Question $2(20$ Marks$)$

As illustrated in Fig. $2,$ the high$-$frequency full$-$wave quasi$-$resonant buck converter is operating under the following parameters: input voltage $V_{in}=48V,$ switching frequency $f_s=6\mathrm{.}78MHz,DC$ output inductor $L_F=47H,$ DC output capacitor $C_o=22F,$ resonant inductor $L_r=70nH,$ resonant capacitor $C_r=2\mathrm{.}3nF,$ the parasitic inductance of the switch $L_{SW}=0\mathrm{.}1nH,$ and the junction capacitor of the diode $C_{DF}=0\mathrm{.}2nF.$ The converter operates on the boundary condition of zero current switching $($ZCS$).$

$($a$)$ Calculate the output voltage $v_o$ and current $i_o.$

$(6$ marks$)$

Hint: the voltage gain of the full$-$wave ZCS buck converter can be approximately calculated as $\frac{v_o}{V_{in}}$~~$\frac{f_S}{f_r},$ where $f_r$ is the natural frequency of the resonant components.

$($b$)$ Calculate the peak current of the switch $S$ and the peak voltage of the diode $D_F.$

$(6$ marks$)$

$($c$)$ Sketch the half$-$wave version of the boost converter with zero voltage switching $($ZVS$).(4$ marks$)$

$($d$)$ Provide the values of the resonant inductor, resonant capacitor, and switching frequency corresponding to the half$-$wave ZVS boost converter sketched in $($c$).$

$(4$ marks$)$ Hint: Use the dual circuit principle to obtain the parameters.