Question

The input voltage $V_{DC}$ of the buck-boost converter shown below varies from 32 V to 72 V. Assume that all components are ideal, inductor current is continuous and output voltage is ripple free. The range of duty ratio D of the converter for which the magnitude of the steady-state output voltage remains costant at 48 V is

Answer 1

$V_0=\frac{\alpha V_s}{1-\alpha }$

$when,V_s=32Vand{V}_0=48V$

$\alpha =\frac{3}{5}$

$when,V_s=72V$

$and{V}_0=48V$

$\alpha =\frac{2}{5}$

$\frac{2}{5}\le \alpha \le \frac{3}{5}$

$\therefore Answeris\frac{2}{5}\le D\le \frac{3}{5}$