Connecting vector fitting to barycentric interpolation and the Loewner matrix

Vector fitting (VF) [1] is a popular algorithm among electronic engineers for building rational models from measured or full-wave electromagnetic simulated frequency domain responses (S-, Y-, or Z- parameters). This paper exhibits a connection between the vector fitting formulation, on one hand, and the barycentric form of a rational interpolant and the Loewner matrix, on the other hand. This connection helps address the issues of choosing the starting poles and determining the true model order.