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General One-Ports

An arbitrary interconnection of $ N$ impedances and admittances, with input and output force and/or velocities defined, results in a one-port with admittance expressible as

$\displaystyle \Gamma(s) =
\frac{b_0 s^N + b_1 s^{N-1}
+ \cdots + b_N}{s^N + a_1 s^{N-1} + \cdots + a_N}
\isdef \frac{B(s)}{A(s)}
$

In any mechanical situation we have $ b_0 = 0$, in principle, since at sufficiently high frequencies, every mechanical system must ``look like a mass.''8.3 However, for purposes of approximation to a real physical system, it may well be best to allow $ b_0\neq 0$ and consider the above expression to be a rational approximation to the true admittance function.


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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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