Series Combination of One-Ports

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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 .
$\includegraphics[scale=0.9]{eps/lseries}$

Impedances add in series, so the aggregate impedance is , 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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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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