Problem $3(30$ points$)$: Consider the following Multistage amplifier with VDD $=2\mathrm{.}5$ ; VSS $=-$

$2\mathrm{.}5$V$.$ The device parameters are Iref$=0\mathrm{.}2$ mA; kn$=400$ A$/$V

$2$

$,$ kp$=100$ A$/$V$2$

$,$ and Vtn$=0\mathrm{.}5$

V$,$ Vtp$=-0\mathrm{.}5$ V$.$ For all transistor $($ both PMOS and NMOS$)$ Vov$=0\mathrm{.}5$ V$,|$VA$|=50$V $,$ RL$=20$ K$$

$($a$)$ Identify the different stages of the amplifiers

$($b$)$ Design the circuit i$.$e$.$ find W$/$L of all transistors

$($c$)$ Find the differential gain $($Voltage gain$)$