本論文提出了使用雙諧振及三諧振步階阻抗諧振器設計帶通濾波器的合成理論，並且證明其電路模型可以等效成平行耦合線帶通濾波器的電路模型。為了把等長性雙諧振諧振器的第三個諧振點往高頻移動，藉此抑制高頻響應，同時又能減少電路的總電性長度，本論文也提出使用非等長性的雙諧振諧振器設計帶通濾波器的合成方法。

本論文使用的三諧振模態步階阻抗諧振器，其電性長度為一個波長，雖然一個諧振器就有三個緊靠在一起的諧振模態，但是其電性長度比半波長諧振器的電性長度長了半波長。為了維持諧振器的電性長度為半波長，本論文在最後提出了並聯短路殘段半波長諧振器與其合成帶通濾波器的方法。

此外，本論文在實作方面也完成了數個使用雙諧振步階阻抗諧振器與三諧振模態並聯短路殘段半波長諧振器設計的帶通濾波器的研製，並且與平行耦合線帶通濾波器的設計作比較，以驗證本論文所闡述之設計方法的正確性。

This thesis is on the network models and synthesis of microwave bandpass filters using dual-mode and triple-mode stepped-impedance resonators. It has proved that the circuit models of these filters are equivalent to those of the traditional parallel coupled-line filters. In order to shift the third resonance of commensurate dual-mode stepped-impedance resonators to higher frequency for suppressing spurious response and reduce the total electrical length of the circuit, the synthesis methods using non-commensurate dual-mode stepped-impedance resonators are also derived.

The electrical length of triple-mode stepped-impedance resonators in the thesis is one wavelength. Although these resonators have triple-mode resonance, they are half-wavelength longer than half-wavelength resonators. In order to keep the electrical length of resonators to half-wavelength, the synthesis method of bandpass filter using triple-mode shunt short-circuited stub half-wavelength resonators is studied and presented at the end of this thesis.

Several bandpass filters using dual-mode stepped-impedance resonators and triple-mode shunt short-circuited stub half-wavelength resonators have been fabricated and tested. Comparisons of them with parallel coupled-line filters have been done to verify the proposed methods.

[1.1] L. Zhu, H. Bu, and K. Wu, “Aperture compensation technique for innovative design of ultra-broadband microstrip bandpass filter,” IEEE MTT-S Int. Microw. Symp. Dig. pp.315-318, 2000.
[1.2] J. T. Kuo, and E. Shih, “Wideband bandpass filter design with three-line microstrip structure,” Proc. Inst. Elect. Eng., vol. 149, no. 516, pp. 243-247, Oct./Dec. 2002.
[1.3] L. Zhu, W. Menzel, and K. Wu, 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, 2001.
[1.4] W. Menzel, L. Zhu, K. Wu, and F. Bogelsack, “On the design of novel compact broad-band planar filters,” IEEE trans. Microwave Theory Tech., vol. 51, no. 2, pp. 364-370, Feb., 2003.
[1.5] L. Zhu and W. Menzel, “Compact microstrip bandpass filter with two transmission zeros using a stub-tapped half-wavelength line resonator,” IEEE Microwave Wireless Comp. Letts., vol. 13, no. 1, pp. 16-18, Jan., 2003.
[1.6] L. Zhu, S. Sun, and W. Menzel, “Ultra-wideband(UWB) bandpass filters using multiple-mode resonator,” IEEE Microwave wireless Comp. Letts., vol. 15, no. 11, pp. 796-798, Nov., 2005.
[1.7] R. Li and L. Zhu, “Compact UWB bandpass filter using stub-loaded multiple-mode resonator,” IEEE Microwave wireless Comp. Letts., vol. 17, no. 1, pp. 40-42, Jan., 2007.
[1.8] M. H. Ren, D. Chen, and C. H. Cheng, “A novel wideband bandpass filter using a cross-shaped multiple-mode resonator,” IEEE Microwave wireless Compo. Letts., vol. 18, no. 1, pp. 13-15, Jan., 2008.
[1.9] Y. C. Chiou, J. T Kuo, and E. Cheng, “Broadband Quasi-Chebyshev Bandpass Filters With Multimode Stepped-Impedance Resonators(SIRs)”, IEEE Trans. Microwave Theory Tech., vol. 54, no. 8, pp. 3352-3358, Aug 2006.
[1.10] Y. C. Chiou, Y. F. Lee, J. T. Kuo, and C. C. Chen, “Planar Multimode resonator bandpass filters with sharp transition and wide stopband,” IEEE MTT-S Int. Microw. Symp. Dig., pp. 439-442, 2008.
[1.11] P. Cai, Z. Ma, X. Guan, Y. Kobayashi, and T. Anada, “Synthesis and realization of novel ultra-wideband bandpass filters using 3/4 wavelength parallel-coupled line resonators,” Asia-Pacific Microwave Conf., pp. 159-162, Dec. 2006.
[1.12] C. P. Chen, Z. Ma, N. Nagaoka, and T. Anada, “Synthesis of ultra-wideband bandpass filter employing parallel coupled sirs of one-wavelength,” Proc. 37th Euro. Microwave Conf., pp. 787-790, 2007.
[2.1] S. B. Cohn, “Parallel-coupled transmission-line-resonator filter,” IRE Trans. Microwave Theory Tech., vol. MTT-6, pp. 223-231, April 1958.
[2.2] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Network, and Coupling Structures. Norwood, MA: Artech House, 1980, ch. 10, pp. 585-604.
[2.3] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Network, and Coupling Structures. Norwood, MA: Artech House, 1980, ch. 10, pp. 632-641.
[3.1] M. Makimoto and S. Yamashita, “Bandpass filters using parallel coupled stripline stepped impedance resonators,” IEEE Trans. Microwave Theory Tech., vol. MTT-28, pp. 1413-1417, Dec 1980.
[3.2] 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, 2001.
[3.3] S. Y. Lee and C. M. Tsai, “New cross-coupled filter design using improved hairpin resonators,” IEEE Trans. Microwave Theory Tech., vol. 48, no. 12, pp. 2482-2490, Dec. 2000.
[3.4] Y. C. Chiou, J. T. Kuo, and E. Cheng, “Broadband Quasi-Chebyshev Bandpass Filters With Multimode Stepped-Impedance Resonators(SIRs)”, IEEE Trans. Microwave Theory Tech., vol. 54, no. 8, pp. 3352-3358, Aug. 2006.
[3.5] H.-M Lee and C.-M Tsai, “Improved coupled-microstrip filter design using effective even-mode and odd-mode characteristic impedances,” IEEE Trans. Microwave Theory Tech., vol. 53, no.9, pp. 2812-2818, Sept. 2005.
[3.6] S. B. Cohn, “Parallel-coupled transmission-line-resonator filter,” IRE Trans. Microwave Theory Tech., vol. MTT-6, pp. 223-231, April. 1958.
[3.7] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Network, and Coupling Structures, Norwood, MA: Artech House, 1980, ch.10, pp. 586-605.
[3.8] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Network, and Coupling Structures, Norwood, MA: Artech House, 1980, ch.10, pp. 636-640.
[3.9] R. E. Collin, Foundations For Microwave Engineering, McGraw-Hill, Inc., 1992, ch. 6, pp. 427-432.
[4-1] Y. C. Chiou, J. T Kuo, and E. Cheng, “Broadband Quasi-Chebyshev Bandpass Filters With Multimode Stepped-Impedance Resonators(SIRs)”, IEEE Trans. Microwave Theory Tech., vol. 54, no. 8, pp. 3352-3358, Aug. 2006.
[5.1] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Network, and Coupling Structures, Norwood, MA: Artech House, 1980, ch.5, pp. 221.
[6.1] P. Cai, Z. Ma, X. Guan, Y. Kobayashi, T. Anada, and G. Hagiwara, “A novel compact ultra-wideband bandpass filter using a microstrip stepped-impedance four-modes resonator,” IEEE MTT-S Int. Microwave Sym. Dig., WE3E-05, pp. 751-754, June 2007.
[6.2] J. R. Lee, J. H. Cho, and S. W. Yun, “New compact bandpass filter using microstrip λ/4 resonators with open stub inverter,” IEEE Microwave Guided wave Lett., vol. 10, no. 12, Dec. 2000.
[6.3] L. Zhu and W. Menzel, “Compact microstrip bandpass filter with two transmission zeros using a stub-tapped half-wavelength line resonator,” IEEE Microwave wireless Comp. Letts., vol. 13, no. 1, Jan. 2003.
[6.4] C. Quendo, E. Rius, C. Person, J. F. Favennec, Y. Clavet, A. Manchec, R. Bairavasubramanian, S. Pinel, J. Papaolymerou, and J. Laskr, “Wide band, high rejection and miniaturized fifth order bandpass filter on LCP low cost organic substrate,” IEEE MTT-S Int. Dig., Jun. 2005, pp. 2203-2205.
[6.5] M. H. Ren, D. Chen, and C. H. Cheng, “A novel wideband bandpass filter using a cross-shaped multiple-mode resonator,” IEEE Microwave wireless Comp. Letts., vol. 18, no. 1, pp. 13-15, Jan. 2008.
[6.6] K. Ma, K. C. B. Liang, R. M. Jayasuriya, and K. S. Yeo, “A wideband and high rejection multimode bandpass filter using stub perturbation,” IEEE Microwave wireless Comp. Letts., vol. 19, no. 1, pp. 24-26, Jan. 2009.
[6.7] P. Rizzi, Microwave Engineering, Passive Circuits, Englewood Cliffs, NJ: Prentice-Hall, 1988, pp. 490-493.
[6.8] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Network, and Coupling Structures. Norwood, MA: Artech House, 1980, ch.10, pp. 595-604.