$($Sedra P$16\mathrm{.}28)$ Consider a CMOS inverter fabricated in a $65$ nm CMOS process for which

VDD $=1$ V$,$ Vtn $=$Vtp $=0\mathrm{.}35$ V$,$ and nCox $=5\mathrm{.}4,$ P Cox $=540$ A$/$V$2.$ In addition, QN and

QP have L $=65$nm and $($W$/$L$)$n $=1\mathrm{.}5.$

$($a$)$ Find Wp that results in VM $=$ VDD$/2.$

$($b$)$ For the matched case in $($a$),$ find the values of VOH $,$ VOL, VIH $,$ VIL, N ML$,$ and N MH $.$

$($c$)$ For the matched case in $($a$),$ find the output resistance of the inverter in each of its two

states.