Automatic generation of accurate circuit models of 3-D interconnect

In order to optimize high-speed systems, designers need tools that automatically generate reduced order SPICE compatible models from geometric descriptions of interconnect and packaging. In this paper, we consider structures small compared to a wavelength, and use a discretized integral formulation combined with an Arnoldi-based model-order reduction strategy to compute efficiently accurate reduced-order models from three-dimensional (3-D) structures. Several issues are addressed including: (1) formulation to insure passivity in the reduced-order models; (2) efficient reduction using preconditioned inner-loop iterative methods; (3) expansion about multiple s-domain points. Results are presented on several industrial examples to demonstrate the capabilities and speed of these new methods.