A Note on the Multiplicity of Poles in the Vector Fitting Macromodeling Method

Vector fitting is a robust macromodeling tool for rational approximation of spectral data obtained by full-wave electromagnetic simulators or high-frequency measurements. The technique iteratively calculates a suitable set of poles, and solves the residues of the transfer function in a two-step procedure. If poles with a higher order multiplicity occur during the pole-identification step, numerical problems and inaccuracies can result, especially if the normal equations are solved. This problem is illustrated on an RLC filter, and a generalization of the basis functions is proposed to resolve the issue