GATE EE 2026 Set 1 — Question 48
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Power Electronics → DC-DC Converters → Boost Converter
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Question
Consider the boost converter circuit shown. Assume that the semiconductor devices are ideal. In steady state, the inductor current rises linearly from to in the first and then falls linearly from to in the next of every switching cycle as shown. The load resistance is and the capacitance is .
Neglect the ripple in the output voltage. What is the input voltage ?
Correct answer
(C) 7.5 V
Solution
1.Identify the mode of operation: The inductor current starts at , reaches a peak of at , and returns to at . Since the current returns to zero exactly at the end of the switching cycle (), the converter is operating in Boundary Conduction Mode (BCM).
2.Calculate the average output current (): In a boost converter, the output current is equal to the inductor current when the diode is conducting (i.e., during ). The average output current is the area under the curve during the off-time divided by the total period :
3.Calculate the output voltage (): Given the load resistance and neglecting ripple:
4.Apply Volt-Second Balance: For steady-state operation, the average voltage across the inductor over one cycle must be zero:
Thus, the input voltage is .Continue learning with Success Tracker
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