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An efficient Delaunay-Voronoi modeling of the power-ground planes suitable directly for SPICE compatibity is proposed to deal with the ground bounce noise and decoupling capacitors placement problems for the high-speed digital system designs. The model consists of virtual ports and triangular meshes with the lumped circuit elements, in which all the element values can be related to the mesh geometry shape by the analogy between the circuit equations and Maxwell's equations. Since the analogy fails to apply due to the singular fields near the input/output pins, the via effect of driving and sensing ports is not negligible and an analytical expression from the Hankel function is thus presented for the correction term. A simple rule has been investigated for the model with minimum lumped circuit elements to accurately represent the power-ground planes over the frequency range of interests. The full-wave simulation and measurement results verify the good correlations with the proposed models for the impedance responses of regular and defective plane shapes.
Date of Publication: May 2008