This two-part paper explores 3-D sound field reproduction by combining low order spherical ambisonics and high order circular ambisonics in order to provide higher resolution in the horizontal plane. Part I aims at rigorously establishing the solution of the Sound Field Reproduction (SFR) problem for a circular distribution of sources. This solution is derived from the cylindrical and spherical distributions to obtain two distinct approximate formulations involving either cylindrical harmonic or spherical harmonic expansions. Numerical simulations show that the two formulations lead to similar results. In the context of mixing a dense circular loudspeaker array for SFR in the horizontal plane with a sparse spherical array for 3-D SFR, the spherical harmonic solution for the circular source array will be privileged. It is then possible to combine the two systems in a high-pass/low-pass architecture in the spherical harmonics space. The combined system is described and investigated in Part II.
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