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In this paper, we discuss the influence of a resonance on estimating direction of arrival (DOA) with a circular dipole array in a borehole (CAB). The resonance is caused by the phase-sequence of currents on the dipole antennas. Making use of method of moments (MoM) analysis, we predict resonant frequencies of the CAB and describe a mechanism for the resonance theoretically, making use of the fact that a plane wave can be broken down into cylindrical harmonics. In order to examine the agreement between the MoM and experimental data, we propose a signal processing method to extract phase-sequence components from the actual received array signal. This method is useful for confirming excitation of the phase-sequence resonance in experimental data, as predicted by the MoM. Using the MoM, we examine the influence of the resonances on DOA estimation, and we conclude that the resonances give some spurious solutions. In order to confirm these results, we conduct experiments at a field test site. We arrange the CAB, which consisted of seven receiving dipole antennas. In this experiment, a plane wave is incident on the CAB from a transmitter in another borehole. We apply the proposed signal method, and the measured results demonstrate the existence of the phase-sequence resonance in a physically real CAB. The spurious solutions found to occur in the DOA estimation at the resonant frequencies are also found experimentally.