volume | PIER Journals

Abstract

The dispersion relation is derived for the most general configuration of a passive and reciprocal periodically loaded transmission line in a unique and simple form by introducing two novel parameters. Based on this relation, the phase and group velocities are determined and a simple condition for phase reversal propagation is obtained. The two above mentioned parameters help us to develop a polar diagram to model the behavior of any two-port network as a function of frequency. By this diagram, we can determine the direction of the phase velocity and also the value of the propagation constant. Then, symmetrical cells and thereof the periodic structures composed of them are analyzed. For such structures, it will be shown that the dispersion relation can be rewritten in a form similar to the Lorentz transformation. We design and analyze a bandstop filter to verify the method.

1. Munk, B. A., Frequency Selective Surfaces: Theory and Design, John Wiley & Sons Inc., Apr. 2000.
doi:10.1002/0471723770

2. Guo, C., H.-J. Sun, and X. Lv, "A novel dualband frequency selective surface with periodic cell perturbation," Progress In Electromagnetics Research B, Vol. 9, 137-149, 2008.
doi:10.2528/PIERB08071302

3. Hao, Y. and R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications, Artech House, Inc., 2009.

4. Xie, H.-H., Y.-C. Jiao, K. Song, and Z. Zhang, "A novel multi-band electromagnetic band-gap structure," Progress In Electromagnetics Research Letters, Vol. 9, 67-74, 2009.
doi:10.2528/PIERL09042302

5. Pozar, D. M., Microwave Engineering, Addison-Wesley Publishing Company, 1990.

6. Caloz, C. and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications, Engineering Approach, John Wiley & Sons Inc., Nov. 2005.

7. Collin, R. E., Foundations for Microwave Engineering, McGraw Hill Inc., 1992.

8. Lu, W. B., T. J. Cui, X. X. Yin, Z. G. Qian, and W. Hong, "Fast algorithms for large-scale periodic structures using subentire domain basis functions," IEEE Trans. Antennas Propag., Vol. 53, No. 3, 1154-1162, Mar. 2005.
doi:10.1109/TAP.2004.842635

9. Du, P., B. Z. Wang, and J. Deng, "An extended simplified sub-entire domain basis function method for finite-sized periodic structures," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 11-12, 1479-1488, 2008.
doi:10.1163/156939308786390139

10. Li, D. Y. and C. D. Sarris, "Efficient finite-difference time-domain modeling of driven periodic structures and related microwave circuit applications," IEEE Trans. Microwave Theory Tech., Vol. 56, No. 8, 1928-1937, Aug. 2008.
doi:10.1109/TMTT.2008.927386

11. Wu, Y. L., Y. X. Zhang, and Y. A. Liu, "Novel Smith chart approaches to solve problems in periodic structure," International Conference on Microwave and Millimeter Wave Technology (ICMMT), Vol. 2, 605-608, Apr. 2008.

12. Jackson, J. D., Classical Electromagnetics, 3 Ed., John Wiley & Sons Inc., 1998.

13. Zandi, O., Z. Atlasbaf, and K. Forooraghi, "Flat multilayer dielectric re°ector antennas," Progress In Electromagnetics Research, Vol. 72, 1-19, 2007.
doi:10.2528/PIER07022604

14. Mallick, A. K. and G. S. Sanyal, "Electromagnetic wave propagation in a rectangular waveguide with sinusoidally varying width," IEEE Trans. Microwave Theory Tech., Vol. 26, No. 4, 243-249, Apr. 1978.
doi:10.1109/TMTT.1978.1129358

Mr. Omid Zandi

Dr. Zahra Atlasbaf

Dr. Mohammad Abrishamian