Similarly, you can say the same thing for Cbd, Cmb, Dvbsdt is there to model the

non-reciprocal behavior between drain and body.

And, Cmx takes care of the non-reciprocal behavior between gate and body.

More details are found in the book. We'll come back to Csd in a moment.

So now, we can find expressions for the new capacitance parameters we have

defined by differentiating charge expressions as we have done in the past,

always assuming quasi-static operation. For example, we obtain for Cm this

relation Cox is the total gate capacitance, it's the capacitance for

unitary at times the area of the gate. And this a function of eeta, eeta is the

degree of non-saturation we have used it in the past.

So, if you derive expressions which is done the book, eh, you can get certain

plots that help you see what is happening.

This is, we're assuming now strong inversion.

In non saturation Cdg vie, varies like this and then it becomes a constant value

in saturation, but not 0 unlike what Cdg was doing.

And the other composite are shown here. The solid line is an accurate model based

on surface potential formulation and the broken line is the strong inversion

model. So you can see that the, the model does a

pretty decent job in strong inversion. Now, just like we have done in the past,

you can reason physically about the behavior of these capacitances.

As an example, I will take Csd. So, notice that Csd comes out to be

negative. Now, how can we physically, help explain

this fact? Let us recall what Csd is.

Csd is defined to be minus dqs,dvd. Which means that you look at the charts

going into the source when you vary the voltage at the drain, you take the ratio

of the two changes with a minor sign and that is Csd.

Alright let's try to do that. I'm going to increase the voltage at the

drain over here by a small amount. When you increase the voltage at the

drain you reduce the gate to drain voltage.

And at the same time you increase the drain to body voltage.

Both of these effects will show you that the inversion layer here becomes less

strongly inverted. In fact, if you keep increasing the drain

voltage eventually you get pinch-off here.

In the simplified picture we have discussed for strong inversion in the

past. But in general, when the drain voltage

goes up, the inversion layer charge near the drain decreases in magnitude.

And the total inversion layer charge decreases in magnitude as well.

Now the inversion layer charge is negative so when you say decreases in

magnitude, it means that it becomes less negative which is equivalent to saying it

becomes more positive. So, delta Qi, the change and the

inversion layer charge is positive. We have said in the past that delta Qi is

shared by a delta Qd and a delta Qs. Both of those are positive, and

contribute to a positive delta Qi. So delta Qs is positive, which means that

when you vary the drain voltage by delta vd, corresponding to this denominator,

there is a delta Qs which is positive. And because it was a minus sign in the

definition of the capacitance, the whole thing becomes negative that's why Csd is

negative. It is very instructive to try to, reason

in a similar manner for the other capacitances as well.

You can try this or you can consult the book about it.

Now, some other capacitances, plotted versus Vds are shown here, these are the

three capacitances that I mentioned representing non-recicprocal behavior

between two, two terminals, Cm, Cmb and Cmx.

For, for the strong inversal model in fact, Cmx is predicted to be 0 and very

often, we neglect it. Now, here are the capacitances versus

Vgs, so we start from weak inversion, moderate inversion, and strong inversion.

in weak inversion, all of these capacitances, except for Cgb are

negligible because they have to do something with the channel charge but the

channel charge but the channel charge is negligible in weak inversion and the gate

see's the body directly. So Cgb is definitely is not 0.

Then it goes down and eventually goes towards 0 for reasons we have discussed.

Deeply and strong inversion, non saturation.

The other capacitances behave in this way.