Exercise 4.9 A degenerated NMOS amplifier

Given is the circuit schematic below. The output resistance of the MOS transistor can be assumed to be infinite. The capacitor can be modelled as a short circuit for all signal frequencies. The transistor threshold voltage equals $V_T$, its current factor is $K$ and the transistor operates in saturation.

a)

Derive/draw a small-signal equivalent circuit.

b)

Derive an expression for the transistor’s bias current $I_D$ as a function of e.g. $V_{\mathit{DD}}$, $V_{\mathit{GG}}$, $R_S$ and the given transistor parameters. Note that this question is very much related to chapter 3.

c)

Derive an expression for the transistor’s transconductance $g_m$ as a function of e.g. $V_{\mathit{DD}}$, $R_S$ and the given transistor parameters.

d)

Derive, using the SSEC of (a), a relation for the voltage transfer of $v_{\mathit{in}}$ to $v_{\mathit{out}}$.

e)

Derive a relation for the input resistance of the circuit, as seen from the input source $v_{\mathit{IN}}$.