A robust algorithm for passive reduced-order macromodeling of MTLs with FD-PUL parameters using integrated congruence transform
This paper presents a robust method for guaranteed passive macromodeling of high-speed interconnects characterized by multiconductor transmission lines with frequency-dependent per-unit-length (FD-PUL) parameters, using integrated-congruence-transformation-based model-order-reduction techniques. For this purpose, a new formulation is developed to directly incorporate state-space equations corresponding to the positive-real (PR) rational functions representing the frequency dependence of PUL parameters, in Telegrapher's equations. The proposed formulation overcomes the need for explicit lumped-circuit realization with all positive elements for PR rational functions of FD-PUL parameters. Proof of passivity and numerical examples are presented to validate the theory.
integrated congruence transform high-speed interconnects transmission lines frequency-dependent parameters model order reduction signal integrity