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Large-Signal Dynamic Operation – Charging Currents in QS Operation

Course video 51 of 78

In this module there is a significant departure from what we have done up to this point: we will allow the terminal voltages of the transistor to vary with time. We will determine the resulting terminal currents, which will now include a “charging” component. We will do this both for moderate and for very high “speeds”. The transient response of circuits involves similar calculations, only done by computer for an ensemble of transistors and other devices.

PLEASE NOTE: This version of the course has been formed from an earlier version, which was actively run by the instructor and his teaching assistants. Some of what is mentioned in the video lectures and the accompanying material regarding logistics, book availability and method of grading may no longer be relevant to the present version. Neither the instructor nor the original teaching assistants are running this version of the course. There will be no certificate offered for this course. Learn how MOS transistors work, and how to model them. The understanding provided in this course is essential not only for device modelers, but also for designers of high-performance circuits.

Impartido por:

Yannis Tsividis
Charles Batchelor Professor of Electrical Engineering

Transcripción

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.

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