A Wilkinson power divider is a three$-$port passive device to split the port $1$ incident power equally between port $2$ and $3,$ or combine power from the ports $2$ and $3$ into port $1.$

$($a$)$ Find the ideal S$-$ matrix.

$($b$)$ Find the port $1$ return loss and input impedance if port $2$ is terminated with $75$ and port $3$ with $25.$ Assume $Z_0=50$