Cavity Models of Planar Components Grounded by Via-Holes and Their Experimental Verification

Semianalytical electromagnetic models of grounding via-holes and shorted resonators of different shapes are proposed and experimentally verified. Our models are based on the cavity approach previously used for circular-pad via-holes. For the first time, a model of a square-pad via-hole is developed. By a perturbation approach, an approximate model for slightly rectangular shorted patches is also derived. All our via-hole models are verified experimentally. The influence of the technologically caused eccentricity of the via-hole shape is also modeled and studied by measurements. Additional verification is done by full-wave simulations with Agilent Momentum (2002) and IE3D-10.1. Our models compute the modal resonant frequencies, fields, and equivalent-circuit components of the via-holes. They allow for the study of the frequency limitations of grounding via-holes for high-speed applications, as well as the modes of shorted resonators for printed antennas and filters. The developed models are fast and accurate.