Efficient calculation of transient fields in multilayered media
A scheme for computing fields radiated by transient sources residing above a grounded multilayered medium is proposed. First, the causality trick is invoked to obtain a new representation of the field excited by transient sources. Second, starting from this representation, a novel approach to rapidly computing this field assuming that the mutilayered stack is electrically thin, is developed. Third, the approach is applied to the accelerated calculation of multilayered transient fields.
Leaky-wave analysis of transient fields due to sources in planarly layered media
The transient field due to canonical sources in planarly layered media is obtained using a leaky-wave analysis. By proper choice of integration paths in both the complex frequency and complex wavenumber planes, transient fields are obtained exactly as a temporal inversion integral over a discrete sum of residues. The residues include both proper and improper surface-wave modes, analytically continued into the complex frequency plane. The method is applicable for all times of interest, although for certain source-receiver locations an "early-time" period is identified which encompasses the specular reflection from the nearest interface, and during which time the residue series requires special treatment. The presented analysis leads to a computationally simple and efficient method for obtaining transient fields due to sources in layered media. Results are shown for the transient potential due to line and point sources over a grounded dielectric slab, although the technique is applicable to multiple planar layers.
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.