Question $2$: The CS amplifier stage shown below has a voltage gain of $15$ at a bias current of $0\mathrm{.}5$ mA $.$ Determine the required value of $(\frac{W}{L}{)}_2.[7\mathrm{.}5-$pts$]$

${}_1=0\mathrm{.}15V^{-1},{}_2=0\mathrm{.}05V^{-1}.{}_n{C}_{ox}=200\frac{A}{V^2},{}_p{C}_{ox}=100\frac{A}{V^2},|V_t|=0\mathrm{.}4V$ for both PMOS and NMOS. $V_b$ is a DC bias voltage. Assume both transistors below are in saturation.