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

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

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.