WOLFRAM SYSTEM MODELER

Introduction

Introduction to phasors

Wolfram Language

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Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

The purely sinusoidal voltage

v=\sqrt{2}V_{\mathrm{RMS}}\cos(\omega t+\varphi_{v})

in the time domain can be represented by a complex rms phasor

\underline{v}=V_{\mathrm{RMS}}e^{j\varphi_{v}}.

For these quasi-static phasor the following relationship applies:

\begin{displaymath}
v=\mathrm{Re}(\sqrt{2}\underline{v}e^{j\omega t})\end{displaymath}

This equation is also illustrated in Fig. 1.

phasor_voltage.png
Fig. 1: Relationship between voltage phasor and time domain voltage

From the above equation it is obvious that for t = 0 the time domain voltage is v = cos(φv). The complex representation of the phasor corresponds with this instance, too, since the phasor is leading the real axis by the angle φv.

The explanation given for sinusoidal voltages can certainly also be applied to sinusoidal currents.

See also

AC circuit, Power, Reference system