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We have achieved 50 Ω input impedance for edge-fed narrow microstrip square-ring antennas by using the circumferential variation of current on the ring. The reference point for the current distribution has been fixed by loading the ring. The antenna has been modeled as a lossy transmission line to determine the variation of resonant frequency and input impedance with load. This model has been validated using the mixed potential integral equation approach. The agreement between the two approaches is found to be good. The concept and the model used here can be applied to any type of ring antenna including loop antennas.