Electrical Engineering ⇒ Topic : Illustration of complex waveforms

Illustration. Fig. a (i) shows an ideal symmetrical square wave. An ideal square wave contains an infinite number of odd harmonics; there are no even harmonics and there is no constant component. Fig. a (ii) shows how an ideal symmetrical square wave can be built up with fundamental and third harmonic; the amplitude of third harmonic being tone-third that of the fundamental. For this square wave, it can be shown by Fourier analysis that instantaneous voltage (v) at any time t is given by ;

                                                                                         figure (a)

If we also add higher harmonics, the equation becomes

Note. Any variation from a pure sine wave produces harmonics. A non-sinusoidal wave is composed of the fundamental and the harmonics. Some types of waveforms have only odd harmonics, some have only even harmonics and some contain both. Generally, only the fundamental, and the first few harmonics are of significant importance in determining the waveshape of the wave.