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A planar antenna operating at 13.56MHz is presented for potential applications in plasma processing. It consists of interconnected elementary resonant meshes composed of inductive and capacitive elements. Due to its structure, the antenna exhibits a set of resonant modes associated with peaks of the real input impedance. Each mode is defined by its particular distribution of current and voltage oscillating at the frequency of the mode. A rectangular antenna of 0.55m x 0.20m has been built and first results obtained with argon plasmas are presented. Efficient plasma generation is shown by plasma densities above 3 x 10(17) m(-3) at 2000 W with reasonable uniformity over the antenna area. The plasma couples inductively with the resonating currents flowing in the antenna above a threshold power of about 60 W. The real input impedance at antenna resonance avoids the problem of strong reactive currents and voltages in the matching box and RF power connections associated with conventional large-area plasma sources. Resonant RF networks have a strong potential interest for various designs of plasma sources.