Learning objective: Use volt-second balance to link duty cycle to output voltage and test whether the inductor current remains continuous.
Understand the idea
An ideal buck converter lowers a DC input voltage by switching the input connection on and off. In steady-state continuous-conduction mode, the inductor's average voltage over one switching period is zero. That physical condition yields the well-known duty-ratio relationship, but it is valid only under the stated operating assumptions.
Worked example: given data
- Input voltage Vin = 48 V and duty ratio D = 0.25.
- Switching frequency fs = 20 kHz, inductance L = 200 μH and load resistance R = 6 Ω.
- Assume ideal components, negligible output ripple, and continuous conduction unless the result contradicts it.
Detailed solution
Apply inductor volt-second balance
During the on interval, vL,on = Vin − Vo. During off time, vL,off = −Vo. Setting D(Vin − Vo) + (1 − D)(−Vo) = 0 yields Vo = DVin = 12 V.
Find average inductor current
The ideal output current is Io = Vo/R = 12/6 = 2 A. In steady state, average inductor current equals the load current.
Compute switching period and on-time
T = 1/fs = 50 μs and Ton = DT = 12.5 μs. During Ton, the inductor sees 48 − 12 = 36 V.
Calculate peak-to-peak ripple
ΔiL = (Vin − Vo)Ton/L = (36 × 12.5 μs)/(200 μH) = 2.25 A peak-to-peak. The same magnitude is obtained from the off interval.
Check conduction mode
IL,min = Io − ΔiL/2 = 2 − 1.125 = 0.875 A; IL,max = 3.125 A. The minimum is positive, so the continuous-conduction assumption is self-consistent.
What the answer means
The average output voltage formula for this problem follows from ideal continuous conduction. If the load current becomes low enough that the inductor current reaches zero, the converter enters discontinuous conduction and the input/output relationship generally changes. Always check the computed minimum current before assuming CCM.
Three mistakes to avoid
- Using 2.25 A as the ripple amplitude instead of peak-to-peak ripple.
- Forgetting the factor D when calculating the on-time.
- Applying Vo = DVin in discontinuous conduction without checking the operating mode.
Try a related question
Keeping the same 48 V input, 12 V output, fs and load, what is the critical inductance at which IL,min just reaches zero?
Show the worked-answer check
At the boundary, ΔiL = 2Io = 4 A. Lcrit = (Vin − Vo)Ton/4 = (36 × 12.5 μs)/4 ≈ 112.5 μH.
How to revise this concept
Study boost-converter volt-second balance and the effects of diode and switch nonidealities. First attempt the example on paper without opening the answer, then compare the intermediate steps. Explain each assumption before memorising a formula.
Content note: This is a newly prepared practice example, not an official GATE previous-year question. It was drafted with AI assistance for this educational website. Students should verify calculations and exam requirements against standard textbooks and official sources; educator review is recommended before publication.