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The use of a single parasitic patch for circular polarization (CP) excitation of the dielectric resonator antenna (DRA) is investigated. For demonstration, the technique is applied to the conformal-strip fed hemispherical DRA, excited at the fundamental TE111 mode. Using the Green's function approach, the integral equations for the conformal-strip and parasitic-patch currents are formulated by matching the appropriate boundary conditions. The equations are then solved using the method of moments (MoM). In using the MoM, both the rigorous and simplified current expansions are used for the parasitic patch, and their results are compared with each other. In each case, the impedance integrals are evaluated by virtue of newly obtained recurrence formulas and direct analytical integration. Hence, the results can be calculated very efficiently without the need for any numerical integration, which greatly facilitates the numerical implementation. The input impedance, axial ratio, and radiation patterns of the CP DRA are calculated, and the results are in good agreement with measurements.