A general variational principle for an ICRF antenna radiating into a slab plasma is presented. The model is three-dimensional and includes the effect of connections to a transmission line. It also assumes an extent of absorption in the plasma that is sufficient to suppress eigenmodes. The variational principle gives the self-consistent currents flowing in the antenna, the fields excited inside the plasma and the antenna impedance at the generator terminals. Numerical computations are made for a TFR and a JET antenna. A study of power coupling shows that the optimum operating frequency lies near the plasma-modified resonance. The fields excited inside the plasma are found to disperse far more in the toroidal than in the poloidal direction. Also, at frequencies far from resonance, the large currents in the connections excite fields of considerably larger spatial extent than at resonance.