在本論文中，吾人提出一準短路三段群延遲傳輸線(quasi-short-circuited three-section group delay transmission line)和一可調式準短路三段群延遲傳輸線(tunable quasi-short three-section transmission line)，其透射係數S21為全通響應(all-pass response)且在中心頻率(center frequency)和高階諧波頻率(high-order harmonic response frequency)會產生極大的群延遲。
準短路三段群延遲傳輸線是由一並聯開路三段傳輸線(open-circuited three-section transmission line)引入準短路結構形成殘段(stub)，再加入其補償而來的槽線結構(slot-line)，其可將由殘斷所造成的阻帶(stop-band) 轉變成通帶(pass-band)，組合成互補式傳輸線結構(complementary transmission line structure)。在此開路三段傳輸線的中心頻率、正規化頻率以及頻寬和阻抗的關係式皆是使用離散時間z域技術(discrete-time z domain)所推導而來。最後，吾人將此結構的模擬和量測結果相互比較，驗證其設計流程，並針對白雲飛學長的研究成果提出進一步改良與更多的群延遲效應。
延續上述的結構，吾人分別在殘段和槽線加入可變電容和可變電感，企圖利用容值和感值來調整互補式結構的中心頻率，實現一可調式準短路三段群延遲傳輸線，在透射係數S21為全通響應下，觀察群延遲大小和其隨頻率所作的位移，最大可調範圍為15%。

In this thesis, a quasi-short-circuited three-section transmission line and a tunable quasi-short-circuited three-section transmission line are presented with the magnitude of insertion loss of all-pass response and excessive group delay at both fundamental frequency and high-order harmonic response frequencies.
A quasi-short-circuited three-section transmission line includes mainly open stub which is open-circuited three-section transmission line with quasi-short-circuited structure in signal plane and accompanied with the complementary slot-line in the ground plane and they combined into complementary transmission line structure. The complementary slot-line is employed to convert the stop-band caused by the stub to a pass-band. The fundamental frequency, normalized frequency, and bandwidth are formulated in the discrete-time z domain to facilitate the study of open-circuited three-section stubs. Finally, measured and simulated results of group delay to compare with each other to verify the design procedure. And provide further improvement and more group delayed effects for Bai,Yun-Fei's research results.
Continuation of the above structure, we join varactors in the stub and join tunable inductors in the slot-line to tune central frequency by varactors and tunable inductors to implement a tunable quasi-short three-section transmission line. When insertion loss is all-pass response, observe the magnitude of group delay and it’s displacement with frequency change. The maximum tuning range of central frequency is 15%.

[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. Azaña, 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. Azaña, 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] Gupta, S., B. Nikfal, and C. Caloz, "Chipless RFID system based on group delay engineered dispersive delay structures," IEEE Antennas and Wireless Propagation Letters, Vol. 10, 1366-1368, 2011.
[15] Y. Horii, S. Gupta, B. Nikfal, and C. Caloz, “Multilayer broadside-coupled dispersive delay structures for analog signal processing,” IEEE Microw. Wireless Compon. Lett., vol. 22, no. 1, pp. 1–3, Jan. 2012.
[16] J.-S. Hong, M. J. Lancaster, “Microstrip Filters for RF/Microwave Applications” Ed., John Wiley & Sons Inc, p.p.77-80, 2001.
[17] K. C. Gupta, R. Garg, I. Bahl, and P. Bhartis, Microstrip Lines and Slotlines, Second Edition, Artech House, Boston, 1996.
[18] E. O. Hammerstard, “Equations for microstrip circuit design,” in Proceedings of the European Microw. Conference, Hamburg, Germany, 1975, pp. 268–272.
[19] E. Hammerstad and O. Jensen, “Accurate Models for Microstrip ComputerAided
Design,” IEEE MTT-S Symposium Digest, pp. 407-409, June 1980.
[20] L. Brillouin, Wave propagation and Group Velocity (Aca-demic, New York, 1960).
[21] L. Brillouin, Wave propagation in Periodic Structures (McGraw-Hill, New York, 1946).
[22] Henrique Salogado, “Dispersion in Optical Fibers,” December 2007.
[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。
[25] D. M. Pozar, “Microwave Engineering,” 3nd Ed., John Wiley & Sons, Inc., 2003.
[26] D. K. Cheng, “Field and Wave Electromagnetics,” Addison-Wesley Publishing Company, Inc., 1989.
[27] I. J Bahl and D. K. Trivedi, “A Designer`s Guide to Microstrip Line,” Microwave, May 1977.
[28] 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.
[29] D. Turner, R. Wihelm, W. Lemberg, “Line Calc.” Agilent Technologies. Palo Alto, CA, 2000.
[30] D. Turner, R. Wilhelm, W. Lemberg, Line Calc. Agilent Technologies. Palo Alto, CA, 2000.
[31] 白雲飛，「使用z域方法設計群延遲傳輸線」，碩士論文，國立台灣科技大學，台北, 2014。
[32] C.-W. Hsue, and Y.-W. Chang, “Comments on ‘Complementary microstrip-slotline stub configuration for group delay engineering’,” Submitted for publication in IEEE Microw. Wireless Compon. Letts.