Vol. 58

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2017-06-20

Fast and Accurate Determination of the Complex Resonant Frequency of a Multilayer Circular Cavity Using Chebyshev's Root-Finder

By David Marques-Villarroya, Felipe Penaranda-Foix, Beatriz Garcia-Banos, Jose Manuel Cataia-Civera, and Jose Daniel Gutierrez-Cano
Progress In Electromagnetics Research M, Vol. 58, 1-10, 2017
doi:10.2528/PIERM17020904

Abstract

In this paper, a general multilayer circular cavity with N slabs is analyzed analytically, obtaining characteristic equations for TE and TM modes to compute the complex resonant frequency efficiently using an algorithm based on Chebyshev's root finder. The accuracy of the solutions is compared with full-wave circuit method, and the computational speed to achieve the roots of the characteristic equations is also compared with Cauchy Integral Method, which is commonly used to obtain complex roots. Furthermore, the relationship between the amplitudes of the different regions is obtained, whereby the whole structure can be analyzed as a single one from now on.

Citation


David Marques-Villarroya, Felipe Penaranda-Foix, Beatriz Garcia-Banos, Jose Manuel Cataia-Civera, and Jose Daniel Gutierrez-Cano, "Fast and Accurate Determination of the Complex Resonant Frequency of a Multilayer Circular Cavity Using Chebyshev's Root-Finder," Progress In Electromagnetics Research M, Vol. 58, 1-10, 2017.
doi:10.2528/PIERM17020904
http://jpier.org/PIERM/pier.php?paper=17020904

References


    1. Conciauro, G., M. Guglielmi, and R. Sorrentino, Advanced Modal Analysis, Wiley, New York, NY, USA, 1999.

    2. Penaranda-Foix, F. L. and J. M. Catala-Civera, "Circuital analysis of cylindrical structures applied to the electromagnetic resolution of resonant cavities," Passive Microwave Components and Antennas, Ch. 7, InTech, Vukovar, Croatia, Apr. 2010.

    3. Harrington, R. F., Time-Harmonic Electromagnetic Fields, New York, 1961, ISBN 047120806X.

    4. Collin, R. E., Foundations for Microwave Engineering, McGraw-Hill, New York, 1966.

    5. Zaki, K. A. and A. E. Atia, "Modes in dielectric-loaded waveguides and resonators," IEEE Transactions on Microwave Theory and Techniques, Vol. 31, No. 12, 1039-1045, Dec. 1983.
    doi:10.1109/TMTT.1983.1131658

    6. Blackburn, J., "Solving the double eigenvalue problem: A study of mode matching in arbitrary-layer dielectric resonators," IEE Proceedings - Microwaves, Antennas and Propagation, Vol. 153, No. 5, 447-455, Oct. 2006.
    doi:10.1049/ip-map:20050106

    7. Xi, W. and W. R. Tinga, "Field analysis of new coaxial dielectrometer," IEEE Transactions on Microwave Theory and Techniques, Vol. 40, No. 10, 1927-1934, Oct. 1992.
    doi:10.1109/22.159630

    8. Chen, S. W. and K. A. Zaki, "A novel coupled method for dual-mode dielectric resonators and waveguide filters," IEEE Transactions on Microwave Theory and Techniques, Vol. 38, No. 12, 1885-1893, Dec. 1990.
    doi:10.1109/22.64570

    9. Penaranda-Foix, F. L., J. M. Catala-Civera, A. J. Canós, and B. Garcia-Banos, "Finding resonant frequencies for high loss dielectrics in cylindrical cavities," Int. J. RF and Microwave Comp. Aid. Eng., Vol. 25, 530-535, 2015.
    doi:10.1002/mmce.20889

    10. Wang, C. and K. A. Zaki, "Generalized multilayer anisotropic dielectric resonators," IEEE Transactions on Microwave Theory and Techniques, Vol. 48, No. 1, 60-66, Jan. 2000.
    doi:10.1109/22.817472

    11. Boyd, J. P., "Computing zeros on a real interval through Chebyshev expansion and polynomial rootfinding," SIAM J. Numer. Anal., Vol. 40, 1666-1682, 2002.
    doi:10.1137/S0036142901398325

    12. Collin, R. E., Field Theory of Guided Waves, IEEE Press, 1991, ISBN 978-0879422370.

    13. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley & Sons, 1989.

    14. Boyd, J. P., "Finding the zeros of a univariate equation: Proxy rootfinders, Chebyshev interpolation, and the companion matrix," SIAM Review, Vol. 55, No. 2, 375-396, 2013.
    doi:10.1137/110838297

    15. Penaranda-Foix, F. L., M. Contelles-Cervera, P. J. Plaza-Gonzalez, and J. M. Catala-Civera, "Solving the cut-off wave numbers in partially filled rectangular waveguides with ferrite by the Cauchy integral method," 2005 IEEE Antennas and Propagation Society International Symposium, Vol. 2B, 626-629, 2005.
    doi:10.1109/APS.2005.1552090

    16. Marqués-Villarroya, D., F. L. Peñaranda-Foix, B. García-Baños, J. M. Catalá-Civera, and J. D. Gutiérrez-Cano, "Enhanced full-wave circuit analysis for modeling of a split cylinder resonator," IEEE Transactions on Microwave Theory and Techniques, Vol. 65, No. 4, 1191-1202, Apr. 2017.
    doi:10.1109/TMTT.2016.2637932