Question $1(20$ Marks$)$

A synchronous boost converter is shown in Fig. $1.$ The switches $T_1$ and $T_2$ operate in a complementary manner, meaning that when $T_1$ is turned $ON,T_2$ is turned OFF $,$ and vice versa. Assume that this converter is lossless, and the converter is operated under continuous conduction mode $($CCM$).$ The specifications are listed as follows:

The inductor current $i_L=0\mathrm{.}5A,$ the input voltage $V_{in}=24V,$ the load resistor $R=300,$ the inductor $L=20H,$ and the switching frequency $f_s=100kHz.$

rig. $1.$ syillimuilius unust culiveiter

$($a$)$ Calculate the output voltage $v_C.$

$(4$ marks$)$

$($b$)$ Calculate the duty ratio of $T_1$ and $T_2.$

$(4$ marks$)$

$($c$)$ Determine the value of output capacitor $C$ so that the peak$-$to$-$peak voltage ripple on $v_C$ will be $10\%$ of $v_C.$

$(6$ marks$)$

$($d$)$ Sketch the waveforms of inductor current $i_L$ and $v_{T1}.($Specify the peak$-$to$-$peak and average values of $i_L$; specify the duty ratio and peak voltage value of $v_{T1}).$

$(6$ marks$)$