Signal integrity: Efficient, physics-based via modeling: Principles and methods

This article discusses the high-frequency behavior of thru-hole vias enclosed by solid reference planes in packages and printed circuit boards and reviews some efficient modeling alternatives for signal and power integrity applications. The electromagnetic behavior of vias, including the excitation of parallel-plate modes and the role of return vias, is introduced as preamble to the modeling approaches. The physics-based via model and its building blocks are then discussed. The last section reviews some improvements to the via model, covering intrinsic models for the near field of vias and the utilization of contour integral and multiple scattering methods.