Why transconductance(gm) of a MOSFET is expressed with two different ways?


Joined Jan 27, 2015
By using a difference function, as it's limit goes to zero, ... so w/ infintesimals, differentials, you are really making vectors, and so the differential of I wrt V will be a different type of quantity, than just dividing the instantanous values of I/V


Joined Aug 7, 2020
If you post a copy of your circuit, I will show you how you derive the various voltages and currents.
Your second equation should be shown with a lower case "v" and "i" to indicate that it refers to small signal analysis.