Question

A periodic square wave is formed by rectangular pulses ranging from -1 to +1 and period = 2 units. The ratio of the power in the 7th harmonic to the power in the 5th harmonic for this waveform is equal to ____________

(a) 1

(b) 0.5

(c) 2

(d) 2.5

The question was asked in homework.

Enquiry is from Miscellaneous Examples on Fourier Series in chapter Fourier Series of Signals and Systems

Answer 1

Correct choice is (b) 0.5

The explanation is: For a periodic square wave nth harmonic component ∝ \(\frac{1}{n}\)

Thus the power in the nth harmonic component is ∝ \(\frac{1}{n^2}\)

∴ Ratio of power in 7th harmonic to 5th harmonic for the given wage form = \(\frac{\frac{1}{7^2}}{\frac{1}{5^2}}\)

= \(\frac{25}{4}\) ≅ 0.5.