Evaluation of Green’s functions for PEEC models in the air and lossy-ground space

Abstract

This article presents the numerical evaluation of Green's functions for the generalized partial element equivalent circuit (PEEC) formulation in the air and lossy-ground space. Both the source and field points can be located in any layer of the air-ground space. Green's functions are expressed using Sommerfeld integrals (SIs), which have highly oscillating and slowly decaying integrands. As a robust and easy-implemented approach, the direct real-axis integration is presented with the techniques for removing the singularity and accelerating the convergence. Closed-form expressions are derived for the quasi-static and asymptotic approximation of SIs. The results are compared with numerical electromagnetics code NEC2, and good agreements were observed. An image model is developed for quasi-static SIs. Greens' functions can then be contributed by the source and/or its image. This model is used to derive the frequency-invariant PEEC model for fast transient simulation in the time domain. The proposed numerical procedure can be applied to generate lookup tables of SIs, which are indispensable in the evaluation of PEEC circuit parameters for massive wire segments.