Generation of passive macromodels for lossy multiconductor transmission lines

This paper presents an algorithm for the enforcement of passivity in delay-based multiconductor transmission line macromodels based on the Generalized Method of Characteristics. The algorithm enforces passivity via an iterative procedure based on first-order perturbations. More precisely, the short-circuit admittance matrix of the macromodel is iteratively modified until it becomes positive real. This iterative perturbation is performed on the solutions of a nonlinear eigenvalue problem, whereas the passivity verification is performed using an adaptive frequency sampling process. The proposed technique results in passive, accurate, and efficient macromodels for arbitrary lossy multiconductor transmission lines, which can be synthesized in SPICE netlists for system-level analysis and design.