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A Rectangular Dielectric Resonator Antenna (RDRA) made of a high permittivity (εr = 30) ceramic material is presented. It is shown that by selecting the resonator shape and creating a L-shape hole inside the dielectric resonator, it is possible to design RDRA which compact size and wide frequency coverage. The radiation characteristics of the RDRA are broad and stable across a matching band of 3.6 to 9.6 GHz. Also, left hand circular polarization (LHCP) is occurred in the center frequency of 4.3 GHz. The proposed antenna has good radiation characteristics over the operating bandwidth.