GATE Electrical Engineering - Complete Master Library

 

GATE Electrical – Power Electronics

Module 1: Uncontrolled Rectifiers

Page 2: Single Phase Half Wave Rectifier (R Load)

                                      

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1. Circuit Description

A Half Wave Rectifier consists of:

• Single phase AC source
• One Power Diode
• Pure Resistive Load (R)

The diode conducts only during the positive half cycle of input voltage.

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2. Working Principle

Positive Half Cycle (0 to π)

• Diode is forward biased
• Current flows through load
• Output voltage equals input voltage

Negative Half Cycle (π to 2π)

• Diode is reverse biased
• No current flows
• Output voltage = 0

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3. Waveform Explanation

Input: Sinusoidal waveform Output: Only positive half cycles appear across load Current waveform is identical to voltage waveform (since load is purely resistive).

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4. Mathematical Analysis

Input voltage:

v = V_m sin(ωt)

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4.1 Average Output Voltage

V_avg = (1 / 2π) ∫_{0 to π} V_m sin(ωt) d(ωt)

V_avg = V_m / π

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4.2 RMS Output Voltage

V_rms = √[(1 / 2π) ∫_{0 to π} (V_m sin(ωt))² d(ωt)]

V_rms = V_m / 2

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4.3 Average Load Current

I_avg = V_avg / R = V_m / (πR)

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4.4 RMS Load Current

I_rms = V_rms / R = V_m / (2R)

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5. Peak Inverse Voltage (PIV)

Maximum reverse voltage across diode occurs during negative half cycle.

PIV = V_m

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6. Ripple Factor

Ripple factor (γ):

γ = 1.21

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7. Efficiency

Maximum Efficiency = 40.6%

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8. Important GATE Points

• Remember Vavg = Vm / π
• Remember Vrms = Vm / 2
• PIV = Vm
• Efficiency = 40.6%
• Ripple factor = 1.21

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