# Analyzing a MOSFET circuit

This is the problem:

And this is my attempt to solve it:

For (1): I don't know how to get vgs or how to use the hint to get rid of it.

For (2): I assume that my solution is right but should I add details on how did I get Rout ?

• You're on the right track, you need to substitute in for your unknown (V_gs) using the hing you're given, and solve for V_out/V_in While solving feedback circuits (this is a voltage feedback, also called an source degeneration circuit) you'll generally need to use this kind of a trick. – deadude Dec 2 '14 at 20:48

You have an equation for $v_o$ of the form $v_o = kv_{gs}$ but you need $v_{o}/v_i$. Use the hint (which is just KVL) to substitute for $v_{gs}$: $$v_o = kv_{gs} = k(v_i - v_o)$$ and solve for $v_o/v_i$.
For $R_o$ you have forgotten the contribution of the dependent current source. To calculate $R_o$ set $v_i = 0$, apply a test voltage $v_t$ across the output, and calculate the test current $i_t$ flowing from that test voltage. Then $R_o = v_t/i_t$. Since $v_i = 0$, $v_g = 0$ and therefore $v_{gs} = -v_s = -v_o = -v_t$. The dependent current source therefore supplies a current $-g_m v_t$. Now use KCL at the output node to calculate $v_t$ in terms of $i_t$ and re-arrange to find $R_o = v_t/i_t$.
• @ammarx Yes, that looks correct. You notice you get a much lower answer than what you originally calculated -- this is good because the circuit is a source follower (buffer) and you want a low $R_o$ for a buffer. – Null Dec 2 '14 at 21:19