The JET antenna has been conceived as a 'limiter antenna', completely recessed in a lateral frame which has the dual purpose of protecting the conductors and limiting the plasma radius. The coupling of this antenna is calculated in slab geometry, using a variational formulation which finds the self-consistent currents in the antenna elements. Full account is taken of the modes excited inside the limiter frame and of their coupling to waves in the inhomogeneous plasma. This yields the antenna impedance as a function of frequency and the field structure inside the plasma, including power fluxes and dispersion, as a function of penetration.