Rational Modeling of Multiport Systems via a Symmetry and Passivity Preserving Mode-Revealing Transformation

Modeling of frequency-dependent components and subnetworks is often based on a terminal description by an admittance matrix in the frequency domain. One challenge in the extraction of state-space models from such data is to prevent possible error magnification when the model is to be applied in time-domain simulations. The error magnification is a consequence of inaccurate representation of small eigenvalues of the admittance matrix. This paper resolves the problem by introducing a similarity transformation matrix which better reveals the eigenvalues of the admittance matrix. The chosen transformation preserves the passivity and symmetry of the original data, allowing the modeling to be performed by standard methods for model extraction and passivity enforcement. The approach is demonstrated for the wideband modeling of subnetworks and power transformers. The new technique is shown to accurately capture the large and small eigenvalues alike, thereby avoiding error magnifications in time-domain simulations.