Stability analysis of multiple-feedback oversampled Σ-Δ A/D converter configurations

This paper is concerned with the estimation of the maximum DC input signal level for five different practical feedforward and multiple-feedback oversampled Σ-Δ A/D converters. This technique is based on replacing the constituent quantizer by a uniformly distributed additive white noise source and a variable gain element, assuming the following conditions are satisfied: a) the quantizer input signal and quantization error are uncorrelated, b) the quantizer input signal is Gaussian distributed, and c) the quantization noise is white. It is shown that the statistical estimation technique is quite accurate for Σ-Δ A/D converters with small noise power gains, but that the accuracy tends to decrease for A/D converters having larger noise power gains. It is further shown that this reduction in accuracy stems from the fact that the assumptions listed under a), b), and c) are not exactly satisfied. It is finally shown that the probability density function of the input signal to the quantizer may be modelled more accurately using the Gram-Charlier series