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Series Combination of One-Ports

Figure 7.6 shows the series combination of two one-ports.

Figure 7.6: Two one-port networks combined in series. The impedance of the series combination is $ R(s) = F(s)/V(s) = R_1(s) + R_2(s)$ .
\includegraphics[scale=0.9]{eps/lseries}

Impedances add in series, so the aggregate impedance is $ R(s) = R_1(s) + R_2(s)$ , and the admittance is

$\displaystyle \Gamma(s) = \frac{1}{\frac{1}{\Gamma_1(s)} + \frac{1}{\Gamma_2(s)}} =
\frac{\Gamma_1(s) \Gamma_2(s) }{\Gamma_1(s) + \Gamma_2(s)}
$

The latter expression is the handy product-over-sum rule for combining admittances in series.


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-06-11 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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