General One-Ports

General one-port admittance

$$\Gamma(s) = {b_0 s^N + b_1 s^{N-1} + \cdots + b_N \over a_0 s^N + a_1 s^{N-1} + \cdots + a_N} \isdef {B(s) \over A(s)}$$

• Physically, must have $b_0 = 0$
  • Every physical system ``looks like a mass'' at infinite frequency
  • For best reduced-order approximation, need $b_0\neq0$
  • Standard normalization: $a_0 = 1$ ($A(z)$ monic)
• $\Gamma(s)$ often a rational approximation to a true physical admittance
  • Filter design problem
  • Try to preserve fundamental physical properties