使用離散時間技術去分析帶拒濾波器的方法被提出，分解柴比雪夫型式二的濾波器為V字形濾波器，利用二段式並聯開路的傳輸線去實現它，用串聯的傳輸線串接二段式並聯開路的傳輸線去近似帶拒濾波器，單一頻帶和雙頻帶帶拒濾波器的實現去指出這個設計方法的可行性。
反之亦然，我們可用多個V字形濾波器去形成寬頻帶的柴比雪夫型式二的帶拒濾波器，寬帶的柴比雪夫型式二的帶拒濾波器的實現，驗證這個設計方法的可行性。
最後，我們使用離散時間技術去設計超寬帶的帶通濾波器，其頻帶和中心頻率的比值接近於140%，我們將量測這個濾波器的散射參數並與理論值進行比對，以証明本方法的可行性。

A synthesis method of bandstop filters using discrete-time domain technique is presented. By decomposing the discrete -time prototype of Chebyshev type II filter into the factorized terms, a transmission line shunted with a two-section shunt -open stub is developed to implement the notch filter. A cascade connection of serial lines shunted with multiple two-section shunt-open stubs is employed to emulate the bandstop filter. Both single-band and dual-band bandstop filters are implemented to illustrate the validity of this design method.
We can use multiple notch filters to compose the wide-band Chebyshev type II bandstop filter and vice versa. Wide-band Chebyshev type II bandstop filter is implemented to illustrate the validity of this design method.
Eventually, we use the discrete-time technique to design the Ultra-wide-band bandpass filter which bandwidth is approximately 140%.We will measure the S-parameter of this filter and compare with the theoretical values to demonstrate the validity of the design method.

[1] R. Levy, ”Tables of Element Values for the Distributed Low-Pass Prototype Filter.” IEEE Trans. Microwave Theory Tech.,vol.MTT-13,
pp.514-536,Sept. 1965
[2] R. Levy, ”Tapered corrugated waveguide low-pass filters,” IEEE Trans. Microwave Theory Tech.,vol.MTT-21,pp.526-532,June 1973
[3] G.L. Matthaei, ”Comb-line Band-pass Filters of Narrow or Moderate Bandwidth.” Microwave J.,vol.6,pp.82-91,Aug.1963.
[4] J.-S. Hong and M.J. Lancaster, ”Microstrip bandpass filter using degenerate modes of a novel meander loop resonator,”IEEE Microwave and Guided Wave Letters.,vol.5,no .11,pp.371-372,Nov.1995
[5] R. J. Wenzel, ”Synthesis of Combine and Capacitively Load Interdigital Bandpass Filters of Arbitrary Bandwidth”IEEE Trans. Microwave Theory Tech.,vol.MTT-19,pp.578-586,Aug.1971
[6] B. M. Schirman and G. L. Matthaei, ”Exact Design of Microwave Bandstop Filters,”IEEE Trans. Microwave Theory Tech.,vol.MTT-12,pp.6-15,Jan. 1964
[7] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave filters, impedance- Matching Networks and Coupling Structures.Artech House: Dedham, Mass.1980
[8] Macro Guglielmi, ”Simple CAD Procedure for Microwave Filters and Multiplxers,” IEEE Trans. Microwave Theory Tech., vol.42,no.7,pp. 1347-1352, July.1994
[9] Riccardo Tascone, Patrizia Savi, Danile Trinchero and Renato Orta,”Scattering Matrix Approach for the Design of Microwave filters,” IEEE Trans. Microwave Theory Tech., vol.48,no.3,pp. 423-430, March.2000
[10] Bryant,T. G. and I. A. Weiss, ”Parameters of Microstrip Transmission Lines and of Coupled Pairs of Microstrip Lines,” IEEE Trans. Microwave Theory Tech., vol.MTT-16,pp.1021-1027,1968
[11] P. I. Richard, ”Resistor-transmission line circuits,”Proc.IRE, vol, 36,pp.217-220,Feb,1948
[12] K. Kurada, ”General properties and synthesis of transmission-line network,”in Microwave Filters and Circuits, A.Mstsumoto, Ed. New York:Academic,1970
[13] R.-L. Lin, C.-W. Chiu and R.-B.Wu, ”Coplanar waveguide bandpass filter-a ribbon-of –brick-wall design,” IEEE Trans. Microwave Theory Tech.,vol.43, pp.1589-1596,July 1995
[14] K. T. Chan, A. Chin, M. -F. Li, D.-L. Kwong, A. P. McAlister, D.S. Duh, W. J. Lin, C. Y. Chang, ”High-performance microwave coplanar bandpass and bandstop filters on Si substrates,’IEEE Trans. Microwave Theory Tech., vol. 51, pp.2036-2040,Sept.2003.
[15] A. V. Beljaev, A. P. Krenitskiy, V. P. Meschanov, and L.V. Shikova,
”Directional filters on coupled nonuniform TEM transmission lines,”IEEE Trans. Microwave Theory Tech., vol. 52, no.1,pp.
133-138,Jan.2004.
[16] A. E. Williams, ”A four-cavity elliptic waveguide filters,”IEEE Trans. Microwave Theory Tech., vol. MTT-18,pp.1109-1114,Dec.1970.
[17] J.-T. Kuo and M. Jiang and H.-J. Chang, ”Design of parallel-coupled microstrip filters with suppression resonances using substrate suspension,” IEEE Trans. Microwave Theory Tech., vol. 52, no.1,pp.83-89,Jan.2004.
[18] H.-M. Lee and C.-M. Tsai, ”Improved coupled-microstrip design using effective even-mode and odd-mode characteristic impedances,” IEEE Trans. Microwave Theory Tech., vol. 53,no.9,pp.2812-2818,Sept.2005
[19] G. L. Matthaei,”Narrow-band,fixed-tuned, and tunable bandpass filters with zig-zag hairpin-comb resonators,” IEEE Trans. Microwave Theory Tech., vol. 51, no.4,pp.1214-1219,April.2003.
[20] D.-C. Chang and C.-W. Hsue, ”Design and implementation of filters using transfer function in the Z domain,” IEEE Trans. Microwave Theory Tech., vol. 49, no.5,pp.979-985,May.2001.
[21] L.-H. Hsieh and K. Chang, ”Compact, low insertion-loss, sharp-rejection, and wide-band microstrip bandpass filters,” IEEE Trans. Microwave Theory Tech.,vol. 51,no.4,pp.1241-1246,April.2003
[22] J. D. Rhodes, ”Waveguide bandstop elliptic function filters,”IEEE Trans. Microwave Theory Tech.,vol.MTT-20,pp.715-718,Nov.1972
[23] G. Matthaei, L. Young,and E. M. T.Jones, Microwave filter, Impedance - Matching Networks and Coupling Structures. Norwood,MA:Artech House, 1980
[24] S. Amari and U. Rosenberg. ”Direct synthesis of a class of bandstop filters,”IEEE Trans. Microwave Theory Tech.,vol. 51,no.4,pp. 1241-1246 ,April.2003
[25] H. Uchida, H. Kamino, K. Totani, N. Miyazaki, Y. Konishi, S. Makino J. Hirokawa and M. Ando, ”Dual-band-rejection filter for distortion reduction and RF transmitter,” IEEE Trans. Microwave Theory Tech.,vol.52,no.11,pp.2550 -2556,Nov.2004
[26] B. Strassner and K. Chang, ”Wide-band low-loss high-isolation microstrip periodic-stub diplexer for multiple-frequency applications,” IEEE Trans. Microwave Theory Tech., vol.49, no.10, pp.1818-1820,Oct.2001
[27] H. C. Bell,” L-resonator bandstop filters,” IEEE Trans. Microwave
Theory Tech.,vol.44, no.12, pp.2669-2672,Dec.1996
[28] C. Rauscha, ”Varactor-tuned active notch filter with low passband noise and signal distortion,” IEEE Trans. Microwave Theory Tech., vol.49, no.8, pp.1431-1437,Aug.2001
[29] A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing,2ndEd.,Prentice Hall,Inc,1999
[30] I. J Bahl and D. k. Trivedi, ”A Designer`s Guide to Microstrip Line,” Microwave, May 1977
[31] K. C. Gupta, R. Garg, and I. J. Bahl, Microstrip Lines and Slotilines, Artech House, Dedham,Mass.
[32] Foundations for Microwave Engineering, IEEE Press Series on Electromagnetic Wave Theory,2002
[33] D. K. Cheng, Field and Wave Electromagnetics, Addison-Wesley
Publishing Company, Inc.,1989.
[34] D. M. Pozar, Microwave Engineering,3ndEd.,John Wiley&Sons, Inc.,1998
[35] Da-Chiang Chang and Ching-Wen Hsue, “Wide-band equal-ripple filters in nonuniform transmission lines”, IEEE Trans.Microwave Theroy Tech.,vol.50, pp.1114-1119,April 2002.
[36] Da-Chiang Chang and Ching-Wen Hsue, “Design and implementation of filters using transfer function in the Z domain”, IEEE Trans. Microwave Theory Tech.,vol.50,pp.979-985,May 2001.
[37] Soo-Chang Pei and Chien-Cheng Tseng, ”IIR Multiple Notch Filter Design Based on Allpass Filter,” IEEE Trans. Circuits Syst.-II,vol.44,NO.2, FEBRUARY 1997
[38] A. H. Gray Jr. and J. D. Markel, “Digital lattice and ladder filter synthesis,” IEEE Trans . Audio Eletroacoust ., vol.AU-21,pp.491
-500, Dec.1973
[39] J. A. Chambers and A. G. Constantinides, “Frequency tracking using constrained adaptive notch filters synthesised from allpass sections,”in Proc. Inst. Elect. Eng., Dec. 1990, vol. 137, Pt. F, pp. 475–481.
[40] P. A. Regalia, S. K. Mitra, and P. P. Vaidyanathan, “The digital
all-pass filter: A versatile signal processing building block,” Proc IEEE, vol. 76, pp. 19–37, Jan. 1988
[41] Lin-Chuan Tsai and Ching-Wen Hsue, “Dual-Band Bandpass Filters Using Equal-Length Coupled-Serial-Shunted Lines and Z-transform Technique,”IEEE Trans.MICROWAVE Theory Tech.,vol.52,No.4,APRIL 2004
[42] N.I Cho and S. U. Lee, “On the adaptive lattice notch filter for the detection of sinusoids,”IEEE Trans. Circuit Syst.,vol.40,no.7,
pp.405-416,July 1993.
[43] Lin-Chuan Tsai, Hwan-Mei Chen and Ching-Wen Hsue, “Z-Domain Formulations of Equal-Length Coupled-Series-Shunted Lines and Their Applications to Filters,” IEE Proceedings-Microwave,Antenna and Propagation,vol.151,pp.97-103,April 2004.
[44] Y. V. Joshi and S. C. Dutta Roy. “Design of IIR notch filters with different passband gains”, IEE Proc-Vis. Image Signal Processing.,
vol.145,No.1,February 1998.
[45]“無線通信之射頻被動電路設計”張盛富.戴明鳳 著,全華科技圖書股份有
限公司 印行
[46] D. Hanselman and B. Littlefield, Mastering Matlab 5. Englewood Cliffs, NJ:Prentice-Hall,1998