The charging component of the drain current is dqd, dt.

Now how does qd depend on time? qd depends on the terminal voltages.

So I can say that, I can take the rate of change of qd, with respect to vd and then

take dvd dt. Okay, so this is the chain rule of

differentiation. But I haven't finished, because qd

doesn't only depend on the drain voltage, it also depends on the gate voltage.

So I must add the component which is dqd, dvg, dvg, dt.

So these are the partial derivatives of the charge, with respect to the voltages.

And then, I must do the same because qd in general will depend on the body

voltage. So it's dqd, dvd, dvb dt, and finally I

can do the same with the source voltage, dqd dvs, dvs dt.

This is the total drain charging component.

I can do the same with the gate charge. The gate charge depends in general on the

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

So therefore, the complete expression for the gate current, must be one that

involves the partial derivatives of that charge, the gate charge, with respect to

each of the terminal voltages, times the corresponding rates of change of those

voltages. We do the same with the body of the

current, so we get an equation like this. And finally, for the source charging

component, dqs dt, we get the corresponding equation like this.

These equations have a nice pattern to them.

you may want to spend a few minutes looking at them, and making sure you

understand these details, because we will be using them later, to calculate the

transient response of transistors. So in this short video, we talked about

charging currents, and how that can be evaluated.

We have seen that we need the charges in terms of voltages, in order to be able to

find the percent derivative shown in this equation.

For example, dqg dvd. So in the next video, we will deal with

the evaluation of the charges, in terms of terminal voltages.