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GATE 2014 EE (EE1) – Question 65

Power Electronics · Single-phase and three-phase voltage and current source inverters, sinusoidal pulse width modulation · 2 marks · Numerical answer

The figure shows one period of inverter output. Choose 60° < α < 90° for fundamental-component rms voltage 50 V. Find α (degrees).

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Correct answer: 76.5 to 78.0

Explanation

The waveform has half-wave antisymmetry, so its fundamental sine coefficient is b1=(2/π)∫₀^πv(θ)sinθdθ=(400/π)(1−2cosα). Its rms is b1/√2in the stated60°<α<90°range. Setting this to50gives cosα=[1−50π√2/400]/2, hence **α=77.1547°**.