An analytical model of an effective permittivity of a composite taking into account statistically distributed orientations of inclusions in the form of prolate spheroids will be presented. In particular, this paper considers the normal Gaussian distribution for either zenith angle, or azimuth angle, or for both angles describing the orientation of inclusions. The model is an extension of the Maxwell Garnett (MG) mixing rule for multiphase mixtures. The resulting complex permittivity is a tensor in the general case. The formulation presented shows that the parameters of the distribution law for orientation of inclusions affect the frequency characteristics of the composites, and that it is possible to engineer the desirable frequency characteristics, if the distribution law is controlled.


Electrical and Computer Engineering

Second Department

Materials Science and Engineering

Keywords and Phrases

Permittivity, Complex permittivity; Dielectric mixtures; Distribution law; Effective permittivity; Frequency characteristic; Maxwell-Garnett; Multi-phase mixtures; Prolate spheroid, Mixtures

International Standard Serial Number (ISSN)

1070-4698; 1559-8985

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2009 EMW Publishing, All rights reserved.

Publication Date

01 Jan 2009