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Two geometries of dielectric ring resonator (DRR) have been investigated as new variants for designing ultrawideband hybrid monopole-DRAs (dielectric resonator antennas) with improved features. They are simply hemispherical and conical in shape and have been implemented individually. Hybrid monopole-DRA is actually a combined configuration using a grounded monopole surrounded by a small DRR touching the same ground plane. Compared to an earlier version using cylindrical DRR of same dielectric material, the proposed ones promise for about 25% larger impedance bandwidth maintaining identical gain and radiation properties. As much as 126% impedance bandwidth with consistent monopole type radiation and 2-4 dBi peak gain has been demonstrated using a set of prototypes shaped from dielectric rod with εr = 10. Physical insight in to the ultrawideband operation along with a comprehensive design guideline is presented.