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Stability Analysis of ΔΣ Modulators Using Wavelets

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Abstract

A new method is presented to predict the occurrence of unstable behavior as a function of the input amplitude in Delta-Sigma modulators using wavelets. By careful analysis it is shown that popular global analysis methods like Fourier transformation are useless in predicting unstable behavior in Delta-Sigma modulators. This necessitates the use of more time-localized analysis methods, such as wavelets. Using wavelets it is possible to calculate a number of open loop gain factors at different frequencies. These gain factors can then be used to construct a Nyquist plot, that can be used to predict whether the system is stable or not. Since only a small number of data points need to be calculated, this method is much faster than the traditional approach of long transient simulations, with only a very small error. The method works for both single-bit and multi-bit topologies and for ideal as well as non-ideal structures as is illustrated by the experimental results.

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  1. K.U. Leuven ESAT-MICAS, Kasteelpark Arenberg 10, 3001, Leuven, Belgium

    Martin Vogels & Georges Gielen

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  1. Martin Vogels
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  2. Georges Gielen
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Vogels, M., Gielen, G. Stability Analysis of ΔΣ Modulators Using Wavelets. Analog Integrated Circuits and Signal Processing 41, 279–291 (2004). https://doi.org/10.1023/B:ALOG.0000041642.88586.ad

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  • DOI: https://doi.org/10.1023/B:ALOG.0000041642.88586.ad

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