Iterative matrix fitting approach of frequency dependent matrices based on vector fitting

Rational fitting techniques are the basis for modeling the physical behaviors of systems with respect to their input and output characteristics. Due to its robustness and accuracy, Vector Fitting (VF) has been widely used to obtain rational models from tabulated frequency domain responses. Three types of systems could be approximated: 1) A scalar function or scalar fitting (SF) case, 2) A column vector function or column fitting (CF) case, and 3) A matrix function or matrix fitting (MF) case. A common set of poles is desired for physical and implementation reasons. This is a fact in the SF case, and the mathematical formulation of VF allows obtaining a rational function-based model with a common set of poles in the CF case. However, as this is not possible in the MF case, a methodology based on the VF iteration is proposed, which ensures a common set of poles. The advantages are demonstrated in three test cases: 1) Multi-phase transmission-line modeling using the Universal Line Model (ULM), 2) Multi-block data analysis, and 3) Printed Circuit Board (PCB) transmission-line characterization.