在論文中，我們提出一個三段開路殘斷 (open-circuited three-section stub) 並加上其互補的槽線 (slot-line) 的架構去實現一個群延遲傳輸線 (group delay transmission line)，此種群延遲傳輸線能產生寬頻響應 (broadband response) 、極大的群延遲 (group delay) 和延伸至高頻的高階諧振響應 (high-order harmonic response)。在此三段開路殘斷中的基頻響應及高階諧振響應的傳輸散射參數 (transmission scattering parameter) S21 皆是使用離散時間z域技術 (discrete-time z domain) 的公式所推導而來。加上互補槽線的用途是可將由開路殘斷所造成的阻帶 (stop-band) 轉變成通帶 (pass-band)。藉由此種互補的殘斷和槽線的設計可以得到一個寬頻的群延遲傳輸線。最後我們將此三段開路殘斷並加上其互補槽線架構的群延遲的模擬及量測結果與傳統的單段開路殘斷 (open-circuited single-section stub) 並加上其互補槽線做比較。
此外我們也提出了一個單段準短路殘斷 (quasi-short-circuited single-section stub) 並加上其互補的槽線來與上述的架構做比較。

In this thesis, an open-circuited three-section stub and its complementary slot-line are employed to implement a group delay transmission line with broadband response, excessive group delay and extended high-order harmonic response. The transmission scattering parameter S21 is formulated in the discrete-time z domain to facilitate the study of both fundamental and higher-order harmonic responses of open-circuited three-section stubs. The complementary slot-line is employed to convert the stop-band caused by the stub to a pass-band. As a result, a group delay transmission line with broadband response is obtained. Measured and simulated results of group delay of open-circuited three-section stub with its complementary slot-line structure are presented to compare with those of conventional open-circuited single-section stub with its complementary slot-line.
In addition, a quasi-short-circuited single-section stub and its complementary slot-line are also presented in this paper in order to compare with the above open-circuited stub and its complementary slot-line structure.

[1] S. Gupta, A. Parsa, E. Perret, , R. V. Snyder, Robert J. Wenzel, and Christophe Caloz, “Group-delay engineered noncommensurate transmission line all-pass network for analog signal processing,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 9, pp. 2392-2407, Sep. 2010.
[2] M. K. Mandal, D. Deslandes, and K. Wu, ”Complementary microstrip-slot stub configuration for group delay engineering,” IEEE Microw. Wireless Compon. Lett., vol. 22, no. 8, pp. 388-390, Aug. 2012.
[3] J. D. Schwartz, I. Arnedo, M. A. G. Laso, T. Lopetegi, J. Azana, and D. Plant, “An electronic UWB continuously tunable time-delay system with nanosecond delays,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 2, pp. 103–105, Feb. 2008.
[4] R. Li and L. Zhu, “Ultra-wideband microstrip-slotline bandpass filter with enhanced rejection skirts and widened upper stopband,” Electronic Lett., vol. 43, no. 24, pp. 1368-1369, Nov. 2007.
[5] Z. Zhang and F. Xiao, ”An UWB bandpass filter based on a novel type of multi-mode resonator,” IEEE Microw. Wireless Compon. Lett., vol. 22, no. 10, pp. 506-508, Oct. 2012.
[6] C.-W. Hsue, C.-W. Ling and W.-T Huang, “Discrete-time notch filter and its application to microwave filter,” Microw. Optical Technol. Lett., vol. 50, no. 6, pp. 1596-1600, Jun. 2008.
[7] A.-S. Liu, T.-Y. Huang, and R.-B. Wu, “A dual wideband filter design using frequency mapping and step-impedance resonators,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 12, pp. 2921-2929, Dec. 2008.
[8] C.-W. Hsue, R. Mittra, Y.-H. Tsai, and C.-C. Hsu, “Microwave notch filter using embedded stubs,” Microw. Optical Technol. Lett., vol. 51, no. 12, pp. 2839-2842, Dec. 2009.
[9] W.H. Tu and K. Chang, “Compact second harmonic-suppressed bandstop and bandpass filters using open stubs,” IEEE Trans. Microw. Theory Tech, vol. 54, no. 6, pp. 2497-2502, Jun. 2006.
[10] M. A. G. Laso, T. Lopetegi, M. J. Erro, D. Benito, M. J. Garde, M. A. Muriel, M. Sorolla, and M. Guglielmi, ” Chirped delay lines in microstrip technology,” IEEE Microw. Wireless Compon. Lett., vol. 11, no. 12, pp. 486–488, Dec. 2001.
[11] J. D. Schwartz, I. Arnedo, M. A. G. Laso, T. Lopetegi, J. Azana, and D. Plant, “An electronic UWB continuously tunable time-delay system with nanosecond delays,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 2, pp. 103–105, Feb. 2008.
[12] B. Xiang, A. Kopa, Z. Fu, and A. Apsel, “Theoretical analysis and practical consideration for the Integrated time-stretching system using dispersive delay line (DDL),” IEEE Trans. Microw. Theory Tech, vol. 60, no. 11, pp. 3449-3457, Nov. 2012.
[13] C.-T. M. Wu, S. Gharavi, B. Daneshrad, and T. Itoh, “A dual-purpose reconfigurable negative group delay circuit based on distributed amplifiers,” IEEE Microw. Wireless Compon. Lett., vol. 23, no. 11, pp. 593-595, Nov. 2013.
[14] S. Gupta, and C. Caloz,” Analog signal processing in transmission line metamaterial structure,“ RADIOENGINEERING, vol. 18, no. 2, pp. 155-167, Jun. 2009.
[15] J.-S. Hong, M. J. Lancaster, “Microstrip Filters for RF/Microwave Applications” Ed., John Wiley & Sons Inc, p.p.77-80, 2001.
[16] K. C. Gupta, R. Garg, I. Bahl, and P. Bhartis, Microstrip Lines and Slotlines, Second Edition, Artech House, Boston, 1996.
[17] E. O. Hammerstard, “Equations for microstrip circuit design,” in Proceedings of the European Microw. Conference, Hamburg, Germany, 1975, pp. 268–272.
[18] D. M. Pozar, “Microwave Engineering,” 3nd Ed., John Wiley & Sons, Inc., 2003.
[19] D. K. Cheng, “Field and Wave Electromagnetics,” Addison-Wesley Publishing Company, Inc., 1989.
[20] I. J Bahl and D. K. Trivedi, “A Designer`s Guide to Microstrip Line,” Microwave, May 1977.
[21] Da-Chiang Chang, Ching-Wen Hsue, “Wide-Band Equal-Ripple Filters in Nonuniform Transmission Lines,” IEEE Transactions on Micro. Theory Tech., vol. 50, pp. 1114-1119, Apr. 2002.
[22] D. Turner, R. Wihelm, W. Lemberg, “Line Calc.” Agilent Technologies. Palo Alto, CA, 2000.
[23] 張大強，「設計微波濾波器的離散時域技術」，博士論文，國立台灣科技大學，台北, 2001。
[24] 宋隆貴，「利用三段並聯傳輸線設計的微波濾波器」，碩士論文，國立台灣科技大學，台北, 2006。