4. The NMOS transistor is biased such that $g_m = 2 mA/V$. The input
signal has no DC component and can be directly coupled to the
amplifier input.
a. Draw the low frequency small signal model of the amplifier
circuit. You may assume $\lambda=0$ for the transistor.
b. Find an expression for the gain $A_v(j\omega)$ of the amplifier in
terms of $g_m$, $R_D$, $R_S$ and $C_S$. Express your answer in standard
form, i.e., poles and zeroes are of the form $1 + j(\omega/\omega_o)$.
c. From your expression for $A_v(j\omega)$, determine the required
value of $R_D$ such that the DC voltage gain of the amplifier is
equal to -2 V/V.
d. Choose a value of $C_S$ so that the pole frequency is 100 Hz.
e. What zero frequency will be introduced by this value of $C_S$?
f. Draw the asymptotic dB log-log plot of the amplifier for low
frequency operation.
g. Draw the corresponding asymptotic phase log plot of the
amplifier.