Active element pattern symmetry for asymmetrical element arrays

In a phased array antenna, particularly with small element spacing, the mutual coupling plays an important role in the radiation pattern of the array. In this paper we briefly discuss about the Floquet analysis method for the AEP and provide expressions for the far field vector components in terms of the Floquet modal amplitudes. We then relate the Floquet modal power and the input power and prove that the active element power pattern must be symmetrical inside the "grating lobe free" region irrespective of the shape of the elements; symmetrical or asymmetrical. The grating lobe free region is defined as the scan region of an array corresponding to which no visible grating lobe exists. We illustrate this important property of AEP with respect to an array of asymmetrical multi-step horns. We show numerically that the isolated element pattern is asymmetrical; however, the AEP is perfectly symmetrical inside the grating lobe free region.