A sparse-matrix/canonical grid method for analyzing densely packed interconnects

Due to the continuous increase of the operating frequency, full-wave electromagnetic characterization of microstrip interconnects plays an important role in electronic packaging. To reduce the size of the package, microstrip interconnects may be densely packed together making the number of unknowns representing the currents large. It is a real challenge to model densely packed interconnects as we have to address both the issues of matrix fill-time and solution time in the moment method solution. We employ the fast Hankel transform (FHT) method to obtain an accurate numerical spatial-domain Green´s function. This is followed by the matrix pencil (MP) method for the closed-form expression in terms of a sum of complex exponents. Taylor series expansions of these complex exponents are than incorporated into the sparse-matrix/canonical grid (SMCG) method for the analysis of densely packed microstrip interconnects. It is demonstrated that applying the FHT and MP procedure can greatly reduce the matrix fill-time while the fast SMCG method greatly reduce the matrix solution time. The efficiency of the method is further improved by implementing the algorithm on a parallel-computing platform.