Scattering Analysis and Design of SAW Resonator Filters

IEEE Transactions on Sonics and Ultrasonics

Volumn 26, Issue 3, 1979, Pages 205-229

  Rosenberg, Robert L ^a   Coldren, Larry A ^a  

^a LUCENT TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC SURFACE WAVE DEVICES;

EID: 0018466289     PISSN: 00189537     EISSN: None     Source Type: Journal    
DOI: 10.1109/T-SU.1979.31088     Document Type: Article

References (62)

1. R. L. Rosenberg and L. A. Coldren, “Fast Synthesis of Finiteloss loss SAW Resonator Filters,” IEEE 1977 Ultrasonics Symp. Proc., 77 CH 1264–1 SU, pp. 882–7.
2. L. A. Coldren, R. L. Rosenberg, and J. A. Rentschler, “Monolithic Transversely Coupled SAW Resonator Filters,” ibid., pp. 888–93.
3. L. A. Coldren and R. L. Rosenberg, “Scattering Matrix Approach to SAW Resonators,” IEEE 1976 Ultrasonics Symp. Proc., 76 CH 1120–5 SU, pp. 266–71.
4. R. L. Rosenberg and L. A. Coldren, “Reflection-Dependent Coupling Between Grating Resonators,” ibid., pp. 281–6.
5. A. I. Zverev, Handbook of Filter Synthesis, New York: John Wiley, 1967, Chap. 6.
6. F. G. Marshall, C. O. Newton, and E. G. S. Paige, “Theory and Design of the Surface Acoustic Wave Multistrip Coupler”; “Surface Acoustic Wave Multistrip Components and Their Applications,” IEEE Trans. Sonics Ultrason., Vol. SU-20, pp. 124-33; 134–43, April, 1973.
7. C. S. Hartmann and R. C. Rosenfeld, U.S. Patent No. 3, 866, 504, May 27, 1975.
8. M. Redwood, R. B. Topolevsky, R. F. Mitchell, and J. S. Palfreeman, man, “Coupled-Resonator Acoustic-Surface-Wave Filter,” Electron. Lett., Vol. lt, pp. 253–4, June, 1975.
9. P. S. Cross, R. S. Smith, and V. H. Haydl, “Electrically Cascaded Surface-Acoustic-Wave Resonator Filters,” Electron. Lett., Vol. 11, pp. 244–5, May 1975.
10. H. F. Tiersten and R. C. Smythe, “Guided Acoustic Surface Wave Filters,” IEEE 1973 Ultrasonics Symp. Proc., 75 CHO 994 -4SU, pp. 293–4.
11. R. C. M. Li, J. A. Alusow, and R. C. Williamson, “Surface-Wave Resonators Using Grooved Reflectors,” Proc. 29th Annual Symp. on Frequency Control, 1975, Electronic Industries Assn., Washington, D.C., pp. 167–76.
12. P. S. Cross, R. V. Schmidt, and H. A. Haus, “Acoustically Cascaded ASW Resonator-Filters,” IEEE 1976 Ultrasonics Symp. Proc., 76 CH 1120-5SU, pp. 277–80.
13. H. A. Haus and R. V. Schmidt, “Transmission Response of Cascaded Gratings,” IEEE Trans. Sonics Ultrason., Vol. SU-24, pp. 94–101, Mar. 1977.
14. R. H. Dicke, MIT Rad. Lab. Series, Vol. 8, Principles of Microwave Circuits, Chap. 5, New York: McGraw-Hill, 1948.
15. D. M. Kerns and R. W. Beatty, Basic Theory of Waveguide Junctions and Introductory Microwave Network Analysis, New York: Pergamon, 1967.
16. J. L. Altman, Microwave Circuits, New York: Van Nostrand, 1964.
17. K. Kurokawa, “Power Waves and the Scattering Matrix,” IEEE Trans. Microwave Theory and Techniques, Vol. MTT-13, pp. 194–202, March 1965. This paper is the basis for the present treatment.
18. A 3-port transducer description implies that only a single acoustic mode is being generated or received at the transducer. To take exact account of bulk modes or other transverse surface modes that might be prominent in a resonator, one would have to add two acoustic ports per additional mode. However, losses to other modes can be included in a 3-port description.
19. It should be realized that the transducer scattering amplitudes S mn incorporate by definition all the physical. contributions to scattering by the 3-port junction. In particular, the acoustic reflection amplitude S 11 automatically includes both regenerative and “mechanical” reflections of the transducer. Also, the scattering parameters may be defined to include a tuning network at the electrical port.
20. Because the resonators in many practical devices are overmoded, these neighboring resonances are usually a potential problem [21] However, if the transducers are positioned for maximum constructive interference at the center of the grating stopband (desired resonant frequency), the interference is found to be almost completely destructive at the frequencies of the neighboring resonances when they occur near the edges of the grating stopband. band. The interference change is caused by a 180° difference in the phase of grating reflection between the stopband center and either edge of an unapodized grating. In terms of present parameters, the phase of r changes roughly by 180 degrees over the frequency interval between the resonances.
21. R. Stevens, P. D. White, R. F. Mitchell, P. Moore, and M. Redwood “Stopband Level of 2-Port SAW Resonators,” IEEE 1977 Ultrasonics Symp. Proc., 77 CH 1264-1SU, pp. 905–8.
22. The results given in Eqs. (5–8) are restricted in two ways. The first is the single-mode restriction noted in [18]. The second is more subtle. It is essential to use the power-wave scattering concepts developed by Kurokawa [17]. His definitions of input and output waves and scattering coefficients yield a junction description in which there are no internal reflections from the junction's own terminations. Input waves carry only the power available at the ports, and output waves carry the power actually transferred by transmission or reflection. Thus, │S mn │ 2 is the ratio of power transferred through port m to power available at port n. In a more conventional traveling-wave description of scattering, the junction's own terminations generally reflect power back through the ports, so that the filter transmission expression would be much more complicated than Eq. (5).
23. P. S. Cross and R. V. Schmidt, “Coupled Surface-Acoustic-Wave Wave Resonators,” Bell System Tech. J., Vol. 56, pp. 1447–82, October, 1977.
24. The propagation lengths between junction ports are determined by the choice of port locations and scattering-angle definitions. The ports of a grating have been chosen to lie in their “natural” positions at the edges of a rectangular grating. For transducers and multistrips, it is desirable to transfer the major transit-angle effects to the propagation phase shifts in the adjoining wave-guides. guides. The ports in these bilaterally symmetric structures have therefore been chosen at the center line of symmetry. The associated scattering phases are then the “natural” phases, referred to the structure edges, corrected for the free-surface transit angle between edges [25]. The resultant scattering phases are nearly independent of transit effects over a broad band.
25. R. L. Rosenberg, “Wave-Scattering Analysis of Transducers for Resonator Filters,” to be published.
26. P. S. Cross, “Reflective Arrays for SAW Resonators,” 1973 Ultrasonics Symp. Proc., 75 CHO 994-4SU, pp. 241–4.
27. G. L, Matthaei, F. Barman, E. B. Savage, and B. P. O’Shaughnessy, “A Study of the Properties and Potential Application of Acoustic-Surface-Wave-Resonators,” Surface-Wave-Resonators,” ibid., pp. 284–9.
28. L. A. Coldren, “Characteristics of Surface Acoustic Wave Resontors Obtained from Cavity Analysis,” IEEE Trans. Sonics Ultrason., son., Vol. SU-24, pp. 212–217, May, 1977.
29. L. A. Coldren and R. L. Rosenberg, “Multipole SAW Resonator Filters,” 1978 IEEE Int. Symp. on Circuits and Systems Proc., 78 CH 1358–1 CAS, pp. 548–52.
30. L. A. Coldren and R. L. Rosenberg, “Surface-Acoustic-Wave Resonator Filters,” Proc. IEEE, vol. 67, Jan. 1979, pp. 147–58.
31. G. L. Matthaei, E. B. Savage, and F. Barman, “Synthesis of Acoustic Surface Wave Resonator Filters Using Any of Various Coupling Mechanisms,” IEEE Trans. Sonics Ultrasonics., Vol. SU-25, March 1978, pp. 72–84.
32. W. R. Smith, H. M. Gerard, J. H. Collins, T. M. Reeder, H. J. Shaw, “Analysis of Interdigital Surface Wave Transducers by Use of an Equivalent Circuit Model,” IEEE Trans. Microwave Theory and Techniques, Vol. MTT-17, pp. 856–64, November, 1969;
33. “Design of Surface Wave Delay Lines with Interdigital Transducers,” ibid., pp. 865–73.
34. W. R. Smith, H. M. Gerard, and W. R. Jones, “Analysis and Design of Dispersive Interdigital Surface-Wave Transducers,” IEEE Trans. Microwave Theory and Techniques, Vol. MTT-20, pp. 458–71, July, 1972.
35. For grooved-grating resonators that we have made at VHF frequencies on ST-X quartz, it is possible to ignore the analytical prescription for the cavity length needed to achieve resonance at a prescribed frequency fo. A simple rule of thumb has proved adequate for exploratory studies with resonant frequencies at 75 and 131 MHz, with groove depths in the range 0.5-1.5% of A.0, with the inter-grating space of about 70 λ 0 essentially filled with Al structures, and with Al thicknesses near 110 nm: The surface wave velocity is assigned the value v = 3156 m/s over the entire signal path within a resonator. The correct separation between effective mirror planes within the grating reflectors is then very close to a multiple of λ0/2 = v/(2f0). Cavity tuning has received more detailed consideration elsewhere, e.g. in [61].
36. When the transducers are offset from their maximum-conversion positions, the resulting skewed response has a true maximum slightly displaced from fo and insignificantly larger than the value given by Eq. (33).
37. E. J. Staples and R. C. Smythe, “SAW Resonators and Coupled Resonator Filters,” Proc. 30th Annual Symp. on Frequency Control, Electronic Industries Assn., June, 1976, pp. 322–7.
38. W. R. Shreve, “Two-Port Quartz SAW Resonators: ibid., PP. 328–33.
39. H. A. Haus, “Modes in SAW Grating Resonators,” Electronics Lett., Vol. 13, 1977, pp. 12–13.
40. L. A. Coldren, H. A. Haus, and K. L. Wang, “Experimental Verification of Mode Shape in SAW Grating Resonators,” ibid., pp. 642–3.
41. R. V. Schmidt and P. S. Cross, “Monolithic, Multipole Filters Using a Windowed Surface Acoustic Resonator Cascade,” IEEE 1977 Ultrasonics Symposium, poster session PP-7.
42. R. V. Schmidt and P. S. Cross, “Externally Coupled Resonator-Filters Filters (ECRF),“ to appear.
43. L. A. Coldren and R. L. Rosenberg, “Acoustically Coupled SAW Resonator Filters with Enhanced Out-of-Band Rejection,” (to be published).
44. L. A. Coldren and R. L. Rosenberg, “SAW Resonator Filter Overview: Design and Performance Tradeoffs,” 1978 IEEE Ultrasonics Symp. Proc., 78 CH 1344–1 SU, pp. 422–32.
45. J. S. Palfreeman, M. Redwood, F. W. Smith, and F. Mitchell, U.S. Patent No. 4, 065, 735.
46. R. F. Milson and M. Redwood, “Interdigital Piezoelectric Rayleigh-Wave Transducer: An Improved Equivalent Circuit,” Electron Lett., Vol. 7, pp. 217–8, May, 1971.
47. L. A. Coldren, (unpublished).
48. L. A. Coldren, “Coupled Slot Waveguide SAW Resonators,” Electron. Lett., Vol. 13, pp. 559–51, September 15, 1977.
49. W. H. Haydl, B. Dischler, P. Hiesinger, “Multimode SAW Resonators-A Method to Study the Optimum Resonator Design,” IEEE 1976 Ultrasonics Symp., 76 CH 1120-5SU, pp. 287–96.
50. C. A. Adams and J. A. Kusters, “Deeply Etched SAW Resonators,” Proc. 31st Annual Symp. on Frequency Control, pp. 246 -50.
51. R. D. Fildes and B. J. Hunsinger, “Application of Unidirectional Transducers to Resonator Cavities,” 1976 IEEE Ultrasonics Symposium Proc., 76 CH 1120-5SU, pp. 303–5.
52. K. Yamanouchi, F. M. Nyffeler, and K. Shibayama, “Low Insertion Loss Acoustic Surface Wave Filter Using Group-Type Unidirectional Interdigital Transducer,” 1975 IEEE Ultrasonics Symposium Proc., 75 CHO 994-4SU, pp. 317–21.
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54. R. S. Krimholtz, G. L. Matthaei, and B. E. Hoiem, “Acoustic-Surface-Wave Interdigital Hybrid-Junction Transducers,” IEEE Trans. Sonics Ultrason., Vol. SU-21, pp. 23–32, January, 1974.
55. R. C. Rosenfeld, C. S. Hartmann, and R. B. Brown, “Low-Loss Unidirectional Acoustic Surface Wave Filters,” Proc. 28th Annual Symp. on Frequency Control 1974, Electronic Industries Assn., Wash., D.C., pp. 299–303.
56. R. L. Rosenberg, (unpublished).
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58. T. W. Bristol, W. R. Jones, P. B. Snow, and W. R. Smith, “Applications of Double Electrodes in Acoustic Surface Wave Device Design,” 1972 IEEE Ultrasonics Symp. Proc., CHO 708-8SU, pp. 343–5.
59. W. J. Tanski and H. van de Vaart, “The Design of SAW Resonators on Quartz with Emphasis on Two-Ports,” 1976 IEEE Ultrasonics Symposium Proc., 76 CH 1120-5SU, pp. 260–65.
60. C. Dunnrowicz, F. Sandy, and T. Parker, “Reflection of Surface Waves from Periodic Discontinuities,” 1976 Ultrasonics Symp. Proc., 76 CH 1120-5SU, pp. 386–90.
61. R. C. M. Li, “310-MHz SAW Resonator with Q at the Material Limit,” Appl. Phys. Lett. 31, pp. 407–9, 1977.
62. W. J. Tanski, “Developments in Resonators on Quartz,” 1977 Ultrasonics Symp. Proc., 77 CH 1264-1SU, pp. 900-904A.