For the converter shown in Fig. $1,$ the input voltage is $200$ V and the output voltage is $48$ V $.$ The converter operates with a duty ratio of $0\mathrm{.}5.$ The peak$-$to$-$peak ripple in the inductor current is $25\%$ of its average value. The peak$-$to$-$peak ripple in the capacitor voltage is $0\mathrm{.}1\%$ of its average value. The output power of the converter is $1920$ W $.$ Assume that the magnetizing inductance of the transformer is very large.

rig. $1.$ Halt$-$briage transtormer$-1$solated buck converter

a$.$ Find out the transformer turns ratio $n.$

b$.$ Draw the waveform of the inductor current $i(t),$ and determine its value.

c$.$ Determine the value of the filter capacitor required.

d$.$ Draw the waveforms of the diode and switch currents, clearly marking the necessary values.

e$.$ Determine the peak voltage and current stresses for all the semiconductor devices $($switches and diodes$).$

f$.$ Draw the waveform of the primary current of the transformer, clearly marking the necessary values.