We now discuss small signal conductance parameters that arise due to the presence of gate and body leakage currents. Let us begin with gate current. 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. Now if you take a small change in the current, you can express it just as we did for the drain source current in the previous video, as a linear combination of the changes in the corresponding terminal voltages. 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. 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