Parallel Combination of One-Ports

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Figure Fig.7.10 shows the parallel combination of two one-ports.

**Figure 7.10:** Two one-port networks combined in parallel. The admittance of the parallel combination is $\Gamma (s) = \Gamma _1(s) + \Gamma _2(s)$ .
$\includegraphics[scale=0.9]{eps/lparallel}$

Admittances add in parallel, so the combined admittance is $\Gamma (s) = \Gamma _1(s) + \Gamma _2(s)$ , and the impedance is

$\displaystyle R(s) = \frac{1}{\frac{1}{R_1(s)} + \frac{1}{R_2(s)}} = \frac{R_1(s) R_2(s) }{R_1(s) + R_2(s)}$

which is the familiar product-over-sum rule for combining impedances in parallel. This operation is often denoted by

$\displaystyle R= R_1 \vert\vert R_2$

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

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