Title :
Multiple scattering among vias in lossy planar waveguides using SMCG method
Author :
Huang, Chung-Chi ; Tsang, Leung ; Chan, Chi H.
Author_Institution :
Dept. of Electr. Eng., Univ. of Washington, Seattle, WA, USA
fDate :
5/1/2002 12:00:00 AM
Abstract :
Large-scale full-wave multiple scattering among cylindrical vias in planar waveguides is modeled using the Foldy-Lax equation. The formulation includes the skin effects of the conducting power/ground plane. Numerical solution of the Foldy-Lax equation with large number of unknowns is computed efficiently using the sparse-matrix canonical-grid method. In this method, interactions among vias are decomposed into the strong interactions part and the weak interactions part. The calculation of the weak part is carried out using two-dimensional (2-D)-fast Fourier transform (FFT) by translating the locations of the vias onto the uniform grids. The final solution of the Foldy-Lax equations is calculated by an iterative method. The results show O (N log N) CPU efficiency and O (N) memory efficiency. This makes large scale via problems possible for computer simulation.
Keywords :
Green´s function methods; circuit simulation; computational complexity; iterative methods; matrix inversion; planar waveguides; printed circuit design; skin effect; sparse matrices; waveguide theory; Foldy-Lax equation; conducting power/ground plane; dyadic Green´s function; iterative method; large-scale full-wave multiple scattering; lossy planar waveguides; memory efficiency; multiple scattering among vias; skin effects; sparse-matrix canonical-grid method; strong interactions; two-dimensional FFT; uniform grids; weak interactions; Electromagnetic scattering; Electromagnetic waveguides; Equations; Equivalent circuits; Frequency; Integrated circuit interconnections; Large-scale systems; Planar waveguides; Skin effect; Transmission line matrix methods;
Journal_Title :
Advanced Packaging, IEEE Transactions on
DOI :
10.1109/TADVP.2002.803262
