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 to be used for performance evaluation and design of the information processing and communication systems of the 21st century. Apart from 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 overcoming this computational bottleneck is model order reduction, where parts of the electromagnetic model are replaced by models which are of substantially lower order, yet are capable of capturing the electromagnetic behaviour 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 proposes a general set of constraints on the state representation of the discrete interconnect model for the reduced order model to be passive.