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In this paper, the performance of a rectangular microstrip patch antenna fed by microstrip line is designed to operate for ultra-wide band applications. It consists of a rectangular patch with U-shaped slot on one side of the substrate and a finite ground plane on the other side. The U-shaped slot and the finite ground plane are used to achieve an excellent impedance matching to increase the bandwidth. The proposed antenna is designed and optimized based on extensive 3D EM simulation studies. The proposed antenna is designed to operate over a frequency range from 3.6 to 15 GHz.