An analytical model of a composite dielectric presented in this paper is the extension of Maxwell Garnett formulation. It takes into account the simultaneous statistical (Gaussian) distribution of conductivity and aspect ratio of inclusions. The inclusions are randomly oriented elongated conducting spheroids at concentrations below the percolation threshold. The formulation presented herein is limited to microwave frequencies. However, taking subtle frequency-dependent effects that play important part at optical frequencies into account is straightforward. Some results of computations of microwave complex effective permittivity of composites with different input parameters have been obtained using analytical and numerical integration in Maple 10 software. It is shown how the parameters of the distribution laws - mean values and standard deviations of aspect ratio and conductivity - affect the resultant complex effective permittivity. The results of computations demonstrate that the most important factors affecting frequency characteristics of microwave effective permittivity are the mean values of the aspect ratio and conductivity. As for the standard deviations of aspect ratio and conductivity, their effects are the most noticeable in the transition between the static and optical limits of the Debye characteristic for the effective permittivity. There is almost no effect in the static and "optic" regions of the Debye curves.


Electrical and Computer Engineering

Second Department

Materials Science and Engineering


Air Force Research Laboratory (Wright-Patterson Air Force Base, Ohio)


This work was supported by the Air Force Research Laboratory under Contract FA8650-04-C-5704 through the Center for Advanced Materials Technology, University of Missouri-Rolla.

Keywords and Phrases

Debye Curves; Composite Dielectric; Microwave Frequencies; Aspect Ratio; Electric Conductivity; Integration; Permittivity; Statistical Methods; Frequency Dependent Effects; Optical Frequencies; Spheroids; Dielectric Materials; Gaussian Distribution

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2007 EMW Publishing, All rights reserved.

Publication Date

29 Jun 2007