In this brief video, we will discuss the high-frequency considerations that

pertain to the modeling of thermal noise. Let us begin with drain current noise.

We have derived the power spectral density.

It turns out that this expression is valid up to about omega 0 which I remind

you is the same radiant frequency as the upper frequency as the upper frequency of

validity of the first order non quasistatic model.

So we're okay with that. This limit is consistent.

But there is another type of noise called induced gate noise that we need to take

into account at high frequencies. And it is due to the random potential

fluctuations in the channel. These potential fluctuations through the

oxide capacitance coupled to the gate and therefore can influence the circuit to

which the gate is connected. Now let us assume saturation, and we will

use the simplified the non-quasi static model that we have derived.

the simplified model looks like this, I remind you that in series with Ggs there

was resistance, Rgs, attributed to the physical resistance of the version layer.

And over here, between gate and drain, we don't show anything because we are

talking about the intrinsic part of the transistor.

And Cgd, the gain brain capacitance is zero, in that case.

The noise in the channel represented by the noise source Ind, and we've seen how

to find this. This resistance, Rgs, turns out to be

noisy, as you might expect. More specifically, a calculation shows,

and I would have to refer you to references in the book for that, that it

is 4 3rd times Rgs that you have to multiply 4kT.

You may recall that the prospect of density of a thermal noise voltage was

4kTr. R now is 4 3rd times Rgs.

So this can be very simply modeled than by a noise voltage source in series with

Rgs. And also it becomes in series with Cgs,

as well. Now, if you look at this, it's a voltage

source in series with an impedance, consisting of the serious combination of

Rgs and Cgs. This is a 7n type circuit, you can

convert it into a Norton type circuit, which will then look like that.

And from the 7n to Norton calculation, you can find Ing.

The current noise here and from that, you can find the prospect or density if you

also use this. The details are in the book, and the

final expression for the participle density of the induced gate noise current

can be found in the book as well. Now, as you might expect, the drain

current noise here. And the induced gate current noise are

correlated, because they're basically originate in the same effect, the noise

fluctuations caused in the channel. Induced gate noise, because it is due to

the channel resistance as I have shown can be modeled, in the same way that we

have used model non quasi static phenomena in the options of, of a

specific non quasi static model. If you may recall, we could divide the

channel into several sub sections, model each of them quasi statically.

And the combination behaves non quasi statically.

If you do the same, you can predict the noise correctly.

So here are some results we use 10 sections for a long time on device.

This is the prospect on density on the drain current noise.

And you can see that up to ft, which is corresponds to approximately omega 0 over

2 pi, the noise is constant, as predicted by the formula we have already derived in

the past. And this is the induced gate current

noise, and using the expression calculated in the book, it turns out that

this is proportional to the square of frequency.

Take into account please that the, both of these axis are logarithmic.

The simple expression is good also to about ft and then things change.