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