表面聲波耦合諧振結構濾波器為一窄頻(一般為0.03%到0.6%)，低損耗和有好的止帶抑制，且無諧波響應。以往對於該元件的討論多在於帶通濾波器，對於其帶拒形式濾波器很少討論到。本論文即利用耦合模態理論來模擬表面聲波耦合諧振結構帶拒形式濾波器之頻率響應，並改變其中部分參數，如IDT根數、中間金屬閘極根數、重疊區長度和延遲距離，以觀察頻率響應的變化。
由實驗可知，耦合諧振結構濾波器有三種耦合狀態，分別為未耦合、耦合和過耦合，其狀態控制於聲波能量的多寡和中間閘極耦合的效果。當IDT根數增加時會影響兩旁通帶的形狀，雖會使插入損減少，但通帶彎曲程度會增大，不利於帶拒濾波器。重疊區長度的增加不會改變帶拒波形，止帶抑制則維持在34dB上下。延遲距離對於聲波分佈的是極重要的，當延遲距離為3/8l時可使表面聲波元件為帶通濾波器，而為1/8l時可使其為帶拒濾波器，此外適當的延遲距離能大幅提昇元件之插入損失至12dB。由以上的討論可以得知，減少IDT的根數，增加重疊區長度和適當的延遲距離，可以得到好的耦合諧振結構濾波器。

SAW CR filter posses narrow bandwidths (typically 0.03% to 0.6%), low insertion loss, and good ultimate rejection without harmonic spurious responses. The past paper discusses mostly CR filter, which is band-pass filters. Band-rejection CR filters neglect in the past. In this research, we use the Coupled-of-mode theory to model the frequency response of the SAW CR band-rejection filters and discuss the influence of number of IDT electrode, length of overlap, and delay-line distance on the frequency response.
In this experiment we know CR filter which has three type of coupled-mode. One type is under- coupled and other are matched and over-coupled. It affect by the number of center grating. With number of IDT electrode increase, insertion loss becomes smaller. But curvature of pass-band response becomes to curve. It is worse to band-rejection filters. When length of overlap increases, shape of filter response does not change so much. And pass-band rejection maintains to 35dB, stop-band rejection maintain 19dB. Delay-line is a major factor in distributing the surface acoustic wave. When delay-line is 3/8λ, SAW device becomes band-pass filters. However delay-line is 1/8λ, SAW device work as band-rejection filters. We can improve the frequency response and low the insertion loss, so appropriate design of the delay-line will be important. According to the discussion of above, a good band-rejection filter is manufactured by using less the number of IDT electrode and suiting delay-line distance and more longer the length of overlap.

1. Lord Rayleigh, “On waves propagating along the plane surface of an elastic
solid”, Proc. London Math. Soc. Vol.17, pp.4-11, 1885.
2. R. M. White and F. M. Voltmer, “Direct piezoelectric coupling to surface
elastic waves”, Appl. Phys. Lett., Vol.7, pp.314-316, 1965.
3. E. A. Ash, “Surface Wave Grating Reflectors and Resonators,” Proceedings
IEEE International Microwave Symposium, May, 1970, pp 385-386.
4. G. L. Mathaei, B. P. O’Shaughnessy, F. Barman, “Relations for Analysis and
Design of Surface Wave Resonators,” IEEE Transactions Sonics & Ultrasonics,
SU-23, March 1976, pp 99-107.
5. Tiersten ,H. F. and R. C. smythe, “Guided acoustic-surface-wave filters,”
Ultrason. Symp. Proc. Pp 293-294, 1975.
6. H. A. Haus, R. V. Schmidt, ”Transmission Response of Cascaded Gratings,”
IEEE Transaction Sonics & Ultrasonics, SU-24, March 1977, pp 94-101.
7. P. S. Cross, R. V. Schmidt, “Coupled Surface-Acoustic-Wave Resonators,” The
Bell System Technical Journal, Vol. 56, No. 8, October 1977, pp 1447-1482.
8. W. J. Tanski, “Multipole SAW Resonator Filters: Elements of Design and
Fabrication,” Proceedings IEEE Ultrasonics Symposium, 1981, pp 100-104.
9. T. F. O’Shea, “SAW Resonator Filters with Optimized Transducer Rejection,”
Proceedings IEEE Ultrasonics Symposium, 1981, pp 105-110.
10. P. C. Meyer, D. Gunes, “Design and Fabrication of SAW Multipole Filters,”
Proceedings IEEE Ultrasonics Symposium, 1983,pp 66-71.
11. M. B. King, L. W. Heep, J. C. Andle, “1500MHz Coupled Resonator Filter,”
Proceedings IEEE Ultrasonics Symposium, 1987,pp 127-130.
12. H. Hung-Chia, Coupled Mode Theory, Utrech, The Netherlands, VNU Science
Press, 1984
13. Y. Koyamada and S. Yoshikawa, “Coupled mode analysis of a long IDT,” Rev.
Elec. Comm. Labs, Nippon Telegraph and Telephone Public Corp., Vol. 27, no.
5-6, 1979, pp. 432-444
14. H. A. Haus and P. V. Wright, “The analysis of grating structures by
coupling-of-modes theory,” IEEE Ultrason, Symp. Proc., 1980, pp.277-281.
15. D. P. Chen and H. A. Haus, “Analysis of metal strip SAW gratings and
transducers,” IEEE Trans. Sonics Ultrason., Vol.SU-32, no. 3, pp 395-408,
1985.
16. M. Koshiba, S. Mitobe. And M. Suzuki, “Finite-element solution of periodic
waveguides for acoustic waves,” IEEE Trans. Ultrason. Ferroelec. Freq.
Contr., Vol UFFC-34, no.4 pp, 472-477, 1987.
17. C. S. Hartmann and B. P. Abbott, “A generalized impulse response model for
SAW transducers including effects of electrode reflections,” IEEE
Ultrasonics Symp, Proc, 1988, pp.29-34.
18. E. K. Sittig and G. A. Coquin, “Filters and dispersive delay lines using
repetitively mismatched ultrasonic transmission lines,” IEEE Trans. Sonics.
Ultrasonics, Vol. SU-15, no,2. pp. 111-119,1968.
19. R. C. M. Li and J. Melngailis, “The influence of stored energy at step
discontinuities on the behavior of surface-wave gratings,” IEEE Trans,
Sonics Ultrasonics, Vol. SU-22, no.3 pp. 189-198,1975.
20. P. V. Wright, “Analysis and design of low-loss SAW device with internal
reflections using coupling of mode theory,” IEEE Ultrasonics Symp. Proc.
1989, pp.141-152
21. Ken-ya Hashimoto, “Surface Acoustic Wave Device in Telecommunications”,pp
191-214, 2000.
22. C. K. Campbell, “Surface Acoustic Wave Device for Mobile and Wireless
Communications”, pp308-314, 1998.
23. P. V. Wright, “A New Generalized Modeling of SAW Transducers and
Gratings”,IEEE Symp.pp.596-605, 1989
24. J.D. Kraus, “Antennas,” McGraw-Hill, New York, pp.66-67, 1950.
25. R.C. Li. And J. Melngailis, “The influence of stored-energy at step
discontinuities on the behavior of surface-wave gratings,” IEEE Trans.
Sonics Ultrason., vol.SU-22, no. 3, pp.189-198, May 1975
26. P.V. Wright and H.A. Haus, “Theoretical analysis of second-order effects in
surface-wave grating,” Proc. 34th Ann. Symp. Frequency Control, pp.262-268,
May 1980
27. P.V. Wright, “Modeling and experimental measurements of the reflection
properties of SAW metallic gratings,” IEEE Ultrason. Symp. Proc. Pp.54-63,
1984
28. W.R.Smith, Jr., “Studies of microwave acoustic transducers and dispersive
delay lines,” PH.D. Thesis in Applied Physics, Stanford University, CA,
December 1969,
29. S.G. Joshi and P. Sudhakar, “Scattering parameters of interdigital surface
acoustic wave transducers,” IEEE Trans. Sonics and Ultrasonics, Vol. SU-24,
pp.201-206, May 1977.
30. W.H. Haydl, B.Dischler, and P. Hiesinger, “Multimode SAW Resonators –A
Method to Study the Optimum Resonator Design,” Proc.1976 IEEE Ultrason.,
SU-22, No.2(March 1975), pp.105-114
31.水瑞鐏，”以耦合模型模擬理論分析耦合式表面聲波共振濾波器及其應用”，大葉大學電
機工程所碩士論文