Question

In a Buck-boost converter, the current waveform through inductor is shown below.


The relation between output voltage and input voltage is,

Answer 1

During the time interval,

$0<t<DT;$ $V_L=V_s$

$0<t<\beta T;$ $V_L=-V_0$
Average voltage across inductor is zero
$V_{s}DT+(-V_0)(\beta -D)T=0$
$V_s-V_0\beta +V_{0}D=0$
$V_0=\left(\frac{D}{\beta -D}\right)V_s=\left(\frac{0.4}{0.6-0.4}\right)V_s$

$V_s=\frac{V_0}{2}$