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A periodic structure approach is presented for the analysis of the impedance properties of large antenna arrays. The method is applied to a two-dimensional array of slots, in which each slot is fed by a separate waveguide and the array radiates into a half-space. The slot spacing and progressive phasing in the array may be arbitrary, however. The periodic structure approach permits a waveguide-type analysis of the half-space which automatically includes all mutual coupling effects. Both the susceptance and conductance of the slot are evaluated for arbitrary scan angle, and the effects associated with the appearance of higher order beams are considered.