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Modal Vector Fitting: A Tool For Generating Rational Models of High Accuracy With Arbitrary Terminal Conditions

This paper introduces a new approach for rational macromodeling of multiport devices that ensures high accuracy with arbitrary terminal conditions. This is achieved by reformulating the vector fitting (VF) technique to focus on eigenpairs rather than matrix elements. By choosing the least squares (LS) weighting equal to the inverse of the eigenvalue magnitude, the modal components are fitted with a relative accuracy criterion. The resulting modal vector fitting (MVF) method is shown to give a major improvement in accuracy for cases with a high ratio between the largest and smallest eigenvalue, although it is computationally more costly than VF. It is also shown how to utilize the impedance characteristics of the adjacent network in the fitting process. The application of MVF is demonstrated for a two-conductor stripline, a coaxial cable, and a transformer measurement. We also show a simplified procedure which achieves similar results as MVF if the admittance matrix can be diagonalized by a constant transformation matrix. The extracted model is finally subjected to passivity enforcement by the modal perturbation method, which makes use of a similar LS formulation as MVF for the constrained optimization problem.