$(40$ pt$)$

Problem $3.$ A MOSFET amplifier is shown in Fig. $4.$ Assume $V_{DD}=20V,R_1=100k,R_2=300k,R_S=700,R_D=1\mathrm{.}2k,V_{Tn}=0\mathrm{.}5V,k_n=10m\frac{A}{V^2},{}_n=0\mathrm{.}02,$ and $=0$

a$)$ Find the Q$-$point $(I_D,V_{DS}).$ For this part $($a$)$ assume ${}_n=0.$

b$)$ Draw the small$-$signal equivalent circuit and calculate the small$-$signal parameter $(g_m$ and $r_o$

c$)$ Determine the input resistance $(R_{in})$ and the output resistance $(($:$R_{\text{O}\text{u}\text{t}}$