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IEEE Transactions on Microwave Theory and Techniques
Volume 48 Number 9, September 2000

Table of Contents for this issue

Complete paper in PDF format

Synthesis of Cross-Coupled Resonator Filters Using an Analytical Gradient-Based Optimization Technique

Smain Amari Member, IEEE

Page 1559.

Abstract:

We propose a general approach to the synthesis of cross-coupled resonator filters using an analytical gradient-based optimization technique. The gradient of the cost function with respect to changes in the coupling elements between the resonators is determined analytically. The topology of the structure is strictly enforced at each step in the optimization thereby eliminating the need for similarity transformations of the coupling matrix. For the calculation of group delays, a simple formula is presented in terms of the coupling matrix. A simple recursion relation for the computation of the generalized Chebychev filtering functions is derived. Numerical results demonstrating the excellent performance of the approach are presented.

References

  1. A. Atia and Williams, "New type of waveguide bandpass filters for satellite transponders", COMSAT Tech. Rev., vol. 1, no. 1, pp.  21-43, 1971.
  2. A. E. Atia and A. E. Williams, "Narrow-bandpass waveguide filters", IEEE Trans. Microwave Theory Tech., vol. MTT-20, pp.  258 -265, Apr.  1972.
  3. A. E. Atia, A. E. Williams and R. W. Newcomb, "Narrow-band multiple-coupled cavity synthesis", IEEE Trans. Circuit Syst., vol. CAS-21, pp.  649-655, Sept.   1974.
  4. R. M. Kurzrok, "General three-resonator filters in waveguides", IEEE Trans. Microwave Theory Tech., vol. MTT-14, pp.  46-47, Jan.  1966.
  5. R. M. Kurzrok, "General four-resonator filters at microwave frequencies", IEEE Trans. Microwave Theory Tech., vol. MTT-14, pp.  295-296, June  1966.
  6. A. E. Williams, "A four-cavity ellpitic waveguide filter", IEEE Trans. Microwave Theory Tech., vol. MTT-18, pp.  1109-1114, Dec.  1970.
  7. R. J. Cameron, "Fast generation of Chebychev filter prototypes with asymmetrically-prescribed transmission zeros", ESA J., vol. 6, pp.  83-95, 1982.
  8. R. J. Cameron, "General prototype network synthesis methods for microwave filters", ESA J., vol. 6, pp.  193-206, 1982.
  9. R. J. Cameron and J. D. Rhodes, "Asymmetric realizations of dual-mode bandpass filters", IEEE Trans. Microwave Theory Tech., vol. MTT-29, pp.  51-58, Jan.  1981.
  10. D. Chambers and J. D. Rhodes, "A low pass prototype allowing the placing of integrated poles at real frequencies", IEEE Trans. Microwave Theory Tech., vol. MTT-31, pp.  40-45, Jan.  1983.
  11. J. D. Rhodes and S. A. Alseyab, "The generalized Chebychev low-pass prototype filter", Circuit Theory Applicat., vol. 8, pp.  113-125, 1980.
  12. R. Levy, "Direct synthesis of cascaded quadruplet (CQ) filters", IEEE Trans. Microwave Theory Tech., vol. 43, pp.  2940-2944, Dec.  1995.
  13. R. Hershtig, R. Levy and K. Zaki, "Synthesis and design of cascated trisection (CT) dielectric resonator filters", in Proc. European Microwave Conf., 1997, pp.  784-791. 
  14. R. Levy, "Filters with single transmission zeros at real or imaginary frequencies", IEEE Trans. Microwave Theory Tech., vol. MTT-24, pp.  172-181, April  1976.
  15. G. Pfitzenmaier, "Synthesis and realization of narrow-band canonical microwave bandpass filters exhibiting linear phase and transmission zeros", IEEE Trans. Microwave Theory Tech., vol. MTT-30, pp.  1300-1311, Sep.  1982.
  16. "IEEE Trans. Microwave Theory Tech. (Special Issue)", vol. MTT-30, Sept.  1982.
  17. W. A. Atia, K. A. Zaki and A. E. Atia, "Synthesis of general topology multiple coupled resonator filters by optimization", IEEE Microwave Theory Tech. Dig., pp.  821-824, 1998.
  18. R. J. Cameron, "General coupling matrix synthesis methods for Chebychev filtering functions", IEEE Trans. Microwave Theory Tech., vol. 47, pp.  433-442, April  1999.
  19. L. O. Chua and P.-M. Lin, Computer-Aided Analysis of Electronic Circuits, Englewood Cliffs, NJ: Prentice-Hall, 1975.
  20. H. J. Orchard, "Filter design by iterated analysis", IEEE Trans. Circuits Syst., vol. 32, pp.  1089-1096, Nov.  1985 .
  21. W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Wetterling, Numerical Recipes, New York, NY: Cambridge Univ. Press, 1986.
  22. K. C. Gupta, R. Garg and R. Chadha, Computer Aided Design of Microwave Circuits, Norwood, MA: Artech, 1981.
  23. K. A. Zaki and A. E. Atia, "Sensitivity analysis of multi-coupled cavity filters", in IEEE Int. Symp. Circuits and Systems, May 1978, pp.  790-793. 
  24. S. Amari, P. Harscher, R. Vahldieck and J. Bornemann, "Novel analytic gradient evaluation techniques for optimization of microwave structures", Microwave Theory Tech. Dig., pp.  31-34, 1999 .
  25. G. L. Matthaei, L. Young and E. M. T. Jones, Microwave Filters, Impedance Matching Networks and Coupling Structures,: Artech, 1980.