Study of rectangular microstrip patch over ground plane with rectangular aperture in the presence of a high-permittivity dielectric layer below the aperture

In this communication, Galerkin's method in the Fourier transform domain is applied to the determination of the resonant frequencies of rectangular microstrip patch over ground plane with rectangular aperture when there is a high-permittivity dielectric layer below the aperture. The numerical calculations show that the results obtained for the resonant frequencies of the patches with apertures in contact with a high-permittivity dielectric layer not only substantially differ from the results without apertures, but they also appreciably differ from the results obtained with apertures in contact with air. Unlike microstrip patch resonators without apertures, the resonant frequency does not vary monotonically with increasing substrate thickness.