Question

In the multiple-pulse width modulation method with two pulses per half cycle of width = d each and ɣ as the distance between the first pulse and ωt=0, has the Fourier coefficient bn =

(a) (8Vs/π) [ cos(ɣπ/2) cos(nd/2) ].

(b) 0

(c) (4Vs/nπ) [sin(nɣ) sin(nd/2)].

(d) (8Vs/nπ) [sin(nɣ) sin(nd/2)].

I had been asked this question in a national level competition.

My question is from PWM Inverters-2 in section Inverters of Power Electronics

Answer 1

Right answer is (d) (8Vs/nπ) [sin(nɣ) sin(nd/2)].

Easy explanation: The Fourier analysis is as under:

bn = (4/π) ∫ Vs sin⁡ nωt .d(ωt) , Where the integration would run from (ɣ + d/2) to (ɣ – d/2)

bn = (8Vs/nπ) [sin(nɣ) sin(nd/2)].