Comparison of Methods for Rational Approximation of Simulated Time-Domain Responses: ARMA, ZD-VF, and TD-VF

This paper compares alternative methods for linear modeling of simulated time-domain responses by a rational approximation. The traditional approach based on autoregressive moving average (ARMA) is compared with two alternative approaches that have been introduced in recent years: Z-Domain Vector Fitting (ZD-VF) and Time-Domain Vector Fitting (TD-VF). Following a description of their implementation and fundamental properties, the methods are applied to the modeling of a frequency-dependent network equivalent. It is shown that TD-VF offers superior results in terms of accuracy and robustness, and the model has guaranteed stable poles. The ARMA approach requires higher orders than the others and the resulting model can be unstable. The ZD-VF approach is robust and gives a model with stable poles, but it produces incorrect simulation results when applied to truncated time-domain responses. The inaccuracy is caused mainly by the conversion of time-domain data into the $z$-domain. The fitting process of ARMA is faster than with the other approaches since it does not involve iterative pole relocations.