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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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``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
CCRMA