PLEASE NOTE: This version of the course has been formed from an earlier version, which was actively run by the instructor and his teaching assistants. Some of what is mentioned in the video lectures and the accompanying material regarding logistics, book availability and method of grading may no longer be relevant to the present version. Neither the instructor nor the original teaching assistants are running this version of the course. There will be no certificate offered for this course. Learn how MOS transistors work, and how to model them. The understanding provided in this course is essential not only for device modelers, but also for designers of high-performance circuits.
Large-Signal Dynamic Operation – Quasi-Static Operation
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Del curso dictado por Columbia University
MOS Transistors
124 calificaciones
De la lección
Large-Signal Dynamic Operation
In this module there is a significant departure from what we have done up to this point: we will allow the terminal voltages of the transistor to vary with time. We will determine the resulting terminal currents, which will now include a “charging” component. We will do this both for moderate and for very high “speeds”. The transient response of circuits involves similar calculations, only done by computer for an ensemble of transistors and other devices.
Conoce a los instructores
Yannis TsividisCharles Batchelor Professor of Electrical Engineering
Fu Foundation School of Engineering and Applied Science
We are now ready to start discussing the device operation with varying terminal
voltages. So far we have assumed that all voltages
applied to the device are constant. In this series of videos, we will discuss
what happens when those voltages, are functions of time.
Most of the discussion, will center around a type of operation, called
Quasi-Static operation. Quasi-Static loosely speaking, Quasi DC.
So, it is an operation that is slow enough to allow us to carry over many of
the results we have derived for DC operation.
And attempt to predict the transient operation of the device, that provided
the speed of change of the voltages is not too high.
If it is, we have to go to known quasi-static operation, which we will
discuss toward the end of this series of videos.
The present video defines quasi-static operation more precisely.
We will now concentrate on the intrinsic part of the device, meaning the device is
only considered between its source and drain.
In other words we concentrate on channel properties until further notice.
Also, until further notice, we will assume that the channels are long.
So, we will assume no short channel effects are present for now .
When we first review DC operation, we will change the way in we define the
terminal voltages rather than talking about voltages from one terminal to
another. We would talk about voltages from one
terminal to terminal called ground. So for example, the gate voltage is v sub
g. The source voltage is v sub s, and so on.
this is no problem, because if for example we want the gate source voltage
from gate to source, from keep this voltage low.
We know that vgs will be equal to VGS minus VS.
Similarly, VDS will be V sub D, minus V sub S, and so on.
It just so happens that this convention is more convenient for our present
purposes. We assume we have a long channel device
in DC steady state, there is no gate current and no body current.
Negative charges are flowing to the right, which means that we have a
positive current in this direction. So, the drain current is equal to the
so-called transport current throughout the channel, and therefore I sub d is
equal to I sub T. Now, as we said already, the gate current
is 0, the body current is 0, and what is is?
Since I sub T is defined in this direction but I sub S is defined in the
opposite direction, Is is equal to minus I sub T.
Again, we assume we are in this assisted state.
Now, the current I sub T, the transport current throughout the channel, is given
by some function of the terminal voltages vd, vg, vb, and vs.
Depending on the model we are using. We could even do it for the old region
model that is based on surface potentials.
Because we can express those surface potentials in principal as functions of
the terminal voltages. And in fact, we can even do so
numerically through a narrative process. So, we will assume that the current is an
explicit function of the terminal voltage.
What about the charges? The total inversion layer charge qi will
be the charge per unit area integrated over the area of the gate.
Now, if you take an element of the gate of length dx, its area is wdx, you
multiply by the charge per unit area so you get the total charge in that element.
Then you integrate from source to drain, and you get the total charge contained in
the channel, qi. W is constant, so we put it outside the
integral, and if we have an expression for qi prime.
Which we do for the various models we have discussed, we go through this
integration and finally we find some function of the terminal voltages.
I will call that F sub I. So, as you can see we are doing things in
a very general way not referring to any particular model at this point.
The same thing we can do with a gate charge.
We integrate the gate charge per unit area over the gate area.
So, we will get another function F sub G of the same terminal voltages.
And the same thing we can do with the box charge, and we'll get a third function, f
sub d of the terminal voltages. All of this is for DC operation.
So, now let us go to quasi-static operation.
Here is the same device as before, the only difference being that instead of
having DC voltages at the terminals, we have time-varying voltages.
This is V sub G of t. This is V sub-s of T.
And so on where T is time. I am using i tripling notation, so total
quantity does not vary with time, will be denoted by a lower case symbol with a
capital subscript. The corresponding currents would be small
i, sub capital D and iG, iS, and iD and the same for the charges.
This is qG, qI, and qB. So, now because the voltages are in
general varying, the charges will be varying too.
We can relate this picture to the corresponding water analog that we have
introduced in our introduction of this course.
So, we have a source type with a certain level of water, a drain pack with a lower
level of water. I remind you that if, if a drain voltage
is more positive than the source voltage you have a higher potential of the drain
than the source. Which means lower potential energy at the
drain than at the source for negatively charged electrons.
That's why the level of, in the drain tank is lower here.
Now we have an arbitrary reference level this corresponds to the source voltage.
This corresponds to the drain voltage and if we make the drain voltage larger, this
level goes down. Now water flows from left to right, and
we assume that we have an external pump. That keeps the levels here and here
fixed. Now in this here operation if you take
any point in the channel the same amount of the water flows through.
Either here of there. The total flow is maintaining the smae
throughout. Which is the same as saying that the
current is the same throughout the channel if you have DC operation.
But now let us assume that we have time-varying operation.
I will allow v sub G of t to change with time.
That means I can grab this handle over here and move the separator between the
source and drain up and down. I will do so very, very slowly.
In such a way that at any given time if I could take a photograph of what happens
to the channel and I look at it. It will look the same as if I had dc
operation where VG had been frozen for a long time.
Repeating this over here. If the voltages are varying very very
slowly and I could take a photograph of what happens inside the transistor.
And then I look at that photograph. This, the distribution of charges looks
the same as what I would have had had I frozen VG of t, VS of t, VB of t, and VD
of t at their values at the moment I took the photograph.
When that happens, I can say that I have quasi-static operation.
Which means that essentially the charges are governed by the laws that we
discussed for this operation. Only instead of fixed voltages I have
varying voltages. So, for example, QI, that was before
given by FI of the DC voltages vD, vG, vB, and vS, now it is given as a function
of time. By the same function, and this is key, by
the same function, which has to be the case for quasi-static operation, of VD of
T, VG of T, VB of T, and VS of T. Similarly I can say the same thing for
the gate[INAUDIBLE], I'm still using the same function as before.
And for the body voltage. So, quasi-static operation is operation
of the device slowly enough so that I'm allowed to use my equations for the
charges derived for DC operation. And the only change I have to do is
replacing dc voltages by time varying voltages otherwise I can assume I have
the same functions as before. Of course you might say, does this not
always hold true? No, it does not.
Because If you take for example the handle here and you start moving it up
and down very fast. You can see that the distribution in the
channel will be different than what you expect.
For example, if you move it all the way up fast the car, the water here doesn't
have time to get up. So, it will take some time for DC like
conditions to be established and the chamber and the same falls through sort
of this. Once Quasi-static operation does not go
through, we have what we call non-quasi-static operation, which we will
discuss later on. So, for now and for the next several
videos, we're assuming quasi-static operation.
In the next video we'll talk about terminal currents in quasi-static
operation.
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