Efficient use of closed-form Green's functions for the analysis of planar geometries with vertical connections

Abstract

An efficient and rigorous method for the analysis of planarly layered geometries with vertical metallizations is presented. The method is based on the use of the closed-form spatial-domain Green's functions in conjunction with the method of moments (MoM). It has already been demonstrated that the introduction of the closed-form Green's functions into the MoM formulation results in significant computational improvement for the analysis of planar geometries. However, in cases of vertical metallizations, such as shorting pin's, via holes, etc., there are some difficulties in incorporating the closed-form Green's functions into the MoM formulation. In this paper, these difficulties are discussed and their remedies are proposed. The proposed approach is compared to traditional approaches from a theoretical point of view, and the numerical implementation is demonstrated through some examples. The results are also compared to those obtained from the commercial software em by SONNET. Index Terms-Closed-form Green's functions, generalized pencil of function method, method of moments, planarly layered media.

Green's functions for vertical current sources embedded in uniform waveguides or cavities filled with multilayered media

“…Lopetag et al [5] report a tapered distribution of a circular-patterned PBG based on the Hamming window. Yun and Chang [13] describe uniplanar 1D PBG structures and resonators on coplanar waveguides, slot lines, and coplanar striplines. Different resonator lines with PBG reflec-…”

Full-Wave Modeling of Stripline Structures in Multilayer Dielectrics

“…Moreover, some methodologies have been proposed to take into account the vertical interconnects between planar structures. [11,12]. However, to the authors' knowledge literature is very thin on topics regarding the modeling of planar multilayer geometries with vertical interconnects in a stripline structure.…”

“…The latter is the most widely employed for the modeling of planar geometries, mainly due to the fact that it does not require the meshing of the whole volume of the structure. Several methods can be found in the literature for the analysis of multilayer microstrip topologies, either for shielded [3][4][5][6][7][8] or unshielded structures [9][10][11][12][13]. Moreover, some methodologies have been proposed to take into account the vertical interconnects between planar structures.…”

Green's functions for vertical current sources embedded in uniform waveguides or cavities filled with multilayered media

“…Most of these techniques, however, deal only with horizontal metallizations. Although some approaches have been derived for the treatment of vertical currents embedded in multilayered media of infinite transverse dimensions [13,14], the same is generally not true when shielded structures are considered.…”