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author | Karl Berry <karl@freefriends.org> | 2009-06-17 21:56:44 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2009-06-17 21:56:44 +0000 |
commit | 75fc8c58c1c50bad4441d167fda8da1157f1d735 (patch) | |
tree | 74d8df5863035192302d10dbe0de69adeefe5cbc /Master/texmf-dist/doc/latex/steinmetz/steinmetz-test.tex | |
parent | 802c96d478e0a3834319a5326fb8977981b454b7 (diff) |
new latex package steinmetz (15jun09)
git-svn-id: svn://tug.org/texlive/trunk@13784 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/steinmetz/steinmetz-test.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/steinmetz/steinmetz-test.tex | 71 |
1 files changed, 71 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/steinmetz/steinmetz-test.tex b/Master/texmf-dist/doc/latex/steinmetz/steinmetz-test.tex new file mode 100644 index 00000000000..8f27b2c1ec9 --- /dev/null +++ b/Master/texmf-dist/doc/latex/steinmetz/steinmetz-test.tex @@ -0,0 +1,71 @@ +%% +%% 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'. |