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 POWER ELECTRONICS – PAGE 12

Full Wave Controlled Rectifier – Derivation (R Load)

                                     

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1️⃣ Input Voltage

Input AC supply:

v = V_m sin ωt

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2️⃣ Conduction Interval

For Full Wave Rectifier:

• SCR1 conducts from α to π
• SCR2 conducts from π + α to 2π

Total conduction interval per cycle = 2(π − α)

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3️⃣ Average Voltage Formula

Average value over one full cycle:

V_avg = (1 / 2π) ∫_α^π V_m sinθ dθ + (1 / 2π) ∫_π+α^2π V_m sinθ dθ

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4️⃣ Using Symmetry

Since waveform is symmetrical:

V_avg = (2 / 2π) ∫_α^π V_m sinθ dθ

= (1 / π) ∫_α^π V_m sinθ dθ

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5️⃣ Integration

∫ sinθ dθ = −cosθ

V_avg = (V_m / π) [ −cosθ ]_α^π

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6️⃣ Substituting Limits

cosπ = −1

V_avg = (V_m / π) (1 + cos α)

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7️⃣ Final Result

V_avg = (V_m / π) (1 + cos α)

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8️⃣ Special Case (Bridge Fully Controlled)

V_avg = (2V_m / π) cos α

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9️⃣ Comparison

• Half Wave → V_m / 2π (1 + cos α)
• Full Wave → V_m / π (1 + cos α)
• Bridge → 2V_m / π cos α

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GATE Tip: Carefully identify midpoint or bridge type before applying formula.