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The electromagnetic field excited by an electric line source in the presence of a printed structure periodic along two directions with arbitrary geometry of the metallization is calculated. The Array Scanning Method (ASM) is adopted to express the field excited by the aperiodic source in terms of an integral superposition of suitable auxiliary Floquet-periodic fields. The latter are solutions of electric-field integral equations that are cast in a mixed-potential formulation in the unit cell and are numerically discretized with an efficient implementation of the method of moments in the spatial domain. The accuracy of the proposed approach is validated through an independent ASM code developed for metal-strip gratings and also against consolidated analytical models available for specific strip- and patch-based periodic structures.