GATE 2020 EE – Question 32
A single-phase inverter is fed from a 100 V dc source and is controlled using a quasi-square wave modulation scheme to produce an output waveform, $v(t)$, as shown. The angle $\sigma$ is adjusted to entirely eliminate the third harmonic component from the output voltage. Under this condition, for $v(t)$, the magnitude of the 5th harmonic component as a percentage of the magnitude of the fundamental component is ________ (rounded off to 2 decimal places).
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Correct answer: 19.90 to 20.20
Explanation
For this quasi-square wave the $n$th harmonic is proportional to $\frac{\cos n\sigma}{n}$. The third harmonic vanishes when $\cos3\sigma=0$, i.e. $\sigma=30^\circ$. Then $\frac{|V_5|}{|V_1|}=\frac{|\cos150^\circ|/5}{\cos30^\circ}=\frac15=20\%$.