volume | PIER Journals

Abstract

A set of algorithms, specifically developed to facilitate an effective modeling of fractal-boundary microstrip antennas in the analysis of such structures through numerical electromagnetic (EM) solvers is presented in this paper. A fractal generator based on the implementation of an Iterated Function System (IFS) produces the geometry specified in accordance with the user-defined input parameters. The structure is created through a solver-specific interface and is thus applicable to a commercially available EM simulation suite. The generation of specific shapes through these algorithms provides a flexible method to study different geometries without the need to modify either the interface or the solver. Three structures based on the Minkowski fractal obtained through these techniques have been studied using two EM solvers for comparison. The frequency-domain results show good agreement between the two solvers, thus validating the algorithms implemented. Complex structures with higher iterations can be studied using these algorithms.

1. Yee, K., "Numerical solution of inital boundary value problems involving maxwell's equations in isotropic media," IEEE Transactions on Antennas and Propagation, Vol. 14, No. 3, 302-307, 1966.
doi:10.1109/TAP.1966.1138693 Google Scholar

2. Cohen, N., "Fractal antenna applications in wireless telecommunications," Electronics Industries Forum of New England, Professional Program Proceedings, 43-49, May 1997.
doi:10.1109/EIF.1997.605374 Google Scholar

3. Mandelbrot, B. B., The Fractal Geometry of Nature, W. H. Freeman, Aug. 1982.

4. Werner, D. H. and R. Mittra, Frontiers in Electromagnetics, Wiley-IEEE Press, 1999.
doi:10.1109/9780470544686

5. Vinoy, K., J. Abraham, and V. Varadan, "On the relationship between fractal dimension and the performance of multi-resonant dipole antennas using Koch curves," IEEE Transactions on Antennas and Propagation, Vol. 51, 2296-2303, Sep. 2003.
doi:10.1109/TAP.2003.816352 Google Scholar

6. Gianvittorio, J. and Y. Rahmat-Samii, "Fractal antennas: A novel antenna miniaturization technique, and applications," IEEE Antennas and Propagation Magazine, Vol. 44, 20-36, Feb. 2002.
doi:10.1109/74.997888 Google Scholar

7. Barnsley, M., Fractals Everywhere, Academic Press, 1988.

8. Peitgen, H. O., H. Jurgens, and D. Saupe, Chaos and Fractals: New Frontiers of Science, Springer, Feb. 1993.

9. Werner, D. and S. Ganguly, "An overview of fractal antenna engineering research," IEEE Antennas and Propagation Magazine, Vol. 45, 38-57, Feb. 2003.
doi:10.1109/MAP.2003.1189650 Google Scholar

10. Sarkar, T. K., S. M. Rao, and A. Djordjevic, "Electromagnetic scattering and radiation from finite microstrip structures," IEEE Transactions on Microwave Theory and Techniques, Vol. 38, 1568-1575, Nov. 1990. Google Scholar

11. Luebbers, R. and H. Langdon, "A simple feed model that reduces time steps needed for FDTD antenna and microstrip calculations," IEEE Transactions on Antennas and Propagation, Vol. 44, 1000-1005, Jul. 1996. Google Scholar

12. Luebbers, R., L. Chen, T. Uno, and S. Adachi, "FDTD calculation of radiation patterns, impedance, and gain for a monopole antenna on a conducting box," IEEE Transactions on Antennas and Propagation, Vol. 40, 1577-1583, Dec. 1992.
doi:10.1109/8.204752 Google Scholar

13. Berenger, J. P., "A perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics, Vol. 114, No. 2, 185-200, 1994.
doi:10.1006/jcph.1994.1159 Google Scholar

14. Berenger, J. P., "Three-dimensional perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics, Vol. 127, 363-379, 1996.
doi:10.1006/jcph.1996.0181 Google Scholar

15. Berenger, J. P., "Making use of the PML absorbing boundary condition in coupling and scattering FDTD computer codes," IEEE Transactions on Electromagnetic Compatibility, Vol. 45, 189-197, May 2003.
doi:10.1109/TEMC.2003.810803 Google Scholar

16. Kunz, K. and L. Simpson, "A technique for increasing the resolution of finite-difference solutions of the maxwell equation," IEEE Transactions on Electromagnetic Compatibility, Vol. 23, 419-422, Nov. 1981. Google Scholar

17. Jurgens, T. and A. Taflove, "Three-dimensional contour FDTD modeling of scattering from single and multiple bodies," IEEE Transactions on Antennas and Propagation, Vol. 41, 1703-1708, Dec. 1993.
doi:10.1109/8.273315 Google Scholar

18. Dey, S. and R. Mittra, "A locally conformal finite-difference timedomain (FDTD) algorithm for modeling three-dimensional perfectly conducting objects," IEEE Microwave and Guided Wave Letters, Vol. 7, 273-275, Sep. 1997.
doi:10.1109/75.622536 Google Scholar

19. Yu, W. H. and R. Mittra, "A conformal FDTD algorithm for modeling perfectly conducting objects with curve-shaped surfaces and edges," Microwave and Optical Technology Letters, Vol. 27, No. 2, 136-138, 2000.
doi:10.1002/1098-2760(20001020)27:2<136::AID-MOP16>3.0.CO;2-Q Google Scholar

Dr. Bruno Camps-Raga

Professor Naz E. Islam