Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search


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.


Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[How to cite this work]  [Order a printed hardcopy]  [Comment on this page via email]

``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4
Copyright © 2023-08-20 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA