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authorKarl Berry <karl@freefriends.org>2009-06-17 21:56:44 +0000
committerKarl Berry <karl@freefriends.org>2009-06-17 21:56:44 +0000
commit75fc8c58c1c50bad4441d167fda8da1157f1d735 (patch)
tree74d8df5863035192302d10dbe0de69adeefe5cbc /Master/texmf-dist/doc/latex/steinmetz/steinmetz-test.tex
parent802c96d478e0a3834319a5326fb8977981b454b7 (diff)
new latex package steinmetz (15jun09)
git-svn-id: svn://tug.org/texlive/trunk@13784 c570f23f-e606-0410-a88d-b1316a301751
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+%%
+%% This is file `steinmetz-test.tex',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% steinmetz.dtx (with options: `example')
+%%
+%% This is a generated file.
+%%
+%% Copyright (C) 2009 by Enrico Gregorio <Enrico dot Gregorio (at) univr dot it>
+%%
+%% This file may be distributed and/or modified under the conditions of
+%% the LaTeX Project Public License, either version 1.3 of this license
+%% or (at your option) any later version. The latest version of this
+%% license is in:
+%%
+%% http://www.latex-project.org/lppl.txt
+%%
+%% and version 1.3 or later is part of all distributions of LaTeX version
+%% 2005/12/01 or later.
+%%
+\documentclass[a4paper]{article}
+\usepackage{steinmetz}
+
+\begin{document}
+
+We will indicate the amplitude and phase relationship through the use
+of complex notation: a complex number is used to indicate only the
+amplitude and phase of voltages and currents in the circuit (since the
+sinusoidal time variation factor is common to all terms). For
+example, a circuit described by the equation
+\[
+i(t)=I_{0}\cos(\omega t+\theta)
+\]
+can be written in complex exponential form as
+\[
+i(t)=\Re\{I_{0}e^{j(\omega t+\theta)}\}=
+\Re\{I_{0}e^{j\theta}e^{j\omega t}\},
+\]
+and in polar complex form as
+\[
+i(t)=\Re\{I_{0}\phase{\theta}e^{j\omega t}\}.
+\]
+Finally, we can simplify the notation by dropping the implied
+$e^{j\omega t}$ term and the $\Re\{~\}$ operator, leaving the phasor
+notation:
+\[
+\mathbf{I}=I_{0}\phase{\theta}=I_{0}e^{j\theta}=
+I_{0}(\cos\theta+j\sin\theta),
+\]
+where the boldface $\mathbf{I}$ reminds us that the phasor quantity
+$\mathbf{I}$ is a complex number. The important advantage of this
+approach is that the mathematics involves mostly simple algebraic
+operations on the magnitudes and phases.
+
+It is interesting to look at the complex ratio of phasor voltage and
+phasor current, $\mathbf{V}\!/\mathbf{I}$, which is called the
+\emph{impedance}~$\mathbf{Z}$. For the basic circuit elements we
+find:
+\begin{itemize}
+\item Resistor, $R$: $\mathbf{Z}=R$,
+\item Inductor, $L$: $\mathbf{Z}=j\omega L=
+ \omega L\phase{90^{\circ}}$,
+\item Capacitor, $C$: $\displaystyle\mathbf{Z}=\frac{1}{j\omega C}=
+ -j\frac{1}{\omega C}=\frac{1}{\omega C}\phase{-90^{\circ}}$.
+\end{itemize}
+\end{document}
+\endinput
+%%
+%% End of file `steinmetz-test.tex'.