Exercise 4.2 An NMOS amplifier circuit

Given in the amplifier circuit schematic below.

a)

Derive an expression for the drain current $I_{D_1}$ expressed in terms of circuit parameters (component values, component parameters ($K$, $V_{\mathit{TH}}$, etc.), supply voltage, etc.). Note that $v_{\mathit{in}}$ is a small signal voltage source with DC value $=0$.

b)

Draw a small signal equivalent circuit.

c)

Derive an equation for the voltage gain $a_v=v_{\mathit{out}}∕v_{\mathit{in}}$ of this circuit. For simplicity reasons, you may assume that the capacitor is low ohmic at signal frequencies.

d)

Derive an equation for the output impedance $r_{\mathit{out}}$ of this circuit. For simplicity reasons, you may assume that the capacitor is low ohmic at signal frequencies.

e)

Derive an equation for the output impedance $r_{\mathit{out}}$ of this circuit. For simplicity reasons, you may assume that the capacitor is low ohmic at signal frequencies.