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Stability Analysis of Continuous Time Sigma Delta Modulators

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Progress in Systems Engineering

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 366))

Abstract

Several methods have been developed for predicting the stability of continuous time sigma delta modulators (CT ΣΔMs). In this paper, an analytical root locus method is used to determine the stability criteria for CT ΣΔMs that include exponential functions in their signal transfer functions and noise transfer functions. This method can be used to determine the minimum quantizer gains that keep a CT ΣΔM stable. Using the minimum quantizer gains, a CT ΣΔM’s maximum input amplitude that guarantees stability can be determined.

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References

  1. J. A. Cherry and W. M. Snelgrove.: Continuous-Time Delta-Sigma Modulators for High Speed A/D Conversion Theory, Practice and Fundamental Performance Limits: Kluwer Academic, New York, NY, USA (2002)

    Google Scholar 

  2. S. H. Ardalan, and J.J. Paulos.: An analysis of non-linear behaviour in Σ-Δ modulators. In: IEEE Trans. on Circuits and Syst., vol. CAS-34, no. 6, pp.1157-1162 (1987)

    Google Scholar 

  3. N. Wong, and N.G. Tung-Sang.: DC stability analysis of higher-order, lowpass sigma-delta modulators with distinct unit circle NTF zeroes. In: IEEE Trans. on Circuits & Syst.-II, vol. 50, issue 1, pp. 12-30 (2003)

    Google Scholar 

  4. J. Zhang, P.V. Brennan, D. Juang, D, E. Vinogradova, and P.D. Smith.: Stable analysis of a sigma-delta modulator. In: Proc. IEEE Int. Symp. Circuits Syst., vol.1, pp.1-961-1-964 (2003)

    Google Scholar 

  5. P, Steiner, and W. Yang.: Stability analysis of the second-order sigma-delta modulator. In: Proc. IEEE Int. Symp. Circuits Syst., vol. 5, pp. 365-368 (1994)

    Google Scholar 

  6. J. Zhang, P.V. Brennan, D. Juang, E. Vinogradova, and P.D. Smith.: Stable boundaries of a 2nd-order sigma-delta modulator. In: Proc. South. Symp.Mixed Signal Design (2003)

    Google Scholar 

  7. N. A. Fraser, and B. Nowrouzian.: A novel technique to estimate the statistical properties of sigma-delta A/D converters for the investigation of DC stability. In: Proc. IEEE Int. Symp. Circuits Syst., vol.3, pp.111-289-111-292 (2002)

    Google Scholar 

  8. D. Reefman, J.D. Reiss, E. Janssen, and M.B. Sandler.: Description of limit cycles in sigma-delta modulators. In: IEEE Trans. on Circuits and Syst-I., vol. 52, issue 6, pp.1211 – 1223 (2005)

    Google Scholar 

  9. S. Hein, and A. Zakhor.: On the stability of sigma-delta modulators. In: IEEE Trans. on Signal Processing, vol. 41, no.7, pp. 2322-2348 (1993)

    Google Scholar 

  10. 10 R. Schreier and W. M. Snelgrove.: Bandpass Sigma-Delta modulator. In: Electronics letters, vol. 25, no. 23, pp. 1560-1561 (1989)

    Google Scholar 

  11. Lars Risbo.: FPGA Based 32 Times Oversampling 8th-order Sigma-Delta Audio DAC. In: Proc. 96th AES Convention, Preprint # 3808 (1994)

    Google Scholar 

  12. W. L. Lee and C. G. Sodini.: A topology for higher interpolative coders. In: Proceedings of ISCAS, pp. 459-462 (1987)

    Google Scholar 

  13. R. Schreier and G.C. Temes.: Understanding delta sigma data converters: Wiley-IEEE express (2004)

    Google Scholar 

  14. John, B.: Essentials of control techniques and theory, CRC pressInc (2009)

    Google Scholar 

  15. Bendrukov,G.A, Teodorchik,K,F: The analytic theory of constructing root loci. In: automation and remote control, vol. 20, pp. 340-344 (1959)

    Google Scholar 

  16. Cogan,B.:Use of the analytic method and computer algebra to plot root loci. In: International journal of electrical engineering education. vol. 35, pp. 350-356 (1998)

    Google Scholar 

  17. D’azzo, J.J, Houpis, C.H.: Linear control system analysis and design conventional and modern, Mc Graw Hill, New York (1988)

    Google Scholar 

  18. Ogata, K.: Modern control engineering, Prentice Hall (2002)

    Google Scholar 

  19. Palm,W.J.:Control system engineering, John Wiley & Sons (1986)

    Google Scholar 

  20. Cogan.B, Paor.A.M.: Analytic root locus and LAMBERT W function in control of a process with time delay. In: Journal of electrical engineering, vol. 62, pp. 327-334 (2011)

    Google Scholar 

  21. K.Kang, P.Stubberud: A comparison of continuous time sigma delta modulator simulation methods. In: IEEE International Midwest Symposium on Circuits and Systems (2014)

    Google Scholar 

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Correspondence to Kyung Kang .

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Kang, K., Stubberud, P. (2015). Stability Analysis of Continuous Time Sigma Delta Modulators. In: Selvaraj, H., Zydek, D., Chmaj, G. (eds) Progress in Systems Engineering. Advances in Intelligent Systems and Computing, vol 366. Springer, Cham. https://doi.org/10.1007/978-3-319-08422-0_71

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  • DOI: https://doi.org/10.1007/978-3-319-08422-0_71

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08421-3

  • Online ISBN: 978-3-319-08422-0

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