volume | PIER Journals

Abstract

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 frequencydependent 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.

1. Koledintseva, M. Y., R. E. DuBroff, and R. W. Schwartz, "A Maxwell Garnett model for dielectric mixtures containing conducting particles at optical frequencies," Progress In Electromagnetics Research, Vol. 63, 223-242, 2006.
doi:10.2528/PIER06052601

2. Koledintseva, M. Y., S. K. R. Chandra, R. E. DuBroff, and R. W. Schwartz, "Modeling of dielectric mixtures containing conducting inclusions with statistically distributed aspect ratio," Progress In Electromagnetics Research, Vol. 66, 213-228, 2006.
doi:10.2528/PIER06110903

3. Koledintseva, M. Y., V. V. Bodrov, I. V. Sourkova, M. M. Sabirov, and V. I. Sourkov, "Unified spectral technique application for study of radiator behavior near planar layered composites," Progress In Electromagnetics Research, Vol. 66, 317-357, 2006.
doi:10.2528/PIER06111701

4. Amirhosseini, M. K., "Three types of walls for shielding enclosures," Journal of Electromagnetic Waves and Apllications, Vol. 19, No. 6, 827-838, 2005.
doi:10.1163/1569393054069109

5. Park, H. S., I. S. Choi, J. K. Bang, S. H. Suk, S. S. Lee, and H. T. Kim, "Optimized design of radar absorbing materials for complex targets," Journal of Electromagnetic Waves and Apllications, Vol. 18, No. 8, 1105-1117, 2004.
doi:10.1163/1569393042955432

6. Calame, J. P. and W. G. Lawson, "A modified method for producing carbon-loaded vacuum-compatible microwave absorbers from a porous ceramic," IEEE Trans. Electron. Devices, Vol. 38, No. 6, 1538-1543, 1991.
doi:10.1109/16.81651

7. Neo, C. P. and V. K. Varadan, "Optimization of carbon fiber composite for microwave absorber," IEEE Trans. Electromagn. Compat., Vol. 46, No. 1, 102-106, 2004.
doi:10.1109/TEMC.2004.823618

8. Ezquerra, T. A., F. Kremer, and G. Wegner, "AC electrical properties of insulator-conductor composites," Progress In Electromagnetic Research, Vol. 06, 273-301, 1992.

9. Nedkov, I.S. Kolev, S. Stavrev, P. Dankov, and S. Alexsandrov, "Polymer microwave absorber with nanosized ferrite and carbon fillers," Proc. IEEE 27th Int. Spring Seminar on Electronics Technology, 577-579, 2004.

10. Maxwell Garnett, J. C., "Colours in metal glasses and metal films," Philos. Trans. R. Soc. London, Vol. 3, 385-420, 1904.

11. Sihvola, A., Electromagnetic Mixing Formulas and Applications, IEE, 1999.

12. Xu, X., A. Qing, Y. B. Gan, and Y. P. Feng, "Effective properties of fiber composite materials," Journal of Electromagnetic Waves and Apllications, Vol. 18, No. 5, 649-662, 2004.
doi:10.1163/156939304774114682

13. Landau, L. D., E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd edition, 1984.

14. Lagarkov, A. N. and A. K. Sarychev, "Electromagnetic properties of composites containing elongated conducting inclusions," Phys. Review B, Vol. 53, No. 9, 6318-6336, 1996.
doi:10.1103/PhysRevB.53.6318

15. Von Hippel, A., Dielectrics and Waves, Artech House, 1995.

16. Koledintseva, M. Y.J. Wu, J. Zhang, J. L. Drewniak, and K. N. Rozanov, "Representation of permittivity for multi-phase dielectric mixtures in FDTD modeling," Proc. IEEE Symp. Electromag. Compat., Vol. 1, 9-13, 2004.

17. Meng, Z.-Q., "Automonous genetic algorithm for functional optimization," Progress In Electromagnetic Research, Vol. 72, 253-268, 2007.
doi:10.2528/PIER07031506

18. Donelli, M., S. Caorsi, F. de Natale, D. Franeeschini, and A. Massa, "A versatile enhanced genetic algorithm for planar array design," Journal of Electromagnetic Waves and Apllications, Vol. 18, No. 11, 1533-1548, 2004.
doi:10.1163/1569393042954893

Professor Marina Koledintseva

Professor Richard DuBroff

Professor Robert Schwartz

Professor James Drewniak