Question $2$

Consider the common$-$source amplifier shown in Figure $2\mathrm{.}1.$ The NMOS transistor has the parameters K$=1$m$($A$)/($V$^(2)),$V$\_($to $)=2$V and r$\_($d$)=\backslash$infty $.$ The circuit of Figure $2\mathrm{.}1$ is to be built with V$\_($DD$)=20$V$,$R$\_(1)=3$M$\backslash$Omega $,$R$\_(2)=1$M$\backslash$Omega $,$R$\_($S$)=2\mathrm{.}7$k$\backslash$Omega $,$R$\_($D$)=4\mathrm{.}7$k$\backslash$Omega $,$R$\_($L$)=10$k$\backslash$Omega and R$=100$k$\backslash$Omega $.$

$($a$)$ Draw the DC bias circuit and Thevenin equivalent of the DC bias circuit for the amplifier shown in Figure $2\mathrm{.}1.$

$[4$ marks$]$

$($b$)$ Calculate the DC bias values of V$\_($GsQ$),$V$\_($DSQ$),$ and IDQ$\_($D$)$

$[4$ marks$]$

$($c$)$ Determine the region of operation of the MOSFET.

$[2$ marks$]$

$($d$)$ Using the small$-$signal model, calculate the transconductance parameter, g$\_($m$),$ input resistance, R$\_($i$),$ output resistance, R$\_($o$),$ the peak amplitude of the output voltage, v$\_($o$),$ produced for a source voltage, v$($t$)=100$sin$(2000$Tt$)$ mV $,$ and the output power delivered to the load.

$[10$ marks$]$