Exercise 5.4 A common gate amplifier

Given is the circuit below. In this circuit schematic, the MOS transistor is operated in the square law region where $i_D=\frac{1}{2}K\cdot {(v_{\mathit{GS}}-V_T)}^2$.

a)

Explain only 1 small-signal parameter is required to describe the behaviour of the MOS transistor for small, low frequency signals. The circuit is used for frequencies where $C_1$ and $C_2$ can be seen as low-ohmic, resulting in a circuit which behaves like a common-gate circuit (CGC).

b)

Draw the small signal equivalent circuit for the circuit for frequencies where $C1$ and $C2$ are (very) low-ohmic AND explain the term “common-gate” for this circuit.

c)

Derive an expression for the input resistance of the circuit.

d)

Derive an expression for the output resistance of the circuit for a frequency where $C_{\mathit{in}}$ and $C_{\mathit{out}}$ have a negligible low impedance.