GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 25 of 65

Marks: +1, -0

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

σ

is adjusted to entirely eliminate the

3^{\;\text "rd "\;}

harmonic component from the output voltage. Under this condition, for

v(t)

, the magnitude of the

5^{\;\text "th "\;}

harmonic component as a percentage of the magnitude of the fundamental component is ___________ (rounded off to 2 decimal places).

Solution:

We know that output waveform can be expressed in Fourier series form
From the given wave form,

V_{\;\text "on "\;}(t)=∑↙{n=1,3,5}↖{∞} \;{4 V_{s}}/{n π} \sin (\;{n π}/{2})

sin nd sin nωt

Π-26=2 d

d=\;{π}/{2}-6

for eliminating

3^{\;\text "rd "\;}

harmonics

\;{4 V_{s}}/{3 π} \sin (\;{3 π}/{2}) \sin 3 d=0

3 d=π ⇒ d=\;{π}/{3}

|\;{V_{05}}/{V_{01}}|=|\;{\;{4 V_{s}}/{5 π} \sin ({5 π}/{2}) \sin 5 d}/{{4 V_{s}}/{π} \sin (\;{π}/{2}) sind}|

=\;{1}/{5} × 100 \%=20 \%

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