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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.