Parallel Combination of One-Ports

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The wave impedance in a propagation medium relates the force-related component of the wave motion to the displacement-related component of the motion. — Click for http://ccrma.stanford.edu/~jos/OnePorts/Impedance.html

The wave impedance in a propagation medium is the force variable (such as pressure for acoustic waves) divided by the velocity variable. In ideal plane waves and traveling waves, the wave impedance is a real, positive number. For spherical waves in air, the wave impedance is different at each frequency. — Click for https://ccrma.stanford.edu/~jos/OnePorts/Impedance.html

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Parallel Combination of One-Ports

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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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

Parallel Combination of One-Ports

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4 Copyright © 2024-06-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2024-06-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University