Phasor Representation and Time-Domain Plot of Distorted Waveforms

In electrical engineering, as well as in other areas, sinusoidal waveforms can be represented by means of phasors. A phasor can be thought of as the representation of a complex number with a constant modulus and a varying angle. As the angle varies continuously from zero to 360º, the length of the projection of the phasor on either the real or complex axis varies according to a time-dependent sine or cosine function.

The waveforms of real-life voltages or currents are seldom sinusoidal. However, they can be decomposed into their (sinusoidal) harmonic components, for example, by means of a discrete Fourier transform, which yields the harmonic spectra for the magnitudes being measured. In power distribution systems, harmonic spectra typically include only odd harmonics with amplitude decreasing with the harmonic frequency. The greater the number of harmonics included, the better the recomposition of the original waveform. In representing power distribution, going up to the 25th harmonic is usually sufficiently accurate.

For the sake of clarity, this Demonstration only includes the fundamental, the third, fifth, and seventh harmonics. You can vary the all the moduli (amplitudes) and the angles except for the one corresponding to the fundamental, which is the reference (zero phase) angle. The initial default settings correspond to the components of a square waveform.