Phasorrepræsentation

Phasorrepræsentation is a mathematical tool used primarily in electrical engineering and physics to represent sinusoidal signals in a simplified manner. It allows for the analysis of alternating current (AC) circuits and systems by converting differential equations into algebraic equations, which are generally easier to solve.

A phasor is a complex number that represents both the magnitude and phase of a sinusoidal waveform. For a sinusoid of the form A cos(ωt + φ), where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle, the corresponding phasor is given by A∠φ. Here, A is the magnitude of the complex number, and φ is its angle. The angular frequency ω is implicitly understood and not explicitly part of the phasor representation itself.

The advantage of using phasors lies in the fact that operations like addition, subtraction, differentiation, and integration of sinusoidal signals can be performed by manipulating these complex numbers. For example, differentiation in the time domain corresponds to multiplication by jω in the phasor domain, and integration corresponds to division by jω. This significantly simplifies the analysis of AC circuits, especially when dealing with multiple sinusoidal sources and components like resistors, inductors, and capacitors, where impedance can also be represented in phasor form. While it is a powerful tool, it is important to remember that phasor representation is strictly valid only for linear systems and signals with constant frequency.