Power Electronics Circuits
Which of the following is the correct basis for deriving the ideal output voltage Vout = D × Vin of a buck converter?
- AIn steady state the inductor current returns to its starting value every period, so the voltage across the inductor averages to zero over a period
- BIn steady state the output capacitor current is always zero, so the capacitor voltage stays constant regardless of whether the switch is on or off
- CWhile the switch is on no voltage appears across the inductor, so the output voltage equals the input voltage
Show answer and explanation
Answer: A. In steady state the inductor current returns to its starting value every period, so the voltage across the inductor averages to zero over a period
The change in inductor current is determined by the time integral of the voltage across it (V = L di/dt). In steady state the current returns to the same value every period, so the voltage across the inductor averages to zero over a period (volt-second balance). In a buck converter, (Vin − Vout) appears while the switch is on and −Vout while it is off, so (Vin − Vout) × D = Vout × (1 − D) gives Vout = D × Vin. The conversion ratios of boost and buck-boost converters are obtained in the same way.
- A. Correct. The conversion ratio comes from volt-second balance.
- B. The capacitor current only averages to zero over a period; it is not always zero. The ripple current flows into the capacitor and becomes the output voltage ripple.
- C. While the switch is on, (Vin − Vout) appears across the inductor and its current rises.