And then we take the derivative of this drain current with respect to V D S the

result Is called the small signal output conductance.

Since the drain depends, has 3 paths, the drain source path.

Then it has a path because of gate leakage in another pathway because of

body leakage. The drain current is the sum of the drain

source current plus the drain body current.

Plus the drained gate current and it is the sum of the three that counts.

So now when you take the derivative of this you get the individual derivative's

of each. Which are gsd, gbd, and ggd.

So graphically let's say we have the drain current here vs vgs.

This is nonsaturation This is saturation where the dominant effects are the the

channel length modulation and DIBL, and if you go to high enough VDSes, you end

up with impact ionization that can increase the slope, like that.

So, now when you plot. The small signal output conductance G

zero, it is high in non saturation, it dips down becaue of channelic modulation

in

[UNKNOWN].

This is what determines the shape here and then if you enter the impact

ionization region, you go back up, as this one predicts, the slope increases.

So what kind of output conductance you get depends on which region you are and

which effect is dominant. Let me further expand on this.

Here is the output conductance on the log scale and I'm assuming that the length of

the device is equal to the minimum allowed length.

So now we have Go, the output conductance versus Gds with Vgs as a parameter.

Because this device is as short as we, you can make it in the given process, the

channel length modulation and dibble effects are significant and they keep the

conductance large. But if you take the.

A different device with a longer length, much longer length.

Now channel length modulation and DIBL are negligible for this device, so the

conductance dips to lower values. And you can even see the beginning of

impact ionization affects over here. The conductance goes back up, as the

previous slide had predicted. You can only see that of course if you go

to large enough values. Fortunately with many processes today,

you stay to, at a low value of vds before such effects can, can interfere with your

design. [COUGH] Now something about the effect of

extrinsic resistances on out of conductance.

First of all, you will recall that we have the extrinsic source resistance, the

extrinsic drain resistance And the effect of this is as the current passes through

them, there is a voltage drop across them which limits the internal voltages of the

device. So for example the actual VGS of the

device which I call VGS hat is the externally applied VGS minus this voltage

drop across this one. So, for a given VGS And a given change in

vgs, the corresponding internal vgs and the corresponding change in vgs are

smaller than what you think from the external variations.

And that has as an effect a reduction in the trans-conductance, the effective

trans-conductance. And you can show summarized in the book

that the effective transconductancy is what you would assume from the

transconductance of the device by itself divided by 1 plus G M R S C.

Another effect is related to the body resistance R B E.

we have said more than once that the body resistance is distributed but for

simplicity we assumed that it is just one lump to resistor.

The drain body leakage current passes through this resistance and creates a

voltage drop rbidb, and this has the plus sign here, the minus thi-, sign there.

So let's say you have a reverse bias vsb, which determines your threshold through

the body effect. Now the effect of vsb internal to the

device Is actually smaller by the voltage drop in this resistance.

So, VSB effective is VSB minus RBE IDB So, the effect of this is the following.

If IDB goes up, for some reason, then the effect of VSB goes down, because a larger

voltage drop is subtracted from the external [INAUDIBLE] VSB, so VSB now is

smaller. Therefore, the threshold is smaller,

which increases IDS further, which can have the have the effect of increasing

IDB further. The result of all this is that the output

conductance that you see here, the slope of the drain current with respect to VDS

Is larger than if you didn't include this effect.

In the book, we summarize the procedure for finding the effective output

conductance and it is given by this expression.

Where you see that g is still matters. The gate drain leak ups conductance

matters, and the body drain conductance is actually amplified by this.

Factor. In this video, we have discussed the

source drain and output small signal conductances.

And at this point, we have finished with our introduction to conductnace small

signal parameters. In the next video, we'll begin discussing

small signal capacitance.