Approximate coupling formulas for the coupling between microstrip resonator antennas

An extension is presented of the mutual impedances solution for identical slots in both the electric and magnetic wall formalism, for application to the case of rectangular microstrip antennas. The formulas, which are sufficiently simple for use in both analysis and synthesis, are found by asymptotic approximations of the integrals previously derived. The method consists of an expansion of the field of two apertures in their plane wave spectra, and then applying Perseval's theorem in order to obtain a spectral expression for the power radiated by two slots in an infinitely extended electric wall. One then identifies this expression with the network analogue for the slots, and arrives at the elements of the admittance matrix.