I would like to start by, stating that the only effects we are considering,

until further notice, here, are compacitive intrinsic effects, in other

words, they have to do with the intrinsic part of the device.

The intrinsic part of a device is a, is assumed to be outside and for now it does

not matter. We are also assuming long channel devices

until further notice. Let me begin by a discussion of the

gate-source and body-source capacitances. Here is the device that I'm considering,

an idealized device where the source and drain regions are not even shown.

it is biased with four voltages with respect to an arbitrary reference,

represented by ground. So this four DC voltages are VG0, VS0,

VB0 and VD0. And they give rise to a depletion region

charge, QB0. And the gate charge is QG0.

I would now like to change the source voltage and see what effect it will have

on the body charge and the gate charge. So I apply a small change in the source

voltage, delta VS. This will cause a change in the depletion

inter-charge delta QB and a change in the gate-charge delta QG.

Let me first try to model the effect of delta VS on delta QG.

The voltage and the charge are related to each other.

Through a small signal capacitance. So, I will attempt to connect a small

signal capacitance between source and gate, and try to find the rate value for

it. Notice that because we're talking about

small signal equivalent circuits. Voltages that are constant, for example

VG0, have a delta v that is zero and therefore they correspond to ground.

Details about this concept can be found in basic electronic circuits books.

So here we are. This is the voltage I'm applying to the

source. It has a value delta Vs.

This is a capacitance CGS, which goes to the gate that is connected to small

signal ground corresponding to a fixed VGO over here.

Notice that I'm applying a delta VS at the bottom plate of CGS, and the top

plate is connected to ground. Now, we know that the charge, the

small-signal charge that entered the gate in order to change the gate charge, was

Delta QG. So this is Delta QG.

And you can see that this Delta QG becomes minus CGS Delta VS.

So I can write Delta QG is minus CGS Delta VS, and from that if you solve for

CGS, you find this. So CGS is approximately minus delta QG

delta VS. And the approximate sine will become an

exact sine as I take delta Vs and allow them to go towards zero, in which case

this will become a partial derivative. And we have done something very similar

for conductances before. Now just like I define capacitance in

this way between gate and source, I can define one between body and source, CBS.

And that will be given by minus delta QB over delta vs, using the same line of

reason. So, this is then what will lead us to the

definitions of the Gate-source and body-source capacitance.

Let me now consider gate drain and body drain capacitance.

So now, I have the original circuit, I will now vary the drain voltage.

By an amount delta V D. That will change the gate, the body

charge by delta Q B and the gate charge by delta Q G.

And using the same reasoning as before I can define Cgd by taking the ratio of

minus delta QG over delta VD, and Cbd, the body drain capacitance By taking the

ratio minus delta QB over delta VD. And more precisely, I will define this by

partial derivatives in a moment. Once more capacitance to be defined.