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In this work, a dielectric resonator antenna (DRA) is miniaturized by using Artificial Magnetic conductor (AMC) surface without disturbing other important parameters. The design has three main features: (i) simple micro-strip line feeding, (ii) use of parasitic metallic strip to achieve impedance matching, and (iii) use of AMC surface for design miniaturization. The miniaturization is performed for dielectric resonator antenna at 3.5 GHz. Without changing the basic characteristic of the antenna such as gain, resonance frequency and efficiency, the size of the antenna was reduced by 85%. The AMC surface and DRA both are positioned on the FR4 substrate. The AMC surface consists of small patches of copper. DRA is mounted on the AMC surface, which significantly reduces the overall DRA volume. Nine AMC patches were introduced with a small gap between them. AMC patches were shorted with the ground metal with the help of small metallic vias. For an overall performance analysis, the design was fabricated, and measured results were taken. The fabricated design covers a bandwidth of 180 MHz for -10 dB reference value of the reflection coefficient, which is mainly used for 5G wireless application. The design has 14.2% impedance bandwidth. Based on the analysis made for the proposed design, it is found that this simple technique highly reduces the DR volume (85%) and ground surface (15.5%) while maintaining the overall performance of the square DRA.