Page 68 – Numerical Marathon (30 Hard Problems – Part 1)
Level: GATE / PSU Intensive Practice
🔹 Problem 1 – Buck Converter
Vin = 36V D = 0.5 R = 9Ω Find output power.Vo = D × Vin = 18V Io = 18/9 = 2A P = 18 × 2 = 36W
---🔹 Problem 2 – Boost Converter
Vin = 12V D = 0.75 R = 24Ω Find output voltage and power.Vo = 12/(1−0.75) = 48V Io = 48/24 = 2A P = 48 × 2 = 96W
---🔹 Problem 3 – Buck-Boost
Vin = 20V D = 0.6 R = 10ΩVo = −(0.6/0.4)×20 = −30V Io = 30/10 = 3A P = 30 × 3 = 90W
---🔹 Problem 4 – Inductor Ripple
Vin=24V D=0.4 L=100µH fs=50kHzΔIL = VinD/(Lfs) = 24×0.4/(100×10⁻⁶×50000) = 9.6/5 = 1.92A
---🔹 Problem 5 – Critical Inductance
R=12Ω D=0.5 fs=25kHzLcritical = R(1−D)²/(2fs) = 12×0.25/(50000) = 3/50000 = 60µH
---🔹 Problem 6 – Rectifier
Vm=325V α=30°Vo=(2Vm/Ï€)cosα = (650/3.14)(0.866) ≈ 179V
---🔹 Problem 7 – Inverter Fundamental
Vdc=200VV1(rms)=(4Vdc)/(Ï€√2) ≈ 180V
---🔹 Problem 8 – Natural Frequency
L=100µH C=25µFω₀=1/√(LC) =1/√(2.5×10⁻⁹) ≈ 20000 rad/s
---🔹 Problem 9 – Boost Duty
Vin=30V Vo=60V60=30/(1−D) 1−D=0.5 D=0.5
---🔹 Problem 10 – DCM Output
Vin=20V D=0.4 R=10Ω L=100µH fs=50kHzVo/Vin=−(D²R)/(2Lfs) =−(0.16×10)/(10) =−0.16 Vo=−3.2V
---Marathon Strategy
✔ Always check CCM/DCM ✔ Write gain formula correctly ✔ Keep calculator accuracy ✔ Manage time – 2 min per problem
Power Electronics Numerical Marathon – Shaktimatha Learning
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