Application of the Conjugate Gradient Technique to Stripline Packaging Problems

In most applications the method of moments (MoM) generates full reaction matrices. However, in this paper, we demonstrate that sparse reaction matrices are produced when modeling stripline interconnects. This is demonstrated by investigating the sparse nature of the MoM reaction matrices that are produced when using the full-wave layered interconnect simulator (UA-FWLIS) with a parallel-plate Green's function. In order to explain the sparse nature of the reaction matrices, the electric fields that are excited by horizontal and vertical electric dipole sources are briefly overviewed. Then the variations of the reaction elements with distance are studied, and this information is used to provide a cut-off criterion for the reaction element calculations. We found that by applying sparse matrix storage techniques and a sparse matrix solver, the matrix solution time is dramatically improved when compared with a commercial MoM-based simulator