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 POWER ELECTRONICS – PAGE 9

Derivation of Average Output Voltage

                                      

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1️⃣ Input Voltage

Input AC voltage:

v = V_m sin ωt

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2️⃣ Conduction Interval

SCR conducts only from firing angle α to π.

Limits of integration: α → π

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3️⃣ Average Voltage Formula

Average value over one complete cycle:

V_avg = (1 / 2π) ∫_α^π V_m sinθ dθ

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4️⃣ Integration

∫ sinθ dθ = −cosθ

V_avg = (V_m / 2π) [ −cosθ ]_α^π

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5️⃣ Substituting Limits

cosπ = −1

V_avg = (V_m / 2π) (1 + cos α)

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6️⃣ Final Result

V_avg = (V_m / 2π) (1 + cos α)

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7️⃣ Special Cases

• α = 0° → Vavg = V_m / π (Maximum)
• α = 90° → Reduced output
• α = 180° → Zero output

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Important: α must be in radians while using formula.