A Novel Statistical Technique for the Estimation of DC Stability in Higher-Order Σ-Δ A/D Converters

Abstract

The existing techniques available for the statistical estimation of the dc input signal stability in general-order Σ-Δ analog-to-digital (A/D) converters are based on the assumption that the constituent quantizer input signal has a Gaussian distribution. However, empirical investigations reveal that this assumption holds adequately true only for the special case of conventional first-order Σ-Δ A/D converters. This paper presents an alternative technique for the accurate estimation of the dc input signal stability for higher-order Σ-Δ A/D converters. This estimation technique is based on the practical assumption that the constituent quantizer operates in its overload-free region, permitting the characterization of the quantizer output signal digit-pattern for the determination of the statistical moments of the corresponding quantizer input signal. The resulting statistical moments are subsequently incorporated in a Gram-Charlier series for an accurate quasi-linear modeling of the quantizer. A typical application example is given to demonstrate the accuracy of the proposed statistical technique for predicting the existence of multiple regions of instability and stability in the Σ-Δ A/D converter operation, and particularly for predicting the point where the A/D converter operation becomes unstable.