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The theoretical evaluation of the input impedance of electromagnetic bandgap (EBG) or leaky wave (LW) antennas is not addressed in the literature. To fill this gap, we present in this letter, an original method to study the input impedance of a line source exciting Fabry-Perot (FP) cavities. The method is based on the generalization of the plane wave expansion of the antenna internal fields to cylindrical wave expansions. This procedure leads to simple and rigorous formulas which are very useful for designing antennas associated with FP, EBG, or LW structures and for understanding their electromagnetic behavior. Results produced by this model are validated by exact electromagnetic simulations.