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This paper presents the theory and analysis of phase mode excitation of both prolate and oblate spheroidal antenna arrays in terms of spheroidal wave functions, which is an extension of the spherical counterparts reported in the literature. Theoretical and numerical results show that a spheroidal phase mode of the excitation function produces a far field radiation pattern with the same spheroidal phase mode form, and the elevation angle of that pattern increases (decreases) with the ratio of the interfocal distance of the prolate (oblate) spheroid antenna array to the wavenumber. [ABSTRACT FROM AUTHOR]