How to get the gain for this MOSFET amplifier?

by joe doe   Last Updated October 20, 2019 00:25 AM

This is a common drain MOSFET amplifier:


simulate this circuit – Schematic created using CircuitLab

This is its small signal model at low frequency:


simulate this circuit

I am at a loss as to how to find Vout/Vin. Vin, in this case, is just Vg not Vgs since the source node is not connected to ground.

My analysis:

Since all of the current source's current is going thru r0 from Vout to GND,

$$\frac{V_{out}}{r_0}=V_{gs}*g_m$$ or $$\frac{V_{out}}{r_0}=(V_{in}-V_{out})*g_m$$. After some algebraic manipulation, you get $$\frac{V_{out}}{V_{in}}=\frac{r_0*g_m}{1+r_0*g_m}$$.

I know $$r_o*g_m=(\frac{\delta I_d}{\delta V_{ds}})^{-1}*\frac{\delta I_d}{\delta V_{gs}}=\frac{\delta V_{ds}}{\delta V_{gs}}$$.

I don't know what to do after this. My professor's solution says Vout/Vin=1. How?

Tags : mosfet amplifier

Related Questions

Updated December 15, 2018 19:25 PM

Updated July 05, 2015 13:10 PM

Updated July 30, 2016 08:10 AM

Updated October 26, 2017 14:25 PM

Updated May 02, 2017 00:25 AM