A C$$k regulator has an input voltage Vs $=15$ V$.$ The duty cycle is k $=0\mathrm{.}45$ and the switching frequency is $25$ kHz$.$ The filter inductance is L$2=350$ H and filter capacitance is C$2=220$ F$.$ The energy transfer capacitance is C$1=400$ F and inductance is L$1=250$ H$.$ The average load current is la $=1\mathrm{.}2$ A$.$ Determine $($a$)$ the average output voltage Va$,($b$)$ the average input current Is$,($c$)$ the peak$-$to$-$peak ripple current of inductor L$1,$ I$1,($d$)$ the peak$-$to$-$peak ripple voltage of capacitor C$1,$ Vc$1,($e$)$ the peak$-$to$-$peak ripple current of inductor L$2,$ I$2,($f$)$ the peak$-$to$-$peak ripple voltage of capacitor C$2,$ Vc$2,($g$)$ the peak current of the transistor Ip$,$ and $($h$)$ find the critical values of L$1,$ C$1,$ L$2,$ and C$2.$