Q$1)$ For an NMOS differential pair with a common$-$mode voltage $V_{CM}$ applied, as shown in figure. Let $V_{DD}=V_{SS}=2\mathrm{.}5V,kn\text{'}\frac{W}{L}-3m\frac{A}{V^2},Vtn=0\mathrm{.}7V,I=0\mathrm{.}2mA,R_D=5k,$ and neglect channel$-$length modulation.

$($a$)$ Find $V_{OV}$ and $V_{GS}$ for each transistor.

$($b$)Fo{r}_{CM}=0,$ find $V_s,I_{D1},I_{D2},V_{DI},$ and $V_{D2}.$

$($c$)$ Repeat $($b$)$ for $V_{CM}=+1V.$

$($d$)$ Repeat $($b$)$ for $V_{CM}=-1V.$

$($e$)$ What is the highest value of $V_{CM}$ for which Q$1$ and Q$2$ remain in saturation?

$($f$)$ If current source I requires a minimum voltage of $0\mathrm{.}3$ V to operate properly, what is the lowest value allowed for $V_s$ and hence for $V_{cm}?$