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Bergman and Milton proved that the effective dielectric constant or conductivity of a two-component composite material is a function of the ratio of the dielectric constants or conductivities of the components which can be described by a series of simple poles and residues. These poles and residues are determined only by the microgeometry of the composite. In this study, we use a simplified three-dimensional Fourier series expansion method to locate the poles and residues for simple cubic, body-centered, and face-centered lattices in different concentrations. Comparison between the simple pole theory and the Fourier series expansion method shows a good agreement. © 1997 American Institute of Physics.