Design a half$-$bridge dc$-$dc converter with a centered$-$tap output transformer with the following specifications: VIN$=480$V$,$ Vo$=240$V@Io$=20$A$,$ duty cycle D$=0\mathrm{.}25,$ fs$=75$kHz and a maximum peak$-$topeak output voltage ripple of $1\%.$ Your design should include the following: a$)$ the transformer turns ratio, b$)$ the critical inductor value Lcrit to maintain Continuous Conduction Mode, $($c$)$ output capacitor value when the output inductor Lx is $2$ Lcrit.