Construction of Reciprocal Macromodels in the Loewner Matrix Framework

Abstract

Many of the passive interconnect systems that arise in applications for analysis of power and signal integrity (PI/SI) are reciprocal by nature, and the transfer matrices of such systems are characterized by symmetry constraints. Therefore, it is natural to think in using reciprocal macromodels for the representation of reciprocal systems. Reciprocal macromodels do not only represent in a more faithful way the systems in which they are based upon, but given a reciprocal stable macromodel, it is computationally cheaper to find its passivity violations. This work shows how to construct reciprocal descriptor systems macromodels from black box data using the Loewner matrix (LM) framework, and also, it shows that it is possible to enforce stability and passivity in reciprocal stable macromodels, keeping its size and structure. Various examples of printed circuit board-based high-speed links and power delivery networks described by scattering parameters are used to demonstrate the effectiveness of the proposed approach.