Phasor

The phasor (English phasor ) or the complex amplitude of the complex is used in preparation of sinusoidal or cosinusoidal time dependent variables. It summarizes the amplitude and zero phase angle together into a complex quantity. Here is the imaginary unit, the letter j is used and the symbols of a complex quantity is indicated by the underscore character ( according to DIN 1304-1 and DIN 5483-3 ).

An oscillating harmonically time-dependent physical size of the general form

With the conversion

Is the original size of it, the real part.

The use of such complex quantities found for example in the context of the complex AC circuit analysis application. This representation has the advantage that operations, such as analytical differentiation and integration can be carried out much easier than with the use of the trigonometric functions.

The phasor has the particular advantage that the ( sinusoidal ) time dependence does not show up at him. When rotated in the complex plane as a rotating phasor, the phasor is stationary. Its orientation is arbitrarily fixed as the time zero or the zero phase angle, but the same for all phasors of a connection. It is solely a matter of convenience, to put a reference in the positive direction of the real axis. For the series connection of impedances in the picture is to offer the partial resistances through all flowing together.

The use of the phasor in the exponential form is also useful for multiply and divide, while the use of the algebraic form is mounted in addition and subtraction.