Abstract
In this chapter we present an unified approach for study the stability and validation of potential limit cycles of one bit high order Sigma-Delta modulators. The approach is general because it uses the general form of a Sigma-Delta modulator. It is based on a parallel decomposition of the modulator and a direct nonlinear systems analysis. In this representation, the general N-th order modulator is transformed into a decomposition of low order, generally complex modulators, which interact only through the quantizer function. The developed conditions for stability and for validation of potential limit cycles are very easy for implementation and this procedure is very fast.
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References
Candy, J.C., Temes, G.C.: Oversampling Delta-Sigma Data Converters. IEEE Press, New York (1992)
Norsworthy, S.R., Schreier, R., Temes, G.C.: Delta-Sigma Data Converters. IEEE Press, New York (1997)
Gray, R.M.: Oversampled sigma-delta modulation. IEEE Trans. Commun. 35, 481–489 (1987)
Feely, O., Chua, L.O.: The effect of integrator leak in Sigma-delta modulation. IEEE Trans. Circuits and Systems 38, 1293–1305 (1991)
Feely, O., Chua, L.O.: Nonlinear dynamics of a class of analog-to-digital converters. Int. J. of Bifurcation and Chaos 2, 325–340 (1992)
Feely, O.: A tutorial introduction to non-linear dynamics and chaos and their application to sigma-delta modulators. Int. J. Circuit Theory and Applications 25, 347–367 (1997)
Steiner, P., Yang, W.: A framework for analysis of high-order sigma-delta modulators. IEEE Transactions on Circuits and Systems II: CAS II 44, 1–10 (1997)
Steiner, P., Yang, W.: Stability of high order sigma-delta modulators. In: International Symposium on Circuits and Systems, ISCAS 1996, vol. 3, pp. 52–55 (1996)
Mladenov, V., Hegt, H., Roermund, A.V.: Stability analysis of high order sigma-delta modulators. In: Proc. of the 15th European Conference on Circuit Theory and Design ECCTD 2001, pp. I-313 – I-316. Helsinki University of Technology, Finland (2001)
Mladenov, V., Hegt, H., van Roermund, A.: On the Stability of High Order Sigma-Delta Modulators. In: Proceedings of the 8th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2001, Malta, pp. 1383–1386 (2001)
Mladenov, V., Hegt, H., van Roermund, A.: On the Stability Analysis of High Order Sigma-Delta Modulators. An International Journal on Analog Integrated Circuits and Signal Processing 36(1-2), 47–55 (2003)
Mladenov, V., Hegt, H., van Roermund, A.: On the Stability Analysis of Sigma-Delta Modulators. In: Proceedings of the 16th European Conference on Circuit Theory and Design, ECCTD 2003, Cracow, Poland, September 1-4, pp. I-97– I-100 (2003)
Friedman, V.: The structure of the limit cycles in sigma delta modulation. IEEE Transactions on Communications 36, 972–979 (1988)
Mann, S., Taylor, D.: Limit cycle behavior in the double-loop bandpass sigma delta a/d converter. IEEE Transactions on Circuits and Systems-II 46, 1086–1089 (1999)
Hyun, D., Fischer, G.: Limit cycles and pattern noise in single-stage single-bit delta-sigma modulators. IEEE Trans. Circuits and Systems I 49, 646–656 (2002)
Reefman, D., Reiss, J., Janssen, E., Sandler, M.: Description of limit cycles in sigma delta modulators. IEEE Trans. on CAS 52(6), 1211–1223 (2005)
Reiss, J.D., Sandler, M.B.: Detection and removal of limit cycles in sigma delta modulators. IEEE Transactions on Circuits and Systems I: Regular Papers 55(10), 3119–3130 (2008)
Mladenov, V.: A Method for Searching the Limit Cycles of High Order Sigma-Delta Modulators. In: Proceedings of the 19th European Conference on Circuit Theory and Design, ECCTD 2009, Antalya, Turkey, August 23-27, pp. 543–546 (2009)
Mladenov, V.: A Method for Validation the Limit Cycles of High Order Sigma-Delta Modulators. In: Proceedings of the 3rd International Workshop on Nonlinear Dynamics and Synchjronization, INDS 2011, Klagenfurt, Austria, July 25-27, pp. 234–238 (2011)
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Mladenov, V. (2013). Stability Analysis and Limit Cycles of High Order Sigma-Delta Modulators. In: Kyamakya, K., Halang, W., Mathis, W., Chedjou, J., Li, Z. (eds) Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering. Studies in Computational Intelligence, vol 483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37781-5_19
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DOI: https://doi.org/10.1007/978-3-642-37781-5_19
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