For an NMOS differential pair with a common$-$mode voltage $V_{CM}$ applied, as shown in the figure below, let $k{n}^{\text{'}}=0\mathrm{.}8m\frac{A}{V^2},(\frac{W}{L}{)}_{1,2}=12,V_{tn}=0\mathrm{.}4V,R_D=5k,$ and $V_{OV}=0\mathrm{.}8V$ neglect channellength modulation $().$

a$)$ Find $V_{\text{G}\text{S}\text{I}}$ and $V_{GS2}.$

b$)$ Find $I_{D1},I_{D2},$ and I.

c$)$ For $V_{CM}=0,$ find $V_S,I_{D1},I_{D2},V_{D1},$ and $V_{D2}.$

d$)$ Repeat $($c$)$ for $V_{CM}=+0\mathrm{.}4V.$

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 $0\mathrm{.}2$ V to operate properly, what is the lowest value allowed for $V_S$ and hence for $V_{CM}?$