$($a$)$ calculate an analytical expression $($a formula with symbols only$)$ for the voltage $50\%$ transfer function H$($$)=$ Vout$($$)/$Vin$($$)$ in terms of Z$1,$ Z$2,$ Z$3$ and Z$4$;

$($b$)$ calculate an analytical expression $($a formula with symbols only$)$ for the $30\%$ transfer function H$($$)$ in terms of R$1,$ R$2,$ C$3,$ C$4$ and ;

$($c$)$ calculate the frequency f$0($in Hz$)$ at which the phase of H$($$)$ is $-90$o; and

$($d$)$ calculate the steady state output voltage Vout$($t$)$ as a function of time when Vin$($t$)=$ A cos$(2$f$0$t$),$ where A $=1$ V$.$