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GATE 2017 EE – Question 48

Power Electronics · DC to DC conversion: Buck, Boost and Buck-Boost Converters · 2 marks · Multiple choice

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

A buck-boost converter with input $V_{DC}$, switch $S_1$, inductor L, diode, capacitor C and load R, with output voltage $V_o$.
  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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Correct answer: (A) $\frac{2}{5} \leq D \leq \frac{3}{5}$

Explanation

For a buck-boost converter $|V_o| = V_{DC}\frac{D}{1 - D}$. For $V_o = 48$ V and $V_{DC} = 32$ V, $\frac{D}{1 - D} = 1.5$, which gives $D = 0.6$. For $V_{DC} = 72$ V, $\frac{D}{1 - D} = \frac{2}{3}$, which gives $D = 0.4$. So $\frac{2}{5} \leq D \leq \frac{3}{5}$.