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Designs of circularly polarized, slender, helical antennas are presented. A capacitive feed structure, which has been proposed previously, with a slender helical structure is used as a back-conductor. The back-conductor is installed close behind the helical element in order to radiate circular polarization (CP) with a low-profile structure at approximately 1 GHz with k0a=0.35 ( k0: wavenumber at the resonance frequency, a: radius of a hypothetical sphere circumventing the antenna). Reasonable agreement between the simulated and measured results for S11, the axial ratio (AR), and the radiation pattern have been obtained. Furthermore, the effect of the back-conductor is discussed for the helical antenna structure with a large ground plane.