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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

  1. $\frac{2}{5}\leq D \leq \frac{3}{5}$
  2. $\frac{2}{3}\leq D \leq \frac{3}{4}$
  3. $0 \leq D \leq 1$
  4. $\frac{1}{3}\leq D \leq \frac{2}{3}$
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