The idea behind the coupling matrix identification is to find the coupling matrix corresponding to the measured or designed scattering characteristics of the microwave filter. The typical attitude towards coupling matrix parameter extraction is to use some optimization methods to minimize the appropriate cost function. In this paper we concentrate on the analytic solutions - how they may be found and their application in further optimization processes. In general case the suggested method generates complex-valued coupling matrix. For a special case of the filter without cross-couplings we give fast and simple recursive method of finding such complex-valued coupling matrix. The method is based on Laplace's formula for expanding the determinant. The complex-valued coupling matrix is used as a good starting point for the optimization methods to find the regular coupling matrix. The examples are presented showing that the optimization arrives to global minimum starting from real parts of complex-valued entries considerably more often than when the starting point is selected randomly.
2. Atia, E. and A. E. Williams, "Narrow-band multiple-coupled cavity synthesis," IEEE Trans. Circuits Syst., Vol. 21, 649-655, September 1974.
doi:10.1109/TCS.1974.1083913
3. Wang, R., J. Xu, C. L. Wei, M.-Y. Wang, and X.-C. Zhang, "Improved extraction of coupling matrix and unloaded Q from S-parameters of lossy resonator filters," Progress In Electromagnetics Research, Vol. 120, 67-81, 2011.
4. Xiao, K., L. F. Ye, F. Zhao, S.-L. Chai, and J. L.-W. Li, "Coupling matrix decomposition in designs and applications of microwave filters ," Progress In Electromagnetics Research, Vol. 117, 409-423, 2011.
5. Corrales, E., P. de Paco, and O. Menendez, "Direct coupling matrix synthesis of bandstop filters," Progress In Electromagnetics Research Letters, Vol. 47, 85-91, 2011.
doi:10.2528/PIERL11091512
6. Cameron, R. J., C. M. Kudsia, and R. R. Mansour, Microwave Filters For Communication Systems, J. Wiley & Sons, 2007.
7. Razalli, M. S., A. Ismail, M. A. Mahdi, and M. N. Hamidon, "Novel compact `via-less' ultra-wide band filter utilizing capacitive microstrip patch ," Progress In Electromagnetics Research, Vol. 91, 213-227, 2009.
doi:10.2528/PIER09020403
8. Mo, S. G., Z. Y. Yu, and L. Zhang, "Design of triple-mode bandpass filter using improved hexagonal loop resonator," Progress In Electromagnetics Research, Vol. 96, 117-125, 2009.
doi:10.2528/PIER09080304
9. Ye, C. S., Y. K. Su, M. H. Weng, C. Y. Hung, and R. Y. Yang, "Design of the compact parallel-coupled lines wideband bandpass filters using image parameter method," Progress In Electromagnetics Research, Vol. 100, 153-173, 2010.
doi:10.2528/PIER09073002
10. Zhang, L., Z. Yu, and S. Mo, "Novel planar multimode bandpass filters with radial-line stubs," Progress In Electromagnetics Research, Vol. 101, 33-42, 2010.
doi:10.2528/PIER09121303
11. Huang, J.-Q. and Q.-X. Chu, "Compact UWB band-pass filter utilizing modified composite right/left-handed structure with cross coupling ," Progress In Electromagnetics Research, Vol. 107, 179-186, 2010.
doi:10.2528/PIER10070403
12. Chiou, Y.-C., P.-S. Yang, J.-T. Kuo, and C.-Y.Wu, "Transmission zero design graph for dual-mode dual-band filter with periodic stepped-impedance ring resonator ," Progress In Electromagnetics Research, Vol. 108, 23-36, 2010.
doi:10.2528/PIER10071608
13. Lopez-Garcia, B., D. V. B. Murthy, and A. Corona-Chavez, "Half mode microwave filters based on epsilon near zero and mu near zero concepts," Progress In Electromagnetics Research, Vol. 113, 379-393, 2011.
14. Vegesna, S. and M. Saed, "Novel compact dual-band bandpass microstrip filter," Progress In Electromagnetics Research B, Vol. 20, 245-262, 2010.
doi:10.2528/PIERB10012210
15. Cameron, R. J., "Advanced coupling matrix synthesis techniques for microwave filter," IEEE Trans. Microwave Theory & Tech., Vol. 51, No. 1, 1-10, 2003.
doi:10.1109/TMTT.2002.806937
16. Cameron, R. J., "General coupling matrix synthesis methods for Chebyshev filtering functions," IEEE Trans. Microwave Theory & Tech., Vol. 47, No. 4, 433-442, 1999.
doi:10.1109/22.754877
17. Harscher, P., R. Vahldieck, and S. Amari, "Automated filter tuning using generalized low-pass prototype networks and gradient-based parameter extraction," IEEE Trans. Microwave Theory & Tech., Vol. 49, No. 12, 2532-2538, 2001.
doi:10.1109/22.971646
18. Meng, W. and K.-L. Wu, "Analytical diagnosis and tuning of narrowband multicoupled resonator filters," IEEE Trans. Microwave Theory & Tech., Vol. 54, No. 10, 3765-3771, 2006.
doi:10.1109/TMTT.2006.881623
19. Ma, H., D. Yang, and J. Zhou, "Improved coupling matrix extracting method for Chebyshev coaxial-cavity filter," PIERS Proceedings, 36-41, Xi'an, China, March 22-26, 2010.
20. Michalski, J. J., "Inverse modelling in application for sequential filter tuning," Progress In Electromagnetics Research, Vol. 115, 113-129, 2011.
21. Wang, R. and J. Xu, "Extracting coupling matrix and unload Q from scattering parameters of lossy filters," Progress In Electromagnetics Research, Vol. 115, 303-315, 2011.
22. Cameron, R. J., J.-C. Faugere, F. Roullier, and F. Seyfert, "Exhaustive approach to the coupling matrix synthesis problem and application to the design of high degree asymmetric filters ," International Journal of RF and Microwave Computer-Aided Engineering , Vol. 17, No. 1, 4-12, January 2007.
doi:10.1002/mmce.20190
23. Kozakowski, P., A. Lamecki, P. Sypek, and M. Mrozowski, "Eigenvalue approach to synthesis of prototype filters with source/load coupling," IEEE Microwave and Wireless Components Letters, Vol. 15, No. 2, 98-100, 2005.
doi:10.1109/LMWC.2004.842838
24. Lamecki, A., P. Kozakowski, and M. Mrozowski, "Fast synthesis of coupled-resonators filters," IEEE Microwave and Wireless Components Letters, Vol. 14, No. 4, 174-176, 2004.
doi:10.1109/LMWC.2004.827111
25. Lamecki, A., P. Kozakowski, and M. Mrozowski, "Fast extraction of coupling matrix for optimization and CAD tuning problems," 34th European Microwave Conference, Vol. 3, 1385-1388, Amsterdam, 2004.
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