# How to get the gain for this MOSFET amplifier?

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?

• The circuit as drawn has zero gain. That is, the output is completely independent of the input. Are you sure you drew it right? – Hearth Oct 20 '19 at 0:19