本論文提出一個製作微波濾波器的方法。利用離散時域技術與二階並聯開路殘段設計窄頻帶通濾波器，將等長二階並聯開路殘段及z轉換技術設計在濾波器上的應用。與一般濾波器設計方法不同，本方法利用離散時域技術設計出先行定義之濾波器，將等長的兩對二階並聯開路殘段分別並接於濾波器上，運用誘發通帶技術使原濾波器二階開路殘段所產生的零點與並接之二階開路殘段的零點之間產生窄頻通帶的效果。
此結構運用串聯之傳輸線，並聯一階開路殘段、一階短路殘段和二階開路殘段完成，由傳輸線所設計的架構，可應用於微波電路。此結果具有較窄的頻寬，並有抑制高次諧波之特性。最後提出實驗結果來驗證此方法的可行性。

In this thesis, we propose an approach to design and implement networks with capability of being microwave filters. Using z-domain technique and parallel two-section stubs to design a narrow bandpass filter. This method present a z-domain transform technique to design an arbitrarily pre-defined filter is implemented by using equal-length transmission lines. Parallel open stubs placed on both sides of the serial transmission line are used to induce a passband that forms a narrow bandpass filter.
The filters are implemented with serial transmission lines, parallel open one-section stub, parallel short one-section stub, and parallel two-section stubs. The filter responses of defined by design can be implemented with the configuration of transmission lines for microwave application. The simulated results show that the passband is narrow, and the filter can suppress the higher order harmonics. Eventually, experimental results are presented to illustrate the validity of the two design method.

[1] David M. Pozar, Microwave Engineering, 2nd Ed.
[2] Jia-Shen Hong and M. J. Lancaster, Microstrip Filters for RF/Microwave Applications.
[3] W. H. Tu, K. Chang, “Compact microstrip low-pass filter with sharp rejection,” IEEE Microwave Wireless Components Letter, vol.15, pp.404-406, (2005).
[4] Da-Chiang Chang, Ching-Wen Hsue, “Wide-Band Equal-Ripple Filters in Nonuniform Transmission Lines,” IEEE Transactions on Microwave Theory Tech., vol. 50, pp. 1114-1119, April (2002).
[5] Da-Chiang Chang and Ching-Wen Hsue, “Design and implementation of filters using transfer function in the Z domain,” IEEE Trans. Microwave Theory, vol. 49, no.5, pp. 979-985, May (2001).
[6] P. I. Richard, “Resistor-transmission line circuits,” Proc. IRE, vol.36, pp. 217-220, Feb. (1948).
[7] K. Kuroda, “General properties and synthesis of transmission-line networks,” Microwave Filters and Circuits, vol.22 Ed. By A. Matsumoto, New York: Academic Press, (1970).
[8] M. L. Roy, A. Perennec, S. Toutain, and L. C. Calvez, “The continuously varying transmission-line technique—Application to filter design,” IEEE Trans. Microwave Theory Tech., vol.47, pp. 1680-1687, Sept. (1999).
[9] C. Quendo, E. Rius and C. Person, “Narrow bandpass filters using dual-behavior resonators,” IEEE Trans. Microwave Theory Tech., vol.51, no. 3, pp.734-743, March (2003).
[10] J. Y. Jhang, C. W. Hsue, C. C. Chen, “Narrow-Band W Filters Using Parallel
Stubs,” AEM2C, 2010 International Conference, pp.177-181, (2010).
[11] A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing, 2ndEd.,Prentice Hall, Inc, (1999).
[12] M. Jachan, G. Matz, F. Hlawatsch, “Time-frequency-autoregressive random process: modeling and fast parameter estimation,” IEEE ICASSP-03, vol.6, pp.125-128, (2003).
[13] Friedlander, B., and B. Porat, “The Modified Yule-Walker Method of ARMA Spectral Estimation,” IEEE Transactions on Aerospace Electronic Systems, AES-20, vol. 2, pp. 158-173, (1984).
[14] Box, George E.P. and Jenkins, Gwilym M. "Time Series Analysis: Forecasting and Control," Holden-Day, Vol.4, pp. 213-220, (1976).
[15] Dickinson, B.W., Kailath, T., and Morf, M., “Canonical Matrix Fraction and State Space Descriptions for Deterministic and Stochastic Linear Systems,” IEEE Transactions on Automatic Control, AC-19, pp. 656-667, (1974).
[16] G. U. Yule, “On a method of investigating periodicitics in disturbed series with special reference toWolfer’s sunspot numbers,” Phil. Trans. R. Soc. A, vol. 226, pp. 267–298, (1927).
[17] Walker, G., “On Periodicity in Series of Related Terms,” Proceedings of the Royal Society, A 13, pp. 518, (1931).
[18] K. C. Gupta, R. Garg, and I. J. Bahl, Microstrip Lines and Slotlines, Artech House, Dedham, Mass.
[19] I. J Bahl and D. K. Trivedi, “A Designer`s Guide to Microstrip Line,” Microwave, May (1977).
[20] D. K. Cheng, Field and Wave Electromagnetics, Addison-Wesley Publishing Company, Inc., (1989).
[21] B. Nowrouzian, “A new approximation theory for Z-domain elliptic transfer functions,” ISCAS ’93, vol.4, pp.2315-2318, (1993).
[22] R. A. Riaz, M. F. U. Butt, S. Chen, L. Hanzo, “Generic z-domain discrete-time transfer function estimation for ultra-wideband systems,” vol.44, pp.1491-1492, (2008).
[23] C. W. Hsue, C. W. Ling and W. T. Hung, “Discrete-time notch filter and its application to microwave filter,” Microwave and Optical Technology Letters, vol. 50, no. 6, pp. 1596-1600, June (2008).
[24] L.-C. Tsai and C.-W. Hsue, “Dual-band band-pass filter using equal-length coupled-serial-shunted lines and Z-domain Technique”, IEEE Trans. Microwave Theory Techn., vol. 52, no. 4, April (2004)
[25] C.-W. Hsue, Jer-Wei Hsue, C.-H. Lu and S.-T. Peng, “Design and implementation of microwave multi-band/multi-level filters using equal-length transmission lines and Yule-Walker scheme,” IET Transactions on Microwave, Antennas and Propagation, vol. 3, issue 5, pp. 826-833, Aug. (2009).