Analytical extraction of via near-field coupling using a multiple scattering approach

This paper studies the near-field coupling between closely spaced vias. The near-field coupling is a consequence of non-propagating (higher order) radial waveguide modes. Although it is a second order effect for typical via geometries in printed circuit boards due to the strong attenuation of these modes with distance, this coupling can become relevant for special cases in high density designs. In this paper we apply a multiple scattering approach to carry out an accurate analysis of two closely coupled vias, and obtain the effective near- and far- end coupling capacitances for this case. An evaluation of the coupling capacitances shows how the near-field coupling depends on the via separation and other geometrical parameters. Based on this evaluation, an empirical formula is provided that allows to estimate the minimum distance above which near-field coupling can be neglected. For typical geometries at board level, the maximum separation to have a noticeable near field coupling is below 30 mil.