Simulation and modeling of mode conversion at vias in multilayer interconnections

Physics-based CAD models for the analysis of vias in parallel-plate environments

“…Indeed, the normalized input admittance looking at the radial distance is (3) which is normalized to the characteristic impedance at the location defined in (2c). Fig.…”

“…The current flowing through the via is coupled to the parallel plates by means of a dependent current source. On the other hand, the reciprocal induction of the parallel-plate mode back to the signal is included by using a dependent voltage source [3], [10]. The two dependent voltage and current sources correspond to an ideal transformer with a turn-ratio equal to the coupling coefficient defined in (4).…”

“…From another perspective, this happens when the stripline mode hits the via and part of its energy transfers to cylindrical waves supported by the parallel plates. To model this partial coupling, a factor can be introduced, which can be derived from a static field capacitance calculation [3], [10].…”

“…2) circuit-oriented methods: modeling the parallel plates with two-dimensional (2-D) LC ladder networks and analyzing them by means of a transient circuit simulator [3]; 3) analytical methods: solution of Maxwell's equation for the dominant mode ( / ) of a radial waveguide and derivation of the pertinent transfer and driving point impedances [4]- [7]; 4) hybrid methods: combining full-wave simulations, analytical solution, or measurement results with circuit simulations either through a dynamic interaction between full-wave and circuit simulators [7] or by processing the data obtained from full-wave analysis, analytical solution, or measurements to extract circuit models and perform subsequent simulations [8]- [10]. In this paper, a combination of the second and third approaches has been utilized to develop computer-aided-design (CAD) models for vias embedded in parallel-plate environments.…”

“…In general, these studies can be classified into the following four categories: 1) full-wave methods: derivation of the Green's function of a resonant cavity to model the finite substrate and subsequent derivation of the port impedances [1] or direct 3-D numerical solution of Maxwell's equations using frequency-or time-domain full-wave techniques such as the finite-element method (FEM) and transmission-line method (TLM) [2], [3];…”