Vol. 58
Latest Volume
All Volumes
PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2017-06-20
Fast and Accurate Determination of the Complex Resonant Frequency of a Multilayer Circular Cavity Using Chebyshev's Root-Finder
By
Progress In Electromagnetics Research M, Vol. 58, 1-10, 2017
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 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://www.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