Phasor

A phasor is a complex-number representation of a sinusoidal quantity’s amplitude and phase. It turns steady-state sinusoidal calculations into algebra with complex numbers.

Euler's formula: The identity relating complex exponentials to sine and cosine: e^(iθ) = cos θ + i sin θ. It converts a sinusoid into a rotating complex exponential, the basis of phasor notation.
Amplitude: The maximum displacement or value of an oscillating quantity from its equilibrium or reference level. A phasor’s magnitude commonly records the sinusoid’s amplitude, though RMS conventions also occur.
Alternating current: Electric current that periodically changes magnitude and direction. Phasors make sinusoidal AC voltage and current relations easier to calculate.
Time-domain analysis: Analysis that describes a system’s signals directly as functions of time. Unlike phasor analysis, it retains explicit time variation in sinusoidal signals.
Complex number: A number with a real part and an imaginary part, often represented as a point in a plane. A phasor uses a complex number to store amplitude and phase together.
Phase (waves): The position within a periodic cycle, usually expressed as an angle or fraction of a period. A phasor’s angle records the sinusoid’s phase relative to a reference.
Phasor diagram: A vector diagram showing sinusoidal quantities as directed segments whose angles represent phase differences. It displays relative phase and magnitude among quantities represented by phasors.
Transient response: A system’s temporary behavior after a change in input or initial condition. Ordinary phasor analysis omits transients and describes steady-state sinusoidal behavior.
Angular frequency: The rate of change of angular phase, measured in radians per unit time. It determines how quickly the sinusoid represented by a phasor rotates.
Root mean square: A measure of magnitude equal to the square root of the mean of squared values. Electrical phasors often use RMS magnitudes instead of peak amplitudes.

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