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In this paper, the radiation patterns due to magnetic sources embedded in a ground plane in the presence of a partially reflective surface are analytically formulated and calculated. Love’s equivalence principle, the transmission-line analogy, and the reciprocity theory are all combined and employed to calculate the far-fields of a four-element $(2\times 2)$ slot array excited by the printed ridge gap waveguide technology operating in the V-band. Since the spacing between the array elements is greater than one wavelength, grating lobes cannot be avoided. Hence, to suppress the grating lobes and enhance the antenna directivity, a dielectric superstrate with the proper properties is utilized. The slot antenna array is operating at 60 GHz for millimeter-wave applications. The obtained results from the proposed analytical formulation agree very well with full-wave numerical simulations obtained from the EM commercial tool HFSS. It is worthwhile to mention that the presented analytical solution is about 30 times faster than its full-wave simulator counterpart.

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Analytical Prediction of the Radiation Characteristics of $2\times2$ Ridge Gap Waveguide Slot Antenna Array With Suppressed Grating Lobes at the V-band