Efficient analysis of the stability of sigma-delta modulators using wavelets

A new method is presented to efficiently estimate the stability boundary for sigma-delta modulators. Wavelet decomposition is used to cut up the input and output signals of the quantizer into different frequency portions. For the portion around the limit cycle an amplification factor and phase shift are calculated. This represents the transfer of the quantizer at that point. The so-formed linear system can then be analyzed using the phase margin. Only a small number of data points need to be evaluated making this method forty times faster than the traditional approach of long transient simulations, with only a very small error.

[1]  John J. Paulos,et al.  An analysis of nonlinear behavior in delta-sigma modulators , 1987 .

[2]  Randy K. Young.  Wavelet theory and its applications , 1993, The Kluwer international series in engineering and computer science.

[3]  Richard Schreier,et al.  An empirical study of high-order single-bit delta-sigma modulators , 1993 .

[4]  G. Zames,et al.  Dither in nonlinear systems , 1976 .

[5]  Rudy J. van de Plassche,et al.  New stability criteria for the design of low-pass sigma-delta modulators , 1997, ISLPED.

[6]  Amara Lynn Graps,et al.  An introduction to wavelets , 1995 .

[7]  Terri S. Fiez,et al.  Stability analysis of high-order delta-sigma modulation for ADC's , 1994 .

[8]  Michel Steyaert,et al.  Optimal parameters for single loop /spl Delta//spl Sigma/ modulators , 1997, Proceedings of 1997 IEEE International Symposium on Circuits and Systems. Circuits and Systems in the Information Age ISCAS '97.