Full wave edge element based analysis of 3D metal-dielectric structures for high clock rate digital and microwave applications

Three-dimensional structures consisting of combinations of metal and dielectric materials are analysed by means of an improved finite-edge element formulation, which incorporates a newly identified term in the standard boundary conditions of the third kind (Cauchy). These conditions take into account both the transverse and longitudinal field components of the propagating signals in the planes of incidence and transmittance. Employing these boundary conditions, in conjunction with the absorbing boundary conditions (ABC) and/or the boundary conditions of the first kind (Dirichlet) and the third kind, a 3D asymmetrical functional is implemented as a hybrid vector edge element method. Numerical examples are presented for air bridges and lossy transmission lines, connected by a through-hole via and a spiral inductor. The equivalent frequency dependent circuit parameters are then extracted from the field solutions. Laboratory measurements and data comparison with previous published results strongly support the newly developed theoretical work.