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Using a Genetic Algorithm to Optimize Capacitance Ratio Approximations in SC Filters

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Abstract

Accurate capacitance matching is one of the main design issues in switched-capacitor (SC) filters. Using identical unit capacitors in parallel to implement each filter capacitor, combined with a careful layout design, can provide an accuracy of 0.1% in the filter coefficients. The disadvantage of this technique is the fact that it can be directly applied only if the coefficients can be expressed as ratios of integer numbers. As a result, coefficient approximations are required, leading to frequency response errors. In this paper, a genetic algorithm (GA) is used to find the optimum capacitance ratio approximations by rational numbers that minimize the total number of unit capacitors for a given error tolerance in the frequency response. Design examples in 0.35 μm CMOS are presented and simulated to illustrate the proposed approach and verify its effectiveness.

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References

  1. F. Brglez, Digital filter design with short word-length coefficients. IEEE Trans. Circuits Syst. CAS-25(12), 1044–1050 (1978)

    Article  Google Scholar 

  2. O. Choksi, L.R. Carley, Analysis of switched-capacitor common-mode feedback circuit. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 50(12), 906–917 (2003)

    Article  Google Scholar 

  3. A.C.M. de Queiroz, P.M. Pinheiro, Exact design of switched-current ladder filters, in Proc. IEEE International Symposium on Circuits and Systems (ISCAS’92), San Diego, CA, USA, May 1992, pp. 855–858

  4. A.C.M. de Queiroz, P.M. Pinheiro, Switched-current ladder band-pass filters, in IEEE International Symposium on Circuits and Systems (ISCAS’94), vol. 5, 30 May–02 June 1994, pp. 309–312

  5. L. Dolivka, J. Hospodka, Switched-capacitor filter optimization with respect to switch on-state resistance and features of real operational amplifiers. Radioengineering 16(2), 34–39 (2007)

    Google Scholar 

  6. G. Fischer, High q sc biquad with a minimum capacitor spread. Electron. Lett. 18, 1087–1089 (1982)

    Article  Google Scholar 

  7. P.E. Fleischer, K.R. Laker, A family of active switched capacitor biquad building blocks. Bell Syst. Technol. J. 58, 2235–2269 (1979)

    MATH  Google Scholar 

  8. S. Fushimi, K. Nakayama, A discrete optimization method of switched capacitor filters. Electron. Commun. Jpn. Part I, Commun. 68(2), 40–49 (1985)

    Article  Google Scholar 

  9. D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, 1989)

    MATH  Google Scholar 

  10. R. Gregorian, G.C. Temes, Analog MOS Integrated Circuits for Signal Processing (Wiley, New York, 1986)

    Google Scholar 

  11. R. Gregorian, K.W. Martin, G.C. Themes, Switched-capacitor circuit design, in Proc. IEEE, vol. 71 (1983), pp. 941–966

  12. M. Haseyama, D. Matsuura, A filter coefficient quantization method with genetic algorithm, including simulated annealing. IEEE Signal Process. Lett. 13(4), 189–192 (2006)

    Article  Google Scholar 

  13. R.L. Haupt, S.E. Haupt, Practical Genetic Algorithms, 2nd edn. (Wiley-Interscience, New York, 2004)

    MATH  Google Scholar 

  14. Q. Huang, W. Sansen, Design techniques for improved capacitor area efficiency in switched-capacitor biquads. IEEE Trans. Circuits Syst. CAS-34(12), 1590–1599 (1987)

    Article  Google Scholar 

  15. D. Johns, K. Martin, Analog Integrated Circuit Design (Wiley, New York, 1997)

    Google Scholar 

  16. W. Ki, G. Temes, Optimal capacitance assignment of switched-capacitor biquads. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 42(6), 334–342 (1995)

    Article  Google Scholar 

  17. G. Kjellström, L. Taxén, P.O. Lindberg, Discrete optimization of digital filters using Gaussian adaptation and quadratic function minimization. IEEE Trans. Circuits Syst. CAS-34(10), 1238–1242 (1987)

    Article  Google Scholar 

  18. D.M. Kodek, Design of optimal finite wordlength fir digital filters using linear programming techniques. IEEE Trans. Acoust. Speech Signal Process. 28(3), 304–308 (1980)

    Article  MathSciNet  Google Scholar 

  19. M.S. Lee, G.C. Temes, C. Chang, M.B. Ghaderi, Bilinear switched-capacitor ladder filters. IEEE Trans. Circuits Syst. CAS-28(8), 811–822 (1981)

    Google Scholar 

  20. Y.C. Lim, S.R. Parker, A.G. Constantinides, Finite word length fir filter design using integer programming over a discrete coefficient space. IEEE Trans. Acoust. Speech Signal Process. 30(4), 661–664 (1982)

    Article  Google Scholar 

  21. K. Martin, Improved circuits for the realization of switched-capacitor filters. IEEE Trans. Circuits Syst. CAS-27(4), 237–244 (1980)

    Article  Google Scholar 

  22. K. Martin, S. Sedra, Exact design of switched-capacitor bandpass filter using coupled biquad structures. IEEE Trans. Circuits Syst. CAS-27(6), 475–496 (1980)

    Google Scholar 

  23. J.L. McCreary, Matching properties and voltage and temperature dependence of mos capacitors. IEEE J. Solid-State Circuits SC-16(6), 608–616 (1981)

    Article  Google Scholar 

  24. M.J. McNutt, S. LeMarquis, J.L. Dunkley, Systematic capacitance matching errors and corrective layout procedures. IEEE J. Solid-State Circuits 29(5), 611–616 (1994)

    Article  Google Scholar 

  25. M. Mitchell, An Introduction to Genetic Algorithms (Complex Adaptive Systems) (MIT Press, Cambridge, 1998)

    Google Scholar 

  26. K. Nakayama, Y. Sato, Y. Kuraishi, Design techniques for switched-capacitor adaptive line equalizer. IEEE Trans. Circuits Syst. CAS-32(8), 759–766 (1985)

    Article  Google Scholar 

  27. J. Porte, A discrete optimization method of cascaded switched capacitor filters. Ann. Télécommun. 47(3–4), 153–158 (1992)

    Google Scholar 

  28. C. Saint, J. Saint, IC Mask Design: Essential Layout Techniques (McGraw-Hill, New York, 2002)

    Google Scholar 

  29. R. Schaumann, M.E.V. Valkenburg, Design of Analog Filters, 2nd edn. (Oxford University Press, Oxford, 2001)

    Google Scholar 

  30. R. Singh, A.B. Bhattacharyya, Matching properties of linear mos capacitors. IEEE Trans. Circuits Syst. 36(3), 465–467 (1989)

    Article  Google Scholar 

  31. C.F.T. Soares, A. Petraglia, An approximation algorithm to improve capacitance matching in the design of sc filters. Analog Integr. Circuits Signal Process. 57(1–2), 49–56 (2008)

    Article  Google Scholar 

  32. K.L. Su, Analog Filters, 2nd edn. (Springer, Berlin, 2006)

    Google Scholar 

  33. H. Tang, A systematic design flow for optimal capacitance assignment in switched-capacitor biquads. IEEE Trans. Circuits Syst. I, Regul. Pap. 55(7), 2076–2086 (2008)

    Article  Google Scholar 

  34. Y.P. Tsividis, Integrated continuous-time filter design—an overview. IEEE J. Solid-State Circuits 29(3), 166–176 (1994)

    Article  Google Scholar 

  35. Y. Tsividis, Mixed Analog–Digital VLSI Devices and Technology: An Introduction (McGraw-Hill, New York, 1995)

    Google Scholar 

  36. M.E.V. Valkenburg, Introduction to Modern Network Synthesis (Wiley, New York, 1960)

    Google Scholar 

  37. J. Yli-Kaakinen, T. Saramaki, A systematic algorithm for the design of lattice wave digital filters with short-coefficient wordlength. IEEE Trans. Circuits Syst. I, Regul. Pap. 54(8), 1838–1851 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. Program of Electrical Engineering COPPE/UFRJ, Federal University of Rio de Janeiro, Rio de Janeiro, RJ, Brazil

    Carlos F. T. Soares, Antonio C. de Mesquita Filho & Antonio Petraglia

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  1. Carlos F. T. Soares
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  2. Antonio C. de Mesquita Filho
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  3. Antonio Petraglia
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Correspondence to Antonio Petraglia.

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Soares, C.F.T., de Mesquita Filho, A.C. & Petraglia, A. Using a Genetic Algorithm to Optimize Capacitance Ratio Approximations in SC Filters. Circuits Syst Signal Process 29, 687–707 (2010). https://doi.org/10.1007/s00034-010-9176-6

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  • DOI: https://doi.org/10.1007/s00034-010-9176-6

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