Application of Extended Matrix Pencil Method in Multiport Frequency-Dependent Network Equivalent and the Transient Analysis of Multiconductor Transmission Line System

Abstract

In this paper, an extended matrix pencil method (EMPM) is proposed to achieve the equivalent analysis of a multiport system. First, the Hankel matrix constructed by the sampling data from multiple ports is integrated into an extended matrix. Then, operations, including singular value decomposition, order reduction, and solution of matrix pencil, are carried out for the extended matrix to calculate the common poles. Further, the residue matrix of the multiport system is solved by the least square method. Furthermore, for the multiconductor transmission line (MTL) system containing the frequency-dependent network (FDN) loads, a combination of the EMPM and piecewise linear recursive convolution (PLRC) is proposed to complete its transient analysis. The corresponding voltage expressions at the connection point of the MTL and FDN are analytically derived. Finally, the effectiveness of the EMPM in analyzing the FDN equivalent and that of the proposed combination of the EMPM and PLRC in analyzing the transient response of the MTL system containing the FDN are verified by numerical examples.