Quasi-Dynamic Green’s Functions for Efficient Full-Wave Integral Formulations for Microstrip Interconnects

Abstract

Integral formulations are widely used for full-wave analysis of microstrip interconnects. A weak point of these formulations is the inclusion of the proper planar-layered Green's Functions (GFs), because of their computational cost. To overcome this problem, usually the GFs are decomposed into a quasi-dynamic term and a dynamic one. Under suitable approximations, the first may be given in closed form, whereas the second is approximated. Starting from a general criterion for this decomposition, in this paper we derive some simple criteria for using the closed-form quasi-dynamic GFs instead of the complete GFs, with reference to the problem of evaluating the full-wave current distribution along microstrips. These criteria are based on simple relations between frequency, line length, dielectric thickness and permittivity. The layered GFs have been embedded into a full-wave transmission line model and the results are first benchmarked with respect to a full-wave numerical 3D tool, then used to assess the proposed criteria.

Efficient inclusion of layered media Green's Functions in full-wave analysis of microstrips

“…This cannot be given in closed form and must be approximated, through one of the many approaches proposed in literature, such as the Discrete Complex Image Method [6], [8], the Rational Fitting Function Method [10] or the Total Least Square Method [13]. Even using the most efficient of these approaches, the computational cost of the complete GF is at least 50 times the cost of the free-space GF [15] . This cost may be dramatically reduced if the GFs reduce to the quasi-dynamic terms (13) and (14), known in closed form.…”