However, apart from the core-shell model, the classical mixing formulas such as the Mean-field approach by Maxwell-Garnett , the Litchenker's Logarithmic mixture formula [13,14], the Bruggeman mixing formula , the analytical approaches using the diagrammatic expansions  and Fourier series  have also the potential to be used for the metal powder composites in a way similar to the dielectric mixtures for which these formulas were originally proposed.
These estimated material properties are then compared with the standard Maxwell-Garnett law , the Logarithmic law of mixing [13, 14], and the Clausius-Mossotti relationship  for various volume fractions and permittivity values in order to validate the proposed approach.
Firstly, the proposed unit cell approach is validated for some standard mixed dielectric samples by comparing the results of the proposed unit cell approach assuming a TEM mode propagation with those obtained by the conventional mixing formulas such as the Maxwell-Garnett, Logarithmic laws etc.
Table 1 shows a comparison of the the complex relative permittivity obtained by the Maxwell-Garnett Law, the Logarithmic Law, and the proposed unit cell approach.
10] Two theoretical formulations were used in the current study, a self-consistent theory similar to that of Webman and a modification of the Maxwell-Garnett theory.
Equation 5 and the more familiar Maxwell-Garnett formulation become numerically equivalent when either the composite constituents have permittivities that are not too different, that is, [Epsilon.
Those results are similar to those that applied the Maxwell-Garnett model in the optimum design of mm-wave windows.
As previously theorized, negligible differences were obtained when comparing Maxwell-Garnett and the EMT of Webman since fiber and polymer permittivities are comparable and the composites tested absorbed less than 5 percent water by volume.
Active Maxwell-Garnett composite with the unit refractive index," Physica B: Condensed Matter, Vol.
Evaluation of extended Maxwell-Garnett theories," Optics Communications, Vol.
Smith, "The consistent application of Maxwell-Garnett effective medium theory to anisotropic composites," Appl.