Substrate resistance extraction using a multi-domain surface integral formulation

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (p. 65-66).In recent years, mixed-signal designs have become more pervasive, due to their efficient use of area and power. Unfortunately, with sensitive analog and fast digital circuits sharing a common, non-ideal substrate, such designs carry the additional design burden of electromagnetic coupling between contacts. This thesis presents a method that quickly extracts the electroquasistatic coupling resistances between contacts on a planar, rectangular, two-layer lossy substrate, using an FFT-accelerated multi-domain surface integral formulation. The multi-domain surface integral formulation allows for multi-layered substrates, without meshing the volume. This method has the advantages of easy meshing, simple implementation, and FFT-accelerated iterative methods. Also, a three-dimensional variant of this method allows for more complex substrate geometries than some other surface integral techniques, such as multilayered Green's functions; this three-dimensional problem and its solution are presented in parallel with the planar substrate problem and solution. Results from a C++ implementation are presented for the planar problem.by Anne M. Vithayathil.S.M

Fast methods for extraction and sparsification of substrate coupling

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Includes bibliographical references (p. 107-111).Substrate coupling effects have had an increasing impact on circuit performance in recent years. As a result, there is strong demand for substrate simulation tools. Past work has concentrated on fast substrate solvers that are applied once per contact to get the dense conductance matrix G. We develop a method of using any underlying substrate solver a near-constant number of times to obtain a sparse approximate representation G [approximately equal to] QGwtQ' in a new basis. This method differs from previous matrix sparsification techniques in that it requires only a "black box" which can apply G quickly; it doesn't need an analytical representation of the underlying kernel or access to individual entries of G. The change-of-basis matrix Q is also sparse. For our largest example, with 10240 contacts, we obtained a Gwt with 130 times fewer nonzeros than the dense G (and Q more than twice as sparse as Gwt), with 20 times fewer solves than the naive method, and fewer than 4 percent of the QGwtQ' entries had relative error more than 10% compared to the exact G.by Joseph Daniel Kanapka.Ph.D

Fast algorithms for ill-conditioned dense matrix problems in VLSI interconnect and substrate modeling

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (leaves 131-135).by Mike Chuan Chou.Ph.D