- #1

Renshai

- 7

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## Homework Statement

We are going over gain, Gm, Ro, and Rin for MOSFETS. We are told to know and memorize certain equations and how to get these equations. In this particular problem we are told to find voltage gain by analyzing small signal. My professor gave this as the answer:

(-gm* Rd)/(1+gm*Rs),

to the gain to a common source with degeneracy... basically a common source MOSFET with a resistor on the source side, but I am not seeing how he got it. I know it comes from the basic common source MOSFET voltage gain: (-gm* Rd). I am not sure how he got the denominator (1+gm*Rs). I know (or think anyway) that he used KCL to get the equation in terms of gm. I am somehow missing that link. I put a picture of the MOSFET below.

## Homework Equations

The equation we are to use to find gain is Vo/Vin

## The Attempt at a Solution

This is the equation I keep coming up with, but I know it is wrong, but I am having a heck of a time figuring out the correct relationship:

(Vo/Rd) + gm(Vin -It*Rs) = 0

This is what I am struggling with. It seems that I am missing something or doing the equation totally wrong (I am becoming aware, due to this problem, of my lack of KVL and KCL skills. It has been a while since I have had to use them, but I am getting back into it, but this is tripping me up). Any help and or guidance will be extremely appreciated.