Page 59 – Buck-Boost Converter Numerical Problems (CCM)
Subject: Power Electronics
Level: GATE / PSU Numerical Practice
🔹 Problem 1 – Output Voltage Calculation
A buck-boost converter operates in CCM with:
Vin = 24 V
Duty cycle D = 0.6
Find output voltage.
Vo / Vin = − D / (1 − D)
Vo = − (0.6 / 0.4) × 24 = −1.5 × 24 = −36 V
Final Answer: −36 V
🔹 Problem 2 – Duty Cycle Required
Vin = 48 V Required Vo = −24 V Find duty cycle.
|Vo/Vin| = D / (1 − D) 24/48 = D/(1−D) 0.5 = D/(1−D) 0.5(1−D) = D 0.5 − 0.5D = D 0.5 = 1.5D D = 0.333
Final Answer: D = 0.333 (33.3%)
🔹 Problem 3 – Inductor Current
Vin = 20 V Vo = −40 V Load resistance R = 10 Ω Find output current and average inductor current.
Io = |Vo| / R = 40 / 10 = 4 A For buck-boost in CCM: IL(avg) = Io / (1 − D) First find D: |Vo/Vin| = D/(1−D) 40/20 = D/(1−D) 2 = D/(1−D) 2(1−D) = D 2 − 2D = D 2 = 3D D = 0.667 Now, IL(avg) = 4 / (1 − 0.667) = 4 / 0.333 ≈ 12 A
Final Answer: Io = 4 A IL(avg) ≈ 12 A
🔹 Problem 4 – Critical Inductance
Vin = 30 V Vo = −60 V R = 12 Ω Switching frequency fs = 25 kHz Find critical inductance.
For buck-boost: Lcritical = (R (1−D)²) / (2 fs)
First find D: |Vo/Vin| = 60/30 = 2 2 = D/(1−D) D = 0.667 Now, L = (12 × (0.333)²) / (2 × 25000) = (12 × 0.111) / 50000 = 1.332 / 50000 = 26.6 μH
Final Answer: 26.6 μH
🔹 Problem 5 – Ripple Current
Vin = 24 V D = 0.5 L = 200 μH fs = 50 kHz Find inductor ripple current.
ΔIL = (Vin × D) / (L × fs) = (24 × 0.5) / (200×10⁻⁶ × 50000) = 12 / 10 = 1.2 A
Final Answer: 1.2 A
Exam Memory Capsule
✔ Vo/Vin = −D/(1−D) ✔ Output is negative ✔ IL(avg) = Io/(1−D) ✔ Lcritical = R(1−D)² / (2fs) ✔ ΔIL = VinD / (Lfs)
Buck-Boost Numerical Series – Shaktimatha Learning
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