Advanced Vector Fitting for Multiport Problems

Summary

This chapter explains the vector fitting (VF) algorithm to the simultaneous fitting of several (scalar) elements collected in a vector of frequency responses. It introduces alternative multi‐input multi‐output (MIMO) model formulations and demonstrates that the common pole fitting capability of VF leads directly to compact state‐space models in a natural way. Particular emphasis is on the extraction of minimal state‐space realizations. The chapter shows that this requirement is necessary for various passivity characterization and enforcement schemes. In addition, it shows how to enforce structural symmetry of the model, which corresponds to preserving system reciprocity. Next, the chapter addresses more advanced versions of VF, with the main objective of preventing error magnification by preserving the information on small modes (eigenvalues) buried in the data. The two main techniques suggested for preventing load sensitivity and error magnification are the mode‐revealing transformations and the modal VF scheme.