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We consider the generation of circularly polarized (CP) waves on the axis of a strip antenna array with N-fold rotational symmetry and one feed per antenna sector. Using Jones vectors, we show mathematically that when the phases of the N feeds are nφ, where φ = ±2π/N, N >; 2, a pure CP wave is generated, with handedness determined by the sign of φ. This is true regardless of the particular structure of each sector. Numerical simulations were carried out for N = 3,4,5, which validate these conclusions. Experiments were performed with a four-sector antenna, and the results are in excellent agreement with theory.