$($a$)$ Assuming that $$VTH $=$ AVTH $/($WL$)1/2,$ where AVTH $=9$mV$$m$,$ and neglecting other mismatches, determine the minimum width of the transistors such that VOS, in $4$mV$.($b$)$ With the dimension of the transistors from $($a$),$ if the tail current ISS is $1\mathrm{.}2$mA$,$ estimate the maximum input swing Vm that gives a THD of $1\%.$ Hint: input signal is vin$($$)=$ Vm cos$($t$).$ The THD of a differential pair approximately equals to AHD$3/$AF$,$ where $($c$)$ Repeat $($a$)$ & $($b$)$ if the tolerable input offset is $2$mV and compare the results.