Exercise 3.5 Biasing an amplifier with an NMOS transistor

The figure below shows a single-transistor amplifier stage. For operation in saturation, $i_D=\frac{1}{2}k{(v_{\mathit{GS}}-V_T)}^2$ with $V_T$ the threshold voltage of $M_1$. The supply voltage $V_{\mathit{DD}}>V_T$.

a)

Show that $M_1$ works in saturation in this circuit.

b)

Derive an expression for the value of $R_D$ to set the bias current of $M_1$ to $I_D$.