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The phase angle of a point on a periodic wave is the distance between the point and a specified reference point, expressed using an angular measure. This angular measure is obtained by projecting a rotating vector onto the real axis of an Argand diagram.

The phase angle of a vector may be written in angle notation as M ∠θ, where M is the magnitude of the vector and θ is the phase angle relative to the specified reference point. The reference point may be fixed in space, or a point on another periodic wave. In the latter case, the waves may be plotted on a suitable coordinate system, such as a Cartesian plot, with degrees or other angular measure usually plotted on the abscissa and amplitude on the ordinate. Usually, at least one full cycle of each wave is plotted, with 360° (2π radians) encompassing one full cycle. The reference points may be any significant instants on the waves, such as where they cross the abscissa.

For example, in electrical engineering, sinusoidal voltage and current can be expressed as a sine function with a magnitude such as:

$v\; =\; V\_m\; \backslash cos(\; \backslash omega\; t\; +\; \backslash phi\; )\; \backslash !\backslash$

Where φ is the phase angle, V_m is the amplitude, ω is the angular frequency, and t is time.

In many cases, the phase angle is expressed in degrees while the product ωt is usually expressed in radians.

See also

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• Phasor (electronics)
• Phasor (physics)

Sources

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• Federal Standard 1037C
• Electric Circuits (7th ed) by James Nilsson and Susan Riedel

Angle

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