class Introduction "Introduction to phasors"
extends Modelica.Icons.Information;
annotation (Documentation(info = "<html>\n\n<p>\nThe purely sinusoidal voltage\n</p>\n\n<p>\n<img\n border=\"0\"\n src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Introduction/img1.png\"\n alt=\"v=\\sqrt{2}V_{\\mathrm{RMS}}\\cos(\\omega t+\\varphi_{v})\">\n</p>\n\n<p>\nin the time domain can be represented by a complex\n<a href=\"modelica://Modelica.Electrical.QuasiStationary.UsersGuide.Glossar\">rms</a> phasor\n</p>\n\n<p>\n<img\n border=\"0\"\n src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Introduction/img2.png\"\n alt=\"\\underline{v}=V_{\\mathrm{RMS}}e^{j\\varphi_{v}}.\">\n</p>\n\n<p>For these quasi stationary\nphasor the following relationship applies:</p>\n\n<p>\n<img\n border=\"0\"\n src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Introduction/img3.png\"\n alt=\"\\begin{displaymath}\nv=\\mathrm{Re}(\\sqrt{2}\\underline{v}e^{j\\omega t})\\end{displaymath}\">\n</p>\n\n<p>\nThis equation is also illustrated in Fig. 1.\n</p>\n\n<table border=\"0\" cellspacing=\"0\" cellpadding=\"2\">\n <tr>\n <td>\n <img src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Introduction/phasor_voltage.png\"\n alt=\"phasor_voltage.png\">\n </td>\n </tr>\n <caption align=\"bottom\">Fig. 1: Relationship between voltage phasor and time domain voltage</caption>\n</table>\n\n<p>\nFrom the above equation it is obvious that for <em>t</em> = 0\nthe time domain voltage is <em>v</em> = cos(<em>φ<sub>v</sub></em>).\nThe complex representation of the phasor corresponds with this instance, too, since\nthe phasor is leading the real axis by the angle <em>φ<sub>v</sub></em>.\n</p>\n\n<p>\nThe explanation given for sinusoidal voltages can certainly also be applied\nto sinusoidal currents.</p>\n\n<h4>See also</h4>\n<a href=\"modelica://Modelica.Electrical.QuasiStationary.UsersGuide.Overview.ACCircuit\">\n AC circuit</a>,\n<a href=\"modelica://Modelica.Electrical.QuasiStationary.UsersGuide.Overview.Power\">\n Power</a>,\n<a href=\"modelica://Modelica.Electrical.QuasiStationary.UsersGuide.Overview.ReferenceSystem\">\n Reference system</a>\n\n</html>"));
end Introduction;