Provided with the $2$N$7000$ N$-$channel MOSFET having a threshold voltage VT$=2\mathrm{.}1$VV$\_$T $=2\mathrm{.}1\backslash ,\backslash$text$\{$V$\}$VT$=2\mathrm{.}1$V and a single power supply VDD$=3$VV$\_\{$DD$\}=3\backslash ,\backslash$text$\{$V$\}$VDD$=3$V:

$($i$)$ Bias the MOSFET at point P$($ID$=1$mA$,$VDS$=1\mathrm{.}5$V$)$P$($I$\_$D $=1\backslash ,\backslash$text$\{$mA$\},$ V$\_\{$DS$\}=1\mathrm{.}5\backslash ,\backslash$text$\{$V$\})$P$($ID$=1$mA$,$VDS$=1\mathrm{.}5$V$).$

$($ii$)$ Determine the voltage gain $($AvA$\_$vAv$)$ of the amplifier.

Assume that the device has nCoxWL$=200$mA$/$V$2\backslash$mu$\_$n C$\_\{\backslash$text$\{$ox$\}\}\backslash$frac$\{$W$\}\{$L$\}=200\backslash ,\backslash$text$\{$mA$/$V$\}^2$n$$Cox$$LW$=200$mA$/$V$2.$