Order reduction of high-speed interconnect electrical models: The issue of passivity

Rapid distributed circuit simulation is now being recognized as a critical component of next-generation computer-aided design frameworks that will be used for performance evaluation and design of the information processing and communication systems of the 21st Century. Except for very simple systems, computer simulation of electromagnetic interactions in high-speed interconnects and packaging structures is hindered by the very large number of degrees of freedom involved in the discrete model. One potentially useful approach to overcooling this computational bottleneck is model order reduction, where parts of the electromagnetic model are replaced by models of substantially lower order, yet capable of capturing the electromagnetic behavior of the original subsystems with sufficient engineering accuracy. Reliable use of the generated reduced-order model in network-oriented simulators depends strongly on its passivity. This paper presents methodologies for the generation of passive reduced-order models of interconnect networks. Furthermore, it puts forward a general set of constraints on the state representation of the discrete model of the interconnect for the reduced order model to be passive.