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This letter derives efficiency formulas and establishes fundamental limitations for longitudinally symmetric periodic leaky-wave antennas (LWAs). The proposed approach is based on an equivalent transmission-line model for periodic structures, which is derived from a lattice topology providing a perfect decoupling between the series and shunt immittances and their respective radiation contributions. A central result of this letter is that a 2-D array composed of uniformly excited 1-D LWAs cannot exceed a radiation efficiency of 50%. The presented theory is validated by comparing measured and finite-difference time-domain (FDTD) simulated radiation efficiencies with the ones predicted by the lattice model for several symmetrical and asymmetrical series-fed patch (SFP) array antenna and composite right/left-handed (CRLH) antenna configurations.