cient Frequency - Domain Modeling and CircuitSimulation of Transmission

In this paper we describe an algorithm for eecient SPICE-level simulation of transmission lines with arbitrary scattering parameter descriptions. That is, the line can be represented in the form of a frequency-domain model or a table of measured frequency-domain data. Our approach initially uses a forced stable decade-by-decadè 2 minimization approach to construct a sum of rational functions approximation, but the approximation has dozens of poles and zeros. This unnecessarily high-order model is then reduced using a guaranteed stable model order reduction scheme based on balanced realizations. Once the reduced-order model is derived, it can be combined with the transmission line's inherent delay to generate an impulse response. Finally, following what is now a standard approach, the impulse response can be eeciently incorporated in a circuit simulator using recursive convolution. An example of a transmission line with skin-eeect is examined to both demonstrate the eeectiveness of the approach and to show its generality.