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.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Power Quality Teaching Toy Edition 3.0.4 by Alex McEachern, available at www.PowerStandards.com.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+