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Simple and general relations characterizing the behavior of infinite phased arrays of printed antenna elements are derived from a model based on infinite current sheets. The Green's function of an electric current source on a grounded dielectric slab is used in various limiting forms to treat arrays in free space, arrays above a ground plane, arrays on a semi-infinite substrate, and arrays on a grounded dielectric slab. Current sheets are selected, using the orthogonality properties of the Floquet modes of the infinite array Green's function, to excite only a few specific low-order Floquet modes. Results from this idealized model, in the form of reflection coefficient magnitudes and input resistance, are compared with rigorous moment method solutions for specific elements (dipoles and microstrip patches). It is shown how the dominant scanning characteristics of a printed phased array, such as reflection coefficient and input resistance trends, scan blindnesses, and grating lobe effects, are dictated more by factors such as element spacing and substrate parameters than by the particular element type itself.