In the previous video, we discussed the total terminal currents in quasi-static operation. We will now focus on the charging components of those currents. Let us consider the same situation as before. We assume the device operating quasi-static mode. And recall that we have shown that the drain current, can be written as a transport component i sub t of t, plus a charging component of i sub da. And correspondingly, the source current is the negative of the transport componen,t plus a charging component iSA. We will now concentrate on the charging component of the currents, iDA, iSA, and the other charging components. So we can write from the discussion in the previous video. We can write iDA is the rate of change of a charge we have called the drain charge, iSA is the corresponding rate of change of the source charge. And we also know that the gate current, will be the corresponding rate of, of change of the gate charge and iB would be, the corresponding rate of change of the bulk charge. This is the set of equations we will concentrate on in this video. To maintain charge neutrality, think of the device as a super node, the sum of all of the currents going into the device must add up to 0. And because id and is contain it and minus it, it cancels in the sum. And you have the same equation being valid for the charging components of the device. So the charging components of all of the currents, must satisfy what is essentially an equation like Keikov's current law. So let us now calculate these currents. 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.
