$4(35$ points$)$ DC$/$DC Buck Converter. A buck DC to DC converter operating in continuous conduction mode has the following data: Input voltage: $28$ V DC$,$ Inductor: L$=8\mathrm{.}4$ uH $($micro Henry$),$ output: $25$ Watts at $12$ VDC $,$ switch frequency: $\backslash (\backslash$mathrm$\{$fs$\}=500\backslash$mathrm$\{$kHz$\}\backslash ).$ Assume the capacitor large enough to justify the assumption of negligible output voltage ripple.

a$.(10$ points$)$ Draw an appropriate circuit diagram for this boost converter, labeling input and output voltages. You need not label other components.

b$.(05$ points$)$ Find the duty cycle D$.$

c$.(10$ points$)$ Sketch the inductor current iL$.$ Label appropriate points.