Validation and application of physics-based via models to dense via arrays

Fast and accurate via models are required to analyze dense via arrays on printed circuit boards with pitches up to 1mm. Fundamentals of physics-based via models are reviewed and their advantages over general-purpose electromagnetic field solvers are discussed. Recent studies extend the models to take into account multiple scattering among vias. This paper also analyzes if anisotropic field distribution on via holes, and boundary reflection due to the finite size of power planes play a role for high speed digital designs. The updated via models are validated by hardware measurement and 3D full-wave simulations.