Consider the common source amplifier shown below. Assume that $+V_{DD}=+5V,$

$-V_{SS}=-5V,I_{\text{R}\text{E}\text{F}}=300A,R_L=1M,W_n=50m,W_p=20m,L=10m$

$k_n^{\text{'}}=136\frac{A}{V^2},k_p^{\text{'}}=100\frac{A}{V^2},V_{tn}=+600mV,V_{tp}=-600mV,{}_n=0\mathrm{.}02V^{-1}$

and ${}_p=0\mathrm{.}03V^{-1}.$ In addition, assume that $W_1=W_n,W_2=3W_p,$ and $W_3=2W_p.$

$($a$)$ Calculate a value for $V_{OV3}$ and $I_{D3}*(50pts)$

$($b$)$ Calculate a value for $V_{OV2}$ and $I_{D2}*(50pts)$

$($c$)$ Calculate a value for $V_{OV1}$ and $V_{\text{I}}$ such that $I_{D1}=I_{D2}*(25pts)$

$($d$)$ Calculate a value for $V_O*(25pts)$

$($e$)$ Calculate a value for $v_{O(min)}$ and $v_{O(max)}.$ You may neglect the effect that $R_L$ may have on the values. $(100$ pts$)$

$($f$)$ The low$-$frequency small$-$signal voltage gain is given by $A_{v(LF)}=-39\mathrm{.}2185\frac{V}{V}.(0$ pts$)$

$($g$)$ Calculate a value for $V_{(max)}$ and $V_{po(max)}*(50pts)$