Input impedance to probe fed microstrip antennas over electrically thick substrates

A general theory has been developed for the analysis of the input impedance to probe fed microstrip patch antennas where the entire spectrum of plane waves emanating from the exciting probe and an angularly dependent wall reflection coefficient has been incorporated. The primary emphasis is toward millimeter wavelength microstrip patch antennas where the substrate is electrically thick and requires the consideration of the dispersive effects of the dielectric. The expressions derived here for the input impedance are for a given probe location, size, and patch dimensions. The theory has no perceivable limitations with respect to substrate thickness or patch dimensions. Numerical results have been presented and compared with those obtained by the cavity model. A discussion of these results points out the primary feature of the present theoretical models, in that the wall susceptance being dynamic in nature, the expression obtained for input impedance is more appropriate for millimeter microstrip antennas. Comparison of this theory to experiment shows that this theory properly incorporates high frequency effects on the open end susceptance of a microstrip patch antenna.