A Phasor is a Complex Number representing a Sinusoidal quantity, usually in Exponential_function form. They are used in engineering to simplify computations involving sinusoids, where they can often reduce a Differential_equation problem to an algebraic one.
generally a sinewave can be expressed in the form (the reason for using cos rather than sin will become apparent later)
where
- y is the quanitity that is varying with time
- φ is a constant offset known as the phase angle
- A is the peak value (aplitude) of the waveform
- ω is the angular frequency ω = 2πf where f is frequency.
- t is time.
this can be expressed as
where
- j is the imaginary unit
- re() represents the real part of a complex number
which in turn can be changed using Euler's formula into
Aeφ is a complex number encoding the magnitude and phase of the sinewave known as a phasor. Phasors are often written in the form A∠φ (∠ is the angle sign U+220).
In electronic circuit analysis, a phasor is a quantity with magnitude and phase used in the analysis of an AC circuit that uses a single frequency of sine wave.
The magnitude of a phasor represents voltage or current. The angle represents the phase with relation to a fixed reference (usually one of the circuit's power supplies).
A positive angle represents leading; a negative angle represents lagging.
Phasors can be represented in either cartesian or exponential form.
Ohm's law can be extended to V=IZ where V and I are phasors represented as complex numbers and Z is the complex impedance of the component.
Other circuit analysis techniques that work for DC voltages, currents and resistances work for phasor voltage and current with complex impedances.
