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A new approach is proposed for the time-domain modeling of antennas over periodic substrates. This class of problems would typically require a time-consuming simulation of the antenna structure with a finite number of unit cells of the periodic substrate, chosen to be large enough to achieve convergence. On the contrary, the present work employs periodic boundary conditions applied at the substrate, to dramatically reduce the computational domain and hence, the cost of such simulations. Emphasis is given on radiation pattern calculation, and the consequences of the truncated computational domain of the proposed method on the computation of the electric and magnetic surface currents invoked in the near-to-far field transformation. The theoretical aspects of the proposed methodology are complemented by numerical examples of a wire and an integrated patch antenna over electromagnetic band-gap substrates.