Your task in this homework is to design a closed$-$loop regulator for the power converter shown below.

Your regulator should regulate the load current $I_o$ to a commanded value. The small signal load current is indicated as tilde$(i{)}_o$ in the control schematic below. The indictor has an ESR of $0\mathrm{.}05$ ohms. Draw the small signal circuit for the buck converter. Derive the small signal transfer function between output current and duty cycle i~$\_$o$($s$)/$d~$($s$).$ Then assume load resistance is $3$ ohms. Find the value of beta and solve for the input reference voltage required to obtain an output current of $1\mathrm{.}3$A$.$Suppose the PWM triangle comparator has a peak value of $3\mathrm{.}5$V$.$ Vt is $75$V$,$ L is $7$mH$,$ and C is $16$uF$.$ Derive the transfer function of the kernel of the loop gain and write it as the multiplication of a constant gain times two poles