GATE EE 2018 Set 1 — Question 63
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Power Electronics → DC-DC Converters → Boost Converter
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Question
A dc to dc converter shown in the figure is charging a battery bank, B2 whose voltage is constant at 150 V. B1 is another battery bank whose voltage is constant at 50 V. The value of the inductor, L is 5 mH and the ideal switch, S is operated with a switching frequency of 5 kHz with a duty ratio of 0.4. Once the circuit has attained steady state and assuming the diode D to be ideal, the power transferred from B1 to B2 (in Watt) is ___________ (up to 2 decimal places).
Correct answer
12 to 12
Solution
The circuit is a boost converter with fixed input and output voltages.
Given:
(B1)
(B2)
Step 1: Calculate peak inductor current ()
Step 2: Determine the conduction mode
During the off-time (), the voltage across the inductor is .
The time taken for the current to reach zero is .
Since (), the converter operates in Discontinuous Conduction Mode (DCM).Step 3: Calculate average power transferred
In a lossless converter, the power transferred from B1 to B2 is equal to the average power drawn from B1.
Average current from B1 () is the average of the inductor current over one cycle:
Power transferred .
Given:
(B1)
(B2)
Step 1: Calculate peak inductor current ()
Step 2: Determine the conduction mode
During the off-time (), the voltage across the inductor is .
The time taken for the current to reach zero is .
Since (), the converter operates in Discontinuous Conduction Mode (DCM).Step 3: Calculate average power transferred
In a lossless converter, the power transferred from B1 to B2 is equal to the average power drawn from B1.
Average current from B1 () is the average of the inductor current over one cycle:
Power transferred .
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