Consider the common$-$source $($CS$)$ amplifier circuit shown in the below figure. Do the following:

$($a$)$ Draw the de bias circuit. This NMOS has $V_t=1V$ and $k_n=4m\frac{A}{V^2}.$

Let $I_D=0\mathrm{.}5mA,V_S=3\mathrm{.}5V,V_D=6V$ and the power supply voltage $V_{DD}=15V.$

$($b$)$ Using the dc bias circuit in part $($a$),$ determine the values of $R_s$ and $R_p$ Assume that this NMOS is operating in the saturation region. Also determine the value of $g_m$ at the dc bias point.

$($c$)$ Replace the MOSFET with its hybrid$-$ model $(g_m{V}_{g^s}-$ version$)$ and draw the small$-$signal equivalent circuit.

Neglect the channel$-$length modulation effect $(r_o).$

$($d$)$ Using the small$-$signal equivalent circuit in part $($c$),$ determine the values of the input resistance $(R_m),$ the output resistance $(R_q)$ and the overall gain $G_r(\frac{v}{v_v}).$

Let $R_{Gl}=5M,R_{G2}=2\mathrm{.}5M,R_{\text{s}\text{i}\text{g}}=100k$ and $R_L=20k.$

$($Hint$)$ Refer to In$-$Class Problems $01$ and $02$ on pages $7$ and $8$ of the "ELEN$3363\_$Lecture$10"$ slides.