Design a low$-$pass third order maximally flat filter that has a series inductor as the first element.

$($a$)$ Derive the prototype of the low pass filter and scale it for $3$ GHz cutoff frequency and $50$

impedance.

$($b$)$ Realize this filter with an open shunt stub for the capacitor and stepped impedance for the

inductors. The maximum and minimum available characteristic impedance of the transmission

line for the stepped impedance section are $200$ and $10$ respectively.