1, this is just how the device is ok. So, that makes life pretty simple, since I 1 is equal to 0 right, so Y 1 1 is equal to 0 and Y 1 2 equal to 0. We do not have to bother about different slopes at different operating points right, as far as the input characteristics is concerned right, as far as the slope between I 1 and V 1 and I 1 and V 2 are concerned. However, I 2 is governed by this following equation, simply say that this is equal to some constant beta times V 1 minus some constant V th whole square right. This is as long as, as long as V 1 is greater than equal to V th and V 2 is greater than equal to V 1 minus V 2. So, this is just how the current equations are right. So, so if I sketch, if I sketch the I 2 versus V 1 characteristics right, what will I get? So, as long as if I, if I let us say I mark out a point V th, all this characteristics is saying is that above, above as long as V 1 is more than V th and V 2 satisfied this condition right, V 2 is greater than V 1 minus V th, then if I keep increasing V 1 right, I should get a parabolic slope, parabolic looking curve ok ok. What happens, this is for let us say certain V 2 q, V 2 equal to certain V 2 q. What happens if I, so this will have to also ensure that V 2 q is greater than equal to V 1 minus V th for all range of V 1 that I have plotted it with, plotted the curve form ok. So, what happens if I change V 2, what happens if I change V 2 from V 2 equal to V 2 q plus small v 2, what do you think will happen if we follow the equation that we have just sketched? Note that this equation is independent of this current I 2 is independent of the voltage V 2 right. So, whatever happens at V 2 will have no bearing on, on the current I 2 which means it will follow the same, same curve ok. So, as long as these two conditions are met. What about, what about the output characteristics of I 2 versus V 2, what is this equation telling you? This equation is telling you that for certain V 1, so V 1 equal to V 1 q right. I will have certain I 2 and the value of I 2 will be say I 2 q which is equal to beta V 1 q minus V th whole square ok. And this value will be constant as long as, as long as what? As long as V 2 is, as long as V 2 is greater than V 1 minus, this is V 1 q minus special voltage right. So, at smaller values of, as you, as you decrease, as you decrease V 2 right, as you decrease V 2 may be at some switch for some, some point here you meet V 2 equal to V 1 q minus special voltage and the boundary of the validity of this equation is, is this, is this line where V 2 is equal to V 1 q minus V th ok. So, what happens if I increase V 1 to V 1 equal to V 1 q plus small v 1, what happens then? Will I 2 change? Surely I 2 is going to change because now I have a, now I have a new V 1 right. So, I 2 will increase to a different value and what will be this increase? This increase will be equivalent to the increase that you, you plug in that new V 1 into the, into the current equation right, you plug in the new V 1 into the current equation and you will get an increase. Or in other words, if V 1, if you assume that the V 1 is small enough, if you assume the V 1 is small enough where you can neglect the higher order terms, that is if you expand this quadratic, if you expand this whole square term, you will get a square law, you will get a, you will get a square term, you will get a linear term, you will get a constant term. So, if you assume that the, the quadratic terms are small enough to be neglected, this increase, increase in I 2 will be how much? This increase, increase in I 2 will be Y 2 1 times V 1 and again what will be the range of validity for, for, for this flat line? This will be L, this new V 1 Q plus V 1 minus V th ok. Now, note that this equation does not tell us anything about what is going to happen, what is going to happen below, below V 2, V 2 below the condition where you reach this limit of V 2 to be greater than equal to V 1 minus V 2 right. As it turns out, as it turns out there is also a nice closed form expression for that, but I mean even if we, even without going there, we know that this is going to, this is going to somehow dive, somehow dive into and go to 0 right. That is all we know at the moment. We do not know the exact equation which will result in this diving right, but we know that it will, it is going to, it is going to go to 0 ok. So, even before, even before moving on, let me make couple of very important points here. As it turns out, these, these IV characteristics that we have sketched here are particular to a MOSFET. But note that the IV characteristics that we arrived at right, the desirable IV characteristics that we arrived at are not particular to a MOSFET. That is particular to any device right, that is particular to any device that has, that you can make, that you can, that you need to make an amplifier right. So, if you go down the history and you will see that before MOSFETs there were BJTs right. BJTs are still present, they are still used, but not as widely used as BJT, as MOSFETs. But however, still there are BJTs whose input output characteristics look almost similar to whatever we see here. Even before BJTs, there used to be vacuum tubes right, whose input output characteristics again looked almost exactly what we came up with from scratch. Tomorrow, if there are new devices, you will, you will see that you will have FinFETs, get all around devices, gallium arsenide, MOSFET, gallium arsenide FETs and so on and so forth. All of them fundamentally have this similar IV characteristics. So, it is not a coincidence that all of them have similar IV characteristics. In fact, the story goes the other way around, the logic goes the other way around. What is the logic? The logic is in order to get an amplifier which can amplify power, we need these type of, we need devices which have these type of IV characteristics. Now, as a circuit designer, if you lay down the law and say that I need these kind of devices which have these kinds of or rather I need devices which have these kinds of IV characteristics, then you go to your, then we go to our device colleagues and ask them, see, this is what we need to get a power amplification. Can you make a device and give it to us? They say sure enough, not only one, we can give you different flavors of devices whose IV characteristics look like this. Now, note that the devices that I named before, right, right from vacuum tubes to BJTs to MOSFETs to gallium arsenide FETs, JFETs and PINFETs and so on, all of them can have completely different underlying physics and have completely different transport phenomena as to how the current flows inside the device, right. However, for the purpose of designing a circuit at the level in which this course will concentrate on, you do not need to know how the transport of current or how the transport of electrons or the holes inside the devices take place, right. All we need to know is the, is the, is the underlying IV characteristics. Now, note that these underlying equations of the IV characteristics will also depend on the type of, type of devices that we are, that one is going to use. However, however, they will look similar, they will look, they will look similar in terms of their incremental properties will look similar and what will they look like? They will look like Y11 will be close to 0 or exactly 0, Y12 will be close to 0 or exactly 0, Y22 will be close to 0 or exactly 0 and Y21 has to be very high, right. If you do not have these properties, you, in a device, you cannot make a good amplifier. Now, as it turns out, all the devices that we talked about, right, are also three terminal devices. However, you can make a two port network with a three terminal device also, right. So, all these devices are three terminal devices and they have input output characteristics which are, which mimic, which mimic the conditions that we have been discussing till now. In this particular course, we will deal solely with MOSFETs and we will, from the next class onwards, from the next lecture onwards, we will concentrate on, on the operation of a MOSFET under different conditions, under different, different operating conditions, right. What happens if I increase V1, what happens if I increase V2, what happens if I increase V1 or decrease V2 and what are the particular governing current voltage equations that we need to, that we need to deal with, but in doing so, we should not lose sight or you should not lose sight of the fact that if tomorrow you are given a different device, right, you should not throw up your hands and say, I did not study, I did, I mean, the course that I took was only on MOSFETs. So, I cannot, I cannot design circuits with these, you should, what you should imbibe is the, the, the thing that you should take away from this course is the fact that the first thing that you have to do is when somebody gives you a device is to, is to plot the I-V characteristics and see whether in some portion of the I-V characteristics are you able to satisfy those four conditions, right, simultaneously, right. So, you should be able to satisfy the conditions of Y11 should be equal to 0 or close to 0, Y12 should be equal to 0, close to 0, Y21 should be as high as possible and again Y22 should be close to 0 or equal to 0, right. As long as the new device that you are encountered with satisfy these, these four conditions, right, you should be able to make a decent amplifier. Now, the details of when, when the, when the current voltage characteristics change from the idealized case will depend on the device physics or on the, which in turn governs the current voltage equations. Then, at the second order level, you need to know the exact, exact current voltage equations which are going to affect your design, right. But as long as you know, as long as you know what your, what your expectations are and the fact that the device that you are dealing with meets your expectations, you should be able to design a amplifier. And from the next lecture onwards, we will concentrate on designing one such amplifier, right, using MOSFETs. Thank you.