Loop‐antenna coupling to toroidal plasmas is simulated in a flat geometry by an infinitely repeated array of finite loops in order to obtain a discrete spectrum along they(azimuthal) as well as thez(toroidal) directions. The electromagnetic field of the entire configuration, including the wall, the plasma, and the Faraday shield, is analytically expressed in terms of the antenna current. The self‐consistent antenna current is determined by variational techniques which also yield the antenna impedance. Finally, the theory is specifically applied to the case of ion‐cyclotron‐wave coupling. An approach for obtaining broadband, reflectionless coupling is introduced.