Bounds for effective permittivities of lossy dielectric composities

A statistically homogeneous and isotropic two-phase composite is considered. The constituents are dielectrics with low loss factors. Bounds are found on the dielectric behavior of the composite using the fact that the imaginary part of the complex permittivity is small compared to the real part. The bounds on loss factor are found generally (with one exception) to be the best possible based only on volume fractions and constituent properties. Further, it is shown that for dielectric constituents whose dielectric constants are nearly unvarying with frequency, the loss factor of the aggregate is simply a linear combination of the loss factors of the constituents.