IEEE Transactions on Dielectrics and Electrical Insulation Vol. 16, No. 3; June 2009 1070-9878/09/$25.00 © 2009 IEEE 793 Prediction of Effective Permittivity of Diphasic Dielectrics as a Function of Frequency Marina Y. Koledintseva, Sandeep K. Patil, Robert W. Schwartz, Wayne Huebner Missouri University of Science & Technology 1870 Miner Circle, Rolla, MO 65409, USA Konstantin N. Rozanov Institute for Theoretical and Applied Electromagnetics, Russian Academy of Sciences 13/19 Izhorskaya ul., Moscow, 125412, Russia Jianxiang Shen, and Ji Chen University of Houston, Department of Electrical and Computer Engineering, Houston, TX 77204, USA ABSTRACT An analytical model based on an equivalent impedance circuit for effective permittivity of a composite dielectric as a function of frequency with complex- shaped inclusions is presented. The geometry of the capacitor containing this composite dielectric is discretized into partial impedance elements, the total equivalent impedance is calculated, and the effective permittivity of the composite dielectric is obtained from this equivalent impedance. An example application using this method is given for an individual cell of a diphasic dielectric consisting of a high-permittivity spherical inclusion enclosed in a low-permittivity parallelepiped. The capacitance and resistance for individual discretized elements in the composite cell are modeled as a function of an inclusion radius. The proposed approach is then extended to a periodic three-dimensional structure comprised of multiple individual cells. The equivalent impedance model is valid for both static and alternating applied electric fields, over the entire range of volume fraction of inclusions. The equivalent impedance model has a few advantages over existing effective medium theories, including no limitations on the shape of inclusions or their separation distance. Index Terms — Dielectric composites, frequency, effective permittivity, equivalent impedance. 1 INTRODUCTION THEORETICAL efforts to predict the dielectric behavior of multiphase composites have been investigated for more than 100 years [1-5], and have resulted in a number of effective medium theories. The fundamental approach is to focus on one particular inclusion and then replace all of the rest by an effective homogenous medium. Any effective medium theory then is invariant to which particular inclusion is taken as a focus [6-9], since each inclusion must be surrounded by the same effective medium. One of the most widely-used formulations for calculating the effective permittivity of mixtures is the Maxwell Garnett (MG) theory [9-12]. MG theory is satisfactory when exact interparticle interactions are not significant, i.e., for small concentrations (inclusion volume fraction< 0.1) of inclusions in a dielectric host [13]. The MG theory is applicable for inclusions of any arbitrary ellipsoidal shape, including spheres, spheroids, cylinders, and disks, through introducing depolarization factors [14]. Complex inclusion shapes can only be approximated by assuming a closest shape [15], which limits the overall applicability. The empirically derived logarithmic mixing rule is also widely applied for fitting experimental data [3]. However, the experimental fit of logarithmic mixing rule in some cases might be fortuitous, as was pointed out by Payne [16]. Properties of composite media have been intensively studied in the last two decades using various numerical techniques. The most prominent among these have been Monte Carlo simulations (MC) [17], the finite element method (FEM) [18, 19], the finite difference method [20] Manuscript received on 28 May 2008, in final form 6 November 2008. Authorized licensed use limited to: Missouri University of Science and Technology. Downloaded on July 13, 2009 at 11:22 from IEEE Xplore. Restrictions apply.