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Broadband DRA using a narrow slot aperture coupled to a microstrip line feed are presented. Two different shapes of dielectric resonators tapered in a stair-like structure have been designed for wideband applications. The resonators are located at the center of the rectangular slot and are excited by a center feed microstrip line. Two flipped step stair shaped dielectric resonators with square and cylindrical cross sections are designed to give an impedance bandwidth of 49.3 % and 32.8 %, respectively. They have broadside radiation patterns across the matching band with an average gain higher than 6 dBi. The simulation results are obtained by using Fidelity by Zeland Software, which is based on the FDTD method.