Problems

$6\mathrm{.}1$ Tapped$-$inductor boost converter. The

boost converter is sometimes modified as

illustrated in Fig. $6\mathrm{.}41,$ to obtain a larger

conversion ratio than would otherwise

occur. The inductor winding contains a

total of $($n$\_(1)+$n$\_(2))$ turns. The transistor is

connected to a tap placed n$\_(1)$n$\_(1)$:n$\_(2)($n$\_(1)+$n$\_(2))$ turn

Fig. $6\mathrm{.}41$ Tapped$-$inductor boost converter, Problem

$6\mathrm{.}1$

winding is L$.$

$($a$)$ Sketch an equivalent circuit model for the tapped inductor, which includes a magnetizing induc$-$

tance and an ideal transformer. Label the values of the magnetizing inductance and turns ratio.

$($b$)$ Determine an analytical expression for the conversion ratio M$=($V$)/($V$\_($R$)).$ You may assume that the

transistor, diode, tapped inductor, and capacitor are lossless. You may also assume that the con$-$

verter operates in continuous conduction mode.

$($c$)$ Sketch M$($D$)$ vs$.$ D for n$\_(1)=$n$\_(2),$ and compare to the nontapped $($n$\_(2)=0)$ case.