A large area antenna generates a plasma by both inductive and capacitive coupling; it is an electromagnetically coupled plasma source. In this work, experiments on a large area planar RF antenna source are interpreted in terms of a multi-conductor transmission line coupled to the plasma. This electromagnetic treatment includes mutual inductive coupling using the complex image method, and capacitive matrix coupling between all elements of the resonant network and the plasma. The model reproduces antenna input impedance measurements, with and without plasma, on a 1.2x1.2 m2 antenna used for large area plasma processing. Analytic expressions are given, and results are obtained by computation of the matrix solution. This method could be used to design planar inductive sources in general, by applying the termination impedances appropriate to each antenna type.