Exercise 4.8 An NMOS amplifier with weird biasing

See the amplifier circuit below. Assume that the impedance of the capacitors is very low at the signal frequency.

a)

Draw a small signal equivalent circuit of this amplifier.

b)

Derive an equation for the voltage gain $a_v=v_{\mathit{out}}∕v_{\mathit{in}}$.

c)

Derive an equation for the output impedance of this circuit.

d)

In the questions so-far, the circuit was driven from a voltage source. Now, let’s replace that voltage source by a current source. Derive an equation for the output impedance of this circuit, assuming that the circuit is driven by a current source.