The circuit shown below is a common source amplifier. The transistor has Vt $=0\mathrm{.}7$ V$,$ and Kn $=11$ mA$/$V$2$

a$)$ Find VGS$,$ ID and VD$.$ Check that the NMOS is in SAT

b$)$ Find gm and ro if VA $=50$ V$.$

c$)$ Draw a complete small $$ signal hybrid$-$ equivalent circuit of the amplifier.

d$)$ Find Rin and Ro

e$)$ Find the voltage gain of the amplifier Av $=$ vo $/$ vi with and without the bypass capacitor across RS

f$)$ Find the overall voltage gain Gv $=$ vo $/$vsig$.$ All capacitors behave as short circuits for signals and open circuits for DC$.$