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 constant at $48$V is
- $\frac{2}{5}\leq D \leq \frac{3}{5}$
- $\frac{2}{3}\leq D \leq \frac{3}{4}$
- $0 \leq D \leq 1$
- $\frac{1}{3}\leq D \leq \frac{2}{3}$