Which gives us this. So now we see the following.

The fact that we're applying the sine total voltage between gate and source

means that there will be a drain current of amplitude Gm epsilon, and there will

be a gate current of amplitude omega Cgs plus Cgb times epsilon.

This is the input current, and this is the output current.

So, in a sense you can think of the current gain between the two.

It will be the ratio of. The output current amplitude to the input

current amplitude. This is A sub i, the pick value of the

train current and divide it by the pick value of the gate current, and it is, as

I said, the ratio gm epsilon to omega cgs plus cgb epsilon, epsilon cancels out and

we get this expression for our current gain.

More precisely, it is the magnitude of the current gain.

and there is also a phase in volts, which we're not considering here.

Now, as the frequency of the input voltage is increased, the current gain

decreases. And if the frequency is made high enough.

The current gain becomes one. What is the frequency at which this

happens? You can set this equal to one, and solve

for the corresponding omega. I will denote this by omega ti, and it

turns out it is simply from here, Gm over CGS plus CGB.

This is called the Intrinsic Transition Frequency.

Again the intrinsic transition frequency is the frequency at which the magnitude

of the current gained becomes 1. It's an indication of how high you can go

in frequency while still expecting that you get more current here, more amplitude

of the current here. Than you get at the input.

For strong inversion, if you go through the expressions we have derived for gm

and for the capaccitances, you find for example that omega ti is approximately gm

over cgs because this is much smaller than cgs and it is.

Three halves of omega 0, for omega 0 turns out to be this quantity here.

Now again this involves only the intrinsic elements, we have not yet

included the extrinsic elements. When you have extrinsic elements you get

something similar but you have to also include the external, the extrinsic

capacitance of this expression. Now in weak inversion, we have a simpler

situation, you have very very few electrons and for that reason it's like

you don't have the bottom plate of the capacitance that we have been assuming.

So CGD, and CGS, and CBD and CBS. In other words the, all of these are

related to channel to gate or channel to body capacitances can be assumed to be

approximately zero. In fact.

You get larger capacitances because of the extrinsic part of the device, which

we have not yet discussed. So these are can be neglected.

On the other hand, the gate and the body see each other directly now because there

is no conductive plate to isolate one from the other.

And Cgb turns out to be non-zero. And in fact from what we had presented

for the two terminal Mos structure, you can find this result.

Cgb depends on VGB in this manner. So the gate sees the body directly and

the corresponding capacitance Cgb is non-zero.

The intrinsic cut off frequency omega Ti for the weak inversion region turns out

to be given by this, where IM is the peak current.

In weak inversion. Deep in depletion, you have approximately

the same situation as before because there you really don't have any inversion

layer charges to speak with. So all of this assumptions become, in

fact, more exact. In accumulation.

In deep accumulation, you have many holes here which help you form the bottom plate

of a capacitance. The top being the gate here.

The bottom being the accumulation layer. So you can expect that between them, you

have a capacitance corresponding to the entire oxide capacitance.

So the Cgb is approximately C ox. And that's the only intrinsic capacitance

we need to take into account. And if you take an accurate surface-based

potential model and you plug CGB versus VGB, then it goes like this.

So you can see that asymptotically this becomes approximately C ox deep in

accumulation. And asymptotically the exact Cgb approach

is the expression I showed you before shown here.

So if you are away from Vfb in other words deep in depletion over here, this

expression is pretty accurate. Now all-region models, the all region

models which we will not discuss because they are very, very involved

analytically, but you can actually derive this results either through analytic

expression or through numerical differentiation of charges.

Here we show capacitance versus vgs, so as you can increase vgs, you go from weak

inversion, over here, to moderate inversion, to eventually strong

inversion. Notice that, for a given drain source

voltage, we are initially in saturation, but if we raise vgs to a large value, to

large values, then the corresponding saturation voltage which is approximately

vgs minus vt, becomes so large that the vds value used to derive this plot is no

longer enough to have the device in saturation.

So, you enter non-saturation. So, you start from saturation.

Then, you go into non-saturation. And so in weak inversions Cgs, Cbs, Cgd

and Cbd are all zero, then they rise in moderate inversion and then they attain

the strong inversion values I showed you before.

Cgb has a considerable value in weak inversion and goes gradually down as we

have already explained. And now, if you have a short channel

device, not on the same process, and not with the same dimensions, this comes from

an entirely different device. So, please don't compare directly the

values, only the general shapes. For a short channel device, short channel

effects matter, charge-sharing matters, everything matters.

And things become different. You cannot really use the long channel

expressions to find the capacitances of a short channel device.

But I'm showing this to you to show you that the general shape, the general

behavior is still proximately the same as for the long channel device.