Comparison of models for the impedance of a probe in a parallel plate waveguide and a microstrip patch

Four different models for the input impedance of a cylindrical coaxial-fed probe of radius a in an infinite parallel plate waveguide of height h are compared. These models include a uniform current model, a cosine current model, a gap voltage source model, and a coaxial frill model. Numerical HFFS simulation data is 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. As an extension of these results, a simple CAD formula for the probe inductance of a coaxial feed probe for a rectangular microstrip patch antenna is also introduced.