0:14

The gate current, due to leakage effects, which we have already discussed.

Is a function of the terminal voltages. It is convenient in this discussion to

choose a different set of terminal voltages.

The gate source gate body and gate drain, gate drain voltage.

If you have a model that is given in terms of different terminal voltages, you

can always write those terminal voltages. As linear combinations of the ones that I

have shown here and come up with a set of equations that exporesses the gate

current in this form. The reason we chose this three as

independent variables is that it leads directly, this choice leads directly to a

simple equivalent circuit, as you will see.

1:20

And the corresponding constant of, of proportionality can be defined as partial

derivatives of the gate current with respect to each of the voltages we are

considering. For example, this one, ggs, is the

partial derivative of the gate current with respect to VGS, assuming VGB and VGD

are held constant. Ggb Is defined as the partial derivative

of the gate current with respect to the gate body voltage.

Assuming V G S and V G D are held constant and V G D is defined as the

partial derivative of the gate current with respect to the gate drain voltage,

assuming V G S and V G D are held constant.now if you look at this

equation, it can be represented by a very simple equivalent circuit like this.

this a small signal equivalent circuit just like the one we had derived for the

[UNKNOWN] current the independent variables are delta-vigious in other

words change in the gate source voltage. Delta VGB and delta VGD and the dependent

variable is delta IG, the change in the gate current.

Now each of these terms can be represented directly by a resistor of a

corresponding conductance, for example the current through this resistor is ggs

delta VGS which is this term The current through this one is ggb, delta Vgb, which

is this term. And the current through this one is ggd,

delta Vgd, which is this term. Therefore, the total current delta Ig, by

Kirchoff's current law, is the sum of these three and it represents this

equation exactly. We can now do the same.

For the body current. For the body current I will choose a

description IB is a function of VBS, VBG, and VBD.

Again I choose this different, this different set of independent variables,

because it is convenient in terms of leading to a simple equivalent circuit.

3:26

So I can write the small change in the body current has a linear combination of

the corresponding small changes in the three terminal voltages and I define the

corresponding coefficients or proportionality if you like as partial

derivatives. GBS is partial delivery with a body

current with respect to VBS, assuming VGB and VBD are constant.

GBG is the partial delivery of the body current with respect to VGB, assuming the

other two are constant. And GBD is the partial delivery of the

body current with respect to the body drain volt, assuming the other voltages

are held constant. Now, I can express this, I can represent

this rather, using an equivalent circuit, but one problem appears.

That the new parameter GBG would have to be represented by a resistor, which would

interfere with another resistor in the same place that came from considerations

of the gates linkups current and that resistance have the conductors Ggb so you

can show that you can avoid these problems by including a controlled

source. The details are in the book, so here I

show you the gate linkups equivalent circuits which consists of Ggs Gbd,

excuse me, Ggb and Ggd. And the corresponding body current for

Delta IB consists of GBD, GBS and the controlled source.

This controlled source has an equivalent constant proportionality GGB GBG delta

VGB. So I believe the delta derivation for you

to read in the book, but essentially what this does is the following: we already

had this resistance that represented part of a gate current, so now it doesn't

represent the corresponding body current by itself.

You need an extra term and this term you can derive mathematically, has to be

given by this. So this equivalent circuit now represents

both gate leakage current chains, and the body leakage current chains in terms of

the corresponding changes of the terminal voltages.

Now if you combine the 3 different equivalent circuits I showed you.

One for the drain source current, one for the gate current and one for the body

current to get this small-signal equivalent circuit.

Now it is very important, when we combine these three different circuits derived

separately, to make sure that when you put these things together they don't

interfere with each other. Now, it can be shown that this is

correct. And the details of that I will leave you

again to read in the book. So this is now a complete very low

frequency small signal equivalent circuit.

In this video we discussed small signal conductance parameters, due to the gate

and body leakage currents. So now we have derived a complete

small-signal equivalent circuit. In the next video I will concentrate on

one of these, I guess, conductance parameters, the gate transconductance gm,

a very important parameter