Substrate resistance extraction using a multi-domain surface integral formulation

Abstract

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.