$[$Bonus problem $-$ No mandatory$]$ The step$-$down ideal transformer is used to increase the load impedance $(50$ ohm $)$ seen by the PA output side. Fig. $2$ shows the simple block diagram of the PA$.$ Please find the value of $\backslash (\backslash$mathrm$\{$L$\}^\{*\}\backslash$mathrm$\{$C$\}\backslash )$ to achieve the maximum gain $($Vout$/$Vin$),$ and specify its corresponding gain. We need to consider the antenna impedance $(50$ ohm $)$ to find the correct gain. Let's assume that this PA works for $5$ GHz frequency. $($Hint : You need to convert to circuit components. The equivalent circuit components for NMOS is called "small signal model". In this model, DC voltage such as power supply is considered as ground$)[10$ points$]$

Fig. $1$ Block diagram of the WiFi Transceiver front$-$end