The amplifier circuit shown below carries a bias current $(I_D)$ of $1$ mA $,$ with ${}_n{C}_{ox}=200\frac{A}{V^2}$ and $V_{TH}=0\mathrm{.}4V$ for the NMOS device, $R_D=1k,$ and $=0(30pts)$

$($a$)$ Calculate $\frac{W}{L}$ for a gate voltage of $1V.(10pts)$

$($b$)$ Calculate the amplifier gain. $(10$pts$)$

$($c$)$ If $=0\mathrm{.}1V^{-1},\frac{W}{L}=25\mathrm{.}7,$ Calculate the amplifier gain. $(10$pts$)$