$22.$ Design a third$-$order maximally flat bandpass filter prototype in a $\backslash (50\backslash$Omega $\backslash )$ system centered at $1$ GHz with a $\backslash (10\backslash \%\backslash )$ bandwidth. The lowpass prototype of a third$-$order maximally flat filter is shown in Figure $2-10.$

$($a$)$ Convert the prototype lowpass filter to a lowpass filter with inverters and capacitors only; that is$,$ remove the series inductors.

$($b$)$ Scale the filter to take the corner frequency from $\backslash (1\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash )$ to $1$ GHz $.$

$($c$)$ Transform the lowpass filter into a bandpass filter. That is$,$ replace each shunt capacitor by a parallel $\backslash ($ L C $\backslash )$ network. This step will establish the bandwidth of the filter.

$($d$)$ Transform the system impedance of the filter from $1$ to $\backslash (50\backslash$Omega $\backslash ).$ Figure $2-20$: Linear amplifier comprising input and output matching networks and an active device in a specific configuration forming a two$-$port. Figure $2-10$: Synthesized maximally flat network with a thirdorder lowpass reflection response.