使用多模諧振器設計微波濾波器大致可分成兩種方法，第一種為先設計多模
諧振器的電路結構及諧振點，再透過調整輸出入埠的饋入以達成整體濾波器的設
計，第二種則為使用近似或精確的合成理論直接合成出整體濾波器的元件值，本
論文主要探討的是第一種設計方法，以等長性步階阻抗多模諧振器的諧振頻率與
特性阻抗為研究重點，發現多模諧振器不只是要對諧振點位置進行設計，諧振器
的特性阻抗值對於整體濾波器響應也非常重要，最後並以圖表的方式呈現如何使
用多模諧振器來設計濾波器。另外，也以諧振頻率位置及特性阻抗值這兩個重要
的設計要點，來進行等長性多模諧振器的替換，提出以非等長性步階阻抗諧振器
及並聯短路殘段諧振器兩種結構，此達到縮小濾波器長度的效果。最後，本論文
以電磁模擬與電路實作完成了設計圖表與相關設計流程的驗證。

The design methods of microwave filters using multimode resonators can generally be divided into two categories. One is to design the structure and resonant frequencies of the multimode resonator first, and then the couplings to input/output ports are adjusted to complete the design. The other is to use approximate or exact synthesis methods to derive all the component values of the filter directly. This thesis mainly studies the first method, and focuses on the effects and designs of the resonant frequencies and characteristic impedances of commensurate step-impedance resonators. It is found that not only the resonant frequencies, but also the characteristic impedances of the multimode resonators are very important design parameters. Design graphs and tables are created to help the design of these kinds of multimode resonator filters. Furthermore, it is proposed to replace commensurate resonators with non-commensurate ones or shunt short-stub resonators, in order to reduce the overall filter size. By keeping the resonant frequencies and the characteristic impedance of the first transmission-line section unchanged, it is found the passband responses are still good after these replacements. Finally, all the above studies are verified by electromagnetic simulations and real circuit measurements.

[1.1] L. Zhu, H. Bu, K. Wu, and M. S. Leong, “Miniaturized multi-pole broad-band microstrip bandpass filter: concept and verification,” Proc. 30th Eur. Microw. Conf., Paris, France, vol. 3, pp. 334–337, Oct. 2000.

[1.2] L. Zhu, W. Menzel, K. Wu, and F. Boegelsack, “Theoretical characterization and experimental verification of a novel compact broadband microstrip bandpass filter,” Proceedings of Asia-Pacific Microwave Conf., Taipei, Taiwan, R.O.C., pp. 625-628, Dec. 2001.

[1.3] W. Menzel, Lei Zhu, Ke Wu, and F. Bogelsack, “On the design of novel compact broad-band planar filters,” IEEE Transactions on Microwave Theory and Techniques, vol. 51, no. 2, pp. 364-370, Feb. 2003.

[1.4] L. Zhu, S. Sun, and W. Menzel, “Ultra-wideband (UWB) bandpass filters using multiple-mode resonator,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 11, pp. 796–798, Nov. 2005.

[1.5] R. Li and L. Zhu, "Compact UWB bandpass filter using stub-loaded multiple-mode resonator," Microwave and Wireless Components Letters IEEE, vol. 17, no. 1, pp. 40-42, Jan. 2007.

[1.6] S. W. Wong and L. Zhu, “EBG-embedded multiple-mode resonator for UWB bandpass filter with improved upper-stopband performance,” IEEE Microwave and Wireless Components Letters, vol. 17, no. 6, pp. 421-423, June 2007.

[1.7] Y. Zhou, B. Yao, Q. Cao, and H. Deng, X. He, “Compact UWB bandpass filter using ring open stub loaded multiple-mode resonator,” Electronics Letters, vol.45, no.11 ,pp.554-556, May 2009.

[1.8] H. W. Deng, Y. J. Zhao, L. Zhang, X. S. Zhang, and S. P. Gao, “Compact quintuple-mode stub-loaded resonator and UWB filter,” IEEE Microwave and Wireless Components Letters, vol.20, no.8, pp.438-440, Aug. 2010.

[1.9] Q. X. Chu and X. K. Tian, “Design of UWB bandpass filter using stepped-impedance stub-loaded resonator,” IEEE Microwave and Wireless Components Letters, vol.20, no.9, pp.501-503, Sept. 2010.

[1.10] Q. X. Chu, X. H. Wu, and X. K. Tian, “Novel UWB bandpass filter using stub-loaded multiple-mode resonator,” IEEE Microwave and Wireless Components Letters, vol.21, no.8, pp.403-405, Aug. 2011.

[1.11] X. Zheng, W. Liu, X. Zhang, and T. Jiang, “Design of dual band-notch UWB bandpass filter based on T-shaped resonator,” Progress In Electromagnetic Research Symposium (PIERS), Shanghai, China, Aug. 2016.

[1.12] S. Y. Yang, Broadband microwave filter design using multimode resonators, Institute of Computer and Communication Engineering, National Cheng Kung University, Tainan, Taiwan, R.O.C., Thesis for Master of Science, July 2009.

[1.13] J. S. Hsieh, Microwave network synthesis and analysis of wide-band filters, compact filters, and dual-band impedance transformers, Department of Electrical Engineering, National Cheng Kung University, Tainan, Taiwan, R.O.C., Dissertation for Doctor of Philosophy, July 2011.

[1.14] M. C. Horton and R. J. Wenzel, “General theory and design of optimum quarter-wave TEM filters,” IEEE Trans. Microwave Theory Tech., vol. 13, no.3, pp.316-327, May 1965.

[1.15] C. P. Chen, Z. Ma, and T. Anada, “Synthesis of ultra-wideband bandpass filter employing parallel-coupled stepped-impedance resonators,” IET Microwaves, Antennas & Propagation, vol. 2, no.8, pp.766-772, Dec. 2008.

[2.1] L. Zhu, W. Menzel, K. Wu, and F. Boegelsack, “Theoretical characterization and experimental verification of a novel compact broadband microstrip bandpass filter,” Proceedings of Asia-Pacific Microwave Conf., Taipei, Taiwan, R.O.C., pp. 625-628, Dec. 2001.

[2.2] L. Zhu, S. Sun, and W. Menzel, “Ultra-wideband (UWB) bandpass filters using multiple-mode resonator,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 11, pp. 796–798, Nov. 2005.

[2.3] M. C. Horton and R. J. Wenzel, “General theory and design of optimum quarter-wave TEM filters,” IEEE Trans. Microwave Theory Tech., vol. 13, no.3, pp.316-327, May 1965.

[2.4] J. S. Hsieh, Microwave network synthesis and analysis of wide-band filters, compact filters, and dual-band impedance transformers, Department of Electrical Engineering, National Cheng Kung University, Tainan, Taiwan, R.O.C., Dissertation for Doctor of Philosophy, July 2011.

[2.5] L. Zhu, H. Bu, K. Wu, and M. S. Leong, “Miniaturized multi-pole broad-band microstrip bandpass filter: concept and verification,” Proc. 30th Eur. Microw. Conf., Paris, France, vol. 3, pp. 334–337, Oct. 2000.

[2.6] R. Li and L. Zhu, "Compact UWB bandpass filter using stub-loaded multiple-mode resonator", Microwave and Wireless Components Letters IEEE, vol. 17, no. 1, pp. 40-42, Jan. 2007.

[3.1] X. M. Lin and Q. X. Chu, "Design of triple-band bandpass filter using tri-section stepped-impedance resonators", Proc. Int. Conf. Microw. Millimeter Wave Tech., pp. 1-3, Apr. 2007.

[3.2] Y. C. Chen, Y. H. Shieh, C. H. Her, and C. I. G. Hsu, "Tri-band microstrip BPF design using tri-section SIRs", IEEE AP-S Int. Symp. Dig., pp. 3113-3116, Jun. 2007.

[3.3] G. L. Matthaei, L. Young, and E. M. T.Jones, Microwave filters, impedance-matching network, and coupling structures. Norwood, MA:Artech House, ch. 5, pp. 191-195, 226-227, 1980.

[3.4] M. C. Horton and R. J. Wenzel, “General theory and design of optimum quarter-wave TEM filters,” IEEE Trans. Microwave Theory Tech., vol. 13, no.3, pp.316-327, May 1965.

[3.5] Q. X. Hong, Automated implementation and analysis of interdigital band-pass filters, Institute of Computer and Communication Engineering, National Cheng Kung University, Tainan, Taiwan, R.O.C., Thesis for Master of Science, July 2017.

[4.1] S. Y. Yang, Broadband microwave filter design using multimode resonators, Institute of Computer and Communication Engineering, National Cheng Kung University, Tainan, Taiwan, R.O.C., Thesis for Master of Science, July 2009.

[4.2] S. W. Wong, R. S. Chen, K. Wang, and Q. X. Chu, “Chebyshev transfer functions for the synthesis of an ultra­wideband(UWB) filter using short-circuit stub Resonator,” 2013 International Workshop on Microwave and Millimeter Wave Circuits and System Technology, Oct. 2013.

[4.3] Q. X. Hong, Automated implementation and analysis of interdigital band-pass filters, Institute of Computer and Communication Engineering, National Cheng Kung University, Tainan, Taiwan, R.O.C., Thesis for Master of Science, July 2017.

[6.1] S. Y. Yang, Broadband microwave filter design using multimode resonators, Institute of Computer and Communication Engineering, National Cheng Kung University, Tainan, Taiwan, R.O.C., Thesis for Master of Science, July 2009.

[6.2] C. P. Chen, Z. Ma, and T. Anada, “Synthesis of ultra-wideband bandpass filter employing parallel-coupled stepped-impedance resonators,” IET Microwaves, Antennas & Propagation, vol. 2, no.8, pp.766-772, Dec. 2008