Comparison of models for the probe inductance for a parallel-plate waveguide and a microstrip patch

Four different models for the probe inductance of a circular probe in an infinite parallel plate waveguide are studied. These models include a uniform-current model, a cosine-current model, a gap-voltage source model, and a coaxial-frill model. These different models treat the vertical variation of the fields within the substrate and the field of the coaxial feed with varying degrees of rigor. Numerical high frequency structure simulator data are also compared with the results of these models in order to draw reliable conclusions about the accuracy of these models as a function of the substrate thickness. A simple computer-aided design formula for the probe inductance of a coaxial feed probe for a rectangular microstrip patch antenna is also introduced.