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A novel modal-based iterative circuit model is described for the calculation of the complex propagation constant of mushroom-like parallel-plate composite right/left handed leaky-wave antennas (PPW CRLH LWAs). The conventional lossless CRLH unit cell circuit is modified in order to consider the electromagnetic coupling to free space through a slot. For this purpose, a slot equivalent radiative structure, based on phased-array theory, is analyzed using a mode matching approach combined with Floquet's theorem. A direct correspondence between lumped elements and this radiative structure is found, leading to a frequency-dependent unit cell circuit model. A quickly converging iterative algorithm is then employed to determine the final element values of the unit cell. The proposed method is accurate, and it takes into account the structure physical dimensions. It also allows to obtain a balanced CRLH unit cell design without requiring any full-wave simulation, is several orders of magnitude faster than full-wave simulations, and provides a deep insight into the physics of the antenna radiation mechanism.