The analysis of a radio-frequency (RF) planar antenna is presented for applications in plasma processing. The antenna is a network of elementary meshes composed of inductive and capacitive elements which exhibits a set of resonant modes. The high currents generated by RF power feeding under resonance are efficient for plasma generation. A general solution is derived for the currents in the driven dissipative network for these conditions. The dominantly real input impedance near antenna resonance avoids the high reactive currents and voltages in the matching box and RF power connections which can be a problem with conventional large-area capacitively and inductively coupled plasma sources. The driven antenna can be approximated by a parallel resonance equivalent circuit whose input impedance can conveniently be measured to interpret the dissipation due to the plasma.