What is "phasor"

n. 1 (context mathematics English) A representation of a complex number in terms of a complex exponential. 2 (context sciences English) and (context engineering English) A plotted line whose length and angle represent the amplitude and phase, respectively, of a sinusoidally varying quantity such as an alternating current.

Phasor is a phase vector representing a sine wave.

Phasor may also be:

• Phasor (sound synthesizer), a stereo music, sound and speech synthesizer for the Apple II computer
• Phasor measurement unit, a device that measures phasors on an electricity grid
• Phasor (radio broadcasting), a network of inductors and capacitors used to control the relative amplitude and phase of the radio frequency currents driving a directional antenna array.

In physics and engineering, a phasor (a portmanteau of phase vector), is a complex number representing a sinusoidal function whose amplitude (A), angular frequency (ω), and initial phase (θ) are time-invariant. It is related to a more general concept called analytic representation, which decomposes a sinusoid into the product of a complex constant and a factor that encapsulates the frequency and time dependence. The complex constant, which encapsulates amplitude and phase dependence, is known as phasor, complex amplitude, and (in older texts) sinor or even complexor.

A common situation in electrical networks is the existence of multiple sinusoids all with the same frequency, but different amplitudes and phases. The only difference in their analytic representations is the complex amplitude (phasor). A linear combination of such functions can be factored into the product of a linear combination of phasors (known as phasor arithmetic) and the time/frequency dependent factor that they all have in common.

The origin of the term phasor rightfully suggests that a (diagrammatic) calculus somewhat similar to that possible for vectors is possible for phasors as well. An important additional feature of the phasor transform is that differentiation and integration of sinusoidal signals (having constant amplitude, period and phase) corresponds to simple algebraic operations on the phasors; the phasor transform thus allows the analysis (calculation) of the AC steady state of RLC circuits by solving simple algebraic equations (albeit with complex coefficients) in the phasor domain instead of solving differential equations (with real coefficients) in the time domain. The originator of the phasor transform was Charles Proteus Steinmetz working at General Electric in the late 19th century.

Glossing over some mathematical details, the phasor transform can also be seen as a particular case of the Laplace transform, which additionally can be used to (simultaneously) derive the transient response of an RLC circuit. However, the Laplace transform is mathematically more difficult to apply and the effort may be unjustified if only steady state analysis is required.

Phasor is a stereo music, sound and speech synthesizer created by Applied Engineering for the Apple II family of computers. Consisting of a sound card and a set of related software, the Phasor system was designed to be compatible with most software written for other contemporary Apple II cards, including the Mockingboard, ALF's Apple Music Synthesizer, Echo+ and Super Music Synthesizer.

A phasor is a network of capacitors and variable inductors used to adjust the relative amplitude and phase of the current being distributed to each tower in a directional array. A typical phasor has separate controls to adjust the phase of the current going to each tower, adjustable power divider controls, and a common point impedance matching network to adjust the system input impedance to 50 ohms with no reactance without disturbing the phase or amplitude of the tower currents.