Direct generation of spice-compatible passive reduced-order models of ground/power planes

The continuing growth of complexity in modern ULSI design, combined with sub-nanosecond switching speeds, have made necessary the careful assessment of issues such as interplane capacitance, decoupling capacitor selection and placement, as well as resonance effects in the power distribution network. Toward this objective, various research groups have proposed modeling methodologies based on a two-dimensional approximation of Maxwell's equations in the space between adjacent power/ground planes. In this paper, a solid power/ground plane pair is discretized by a distributed RLCG circuit. The resulting discrete model is used in conjunction with the passive reduced-order modeling algorithm PRIMA for the generation of low order, multi-port macromodels to be incorporated in non-linear circuit simulators such as SPICE. Through a rigorous mathematical and physical investigation of the distributed electromagnetic effects between power/ground planes, reliable estimates for the order of the reduced model are derived for accurate multiport modeling over a given frequency bandwidth. The numerical results show that the generated rules provide the robustness required for the numerical generation of guaranteed-passive, reduced order electrical models for power/ground plane structures of optimum complexity.