Advancements in Iterative Methods for Rational Approximation in the Frequency Domain

Rational approximation of frequency-domain responses is commonly used in electromagnetic transients programs for frequency-dependent modeling of transmission lines and to some extent, network equivalents (FDNEs) and transformers. This paper analyses one of the techniques [vector fitting (VF)] within a general iterative least-squares scheme that also explains the relation with the polynomial-based Sanathanan-Koerner iteration. Two recent enhancements of the original VF formulation are described: orthonormal vector fitting (OVF) which uses orthonormal functions as basis functions instead of partial fractions, and relaxed vector fitting (RVF), which uses a relaxed least-squares normalization for the pole identification step. These approaches have been combined into a single approach: relaxed orthonormal vector fitting (ROVF). The application to FDNE identification shows that ROVF offers more robustness and better convergence than the original VF formulation. Alternative formulations using explicit weighting and total least squares are also explored.