In the circuit below, assume $\mu_n C_{ox} \left(\frac{W}{L}\right)_1 = \mu_n C_{ox} \left(\frac{W}{L}\right)_2 = 1 mA/V^2$, $I_{D1} = I_{D2} = 0.55 mA$, $V_{DD} = 3.1 V$, $V_{th} = 1 V$, $\lambda = 0.1$, and $R_D = 2 k\Omega$ (neglect body effect)
(a) Calculate $V_B$ and $V_{IN}$ such that $M_1$ is exactly at saturation ($V_{DS} = V_{GS} - V_{th}$)
(b) Draw small signal model and calculate small signal gain $\frac{v_{out}}{v_{in}}$
