Fasors

Fasors are a mathematical representation of sinusoidal functions used primarily in electrical engineering and signal processing. A fasor describes a sinusoid's amplitude and phase as a complex number in the form A∠θ, where A is the magnitude and θ is the phase angle. By representing waves as rotating vectors in the complex plane, complex algebra can replace time‑domain differential equations with algebraic equations that are easier to solve.

The concept emerged in the late nineteenth century when engineers sought a concise way to analyze alternating‐current (AC) circuits. George Washington Pierce and earlier researchers formalized the method under the name “phasor” (from “phase” and “vector”), though the term “fasor” is sometimes used as a variant. Phasors simplify the analysis of linear systems with sinusoidal steady‑state inputs, allowing the use of impedance, admittance, and transfer functions directly in the frequency domain.

In practical applications, a sinusoid expressed as V(t)=Vm cos(ωt+φ) is represented by the fasor Vm∠φ. As ω varies, the fasor’s magnitude and phase can be plotted to illustrate frequency response. In circuit analysis, Ohm’s law applies directly: V=IZ, where V and I are fasors, and Z is complex impedance. The method also underlies Fourier series and Fourier transform techniques, where signals are decomposed into sums of complex exponentials.

The fasor technique remains central to power system analysis, control theory, communications, and many areas where sinusoidal signals dominate. It bridges time‑domain behavior and frequency‑domain insight, providing a powerful tool for engineers and scientists working with periodic phenomena.