Simple Formula for Aperture Efficiency Reduction Due to Grating Lobes in Planar Phased Arrays

This paper numerically validates a simple formula to calculate the aperture efficiency reduction due to grating lobes in planar phased arrays. Array antennas with element spacing greater than one wavelength will produce grating lobes. Grating lobes are not a big problem in most new millimeter-wave applications, except for the fact that they reduce the aperture efficiency and thereby normally the directivity. When the element pattern is known, the simple formula can be used to calculate the aperture efficiency in the presence of grating lobes. The formula is verified by the simulations of a large uniformly excited planar slot array. The agreement is good for both broadside radiation and a phased main beam, even if we use the far field of an isolated slot. Using the far field of the embedded slot element gives almost the same results, except when a grating lobe radiates along the ground plane and the isolated element pattern is nonzero in this direction.