Q$3($Total $30\%)$ The MOSFET in the circuit below has $k_n=4m\frac{A}{V^2},V_t=1V,$ and $V_A=25V.R_D=40k,R_{\text{s}\text{i}\text{g}}=200k$ and $R_L=1k.$

MOSFET operates at the saturation with $V_{OV}=0\mathrm{.}25V.$

$($a$)(5\%)$ Draw small$-$signal equivalent circuit for small$-$signal analysis of the given circuit.

$($b$)(10\%)$ Find small signal parameters, $g_m$ and $r_o.$

$($c$)(15\%)$ Find gain, $\frac{v_o}{v_{\text{s}\text{i}\text{g}}}$

Assume that capacitors act as short circuit at small$-$signal frequency.