An Fft-based Approach to including Non-ideal Ground Planes in a Fast 3-d Inductance Extraction Program

Finite ground-plane conductivity can have an enormous eeect on inductive coupling between signal lines. However, including non-ideal ground planes in 3-D in-ductance extraction programs is computationally expensive , as the ground plane must be nely discretized to insure the current distribution throughout the plane is accurately computed. This makes standard volume-element algorithms unsuitable because they require n 2 computation time and storage, where n is the number of laments into which the ground plane is discretized. In this paper we show that by using a preconditioned iterative method combined with an FFT-based algorithm to compute the iterates, we can reduce the computation time to eeectively n log n, and substantially reduce required storage. Experimental results are presented to show that using the FFT-based approach is more than an order of magnitude faster than computing the iterates explicitly, even on problems with as few as a thousand volume-laments.