Adaptive Generation of Passive Rational Function Approximations for Electromagnetic Simulation

The output of an electromagnetic solver is usually the tabulated data of simulated network parameters as a function of frequency. There is a need to convert this data to an equivalent circuit model if the data was meant to be used in a transient circuit simulator. This conversion can be done by obtaining first a rational function approximation. Electromagnetic simulations usually involve analysis of passive distributed networks, hence only an approximate finite rational function can be obtained. Moreover, there is no a priori way of determining the order of the rational function. This paper introduces a new method for rational function approximation of frequency-domain electromagnetic simulation data. The proposed adaptive generation (AG) approach allows estimation of the model order for a given error tolerance and does not require any initial estimates or adjustment of hyperparameters. We present an implementation of AG using the recently developed sum of squares (SOS) orthogonal rational approximation (ORA) for extraction of passive equivalent circuit models from simulated input admittance or impedance parameters.