On the stability of high order Sigma-Delta modulators

In this paper we present an approach for stability analysis of high order Sigma-Delta modulators. The approach is based on a parallel decomposition of the modulator. In this representation, the general N-th order modulator is transformed into decomposition of low order modulators, which interact only through the quantizer function. In the simplest case of the loop filter transfer function with real distinct poles, the low order modulators are N first order ones. The decomposition considered helps to extract the stability conditions of the N-th order modulator. They are determined by the stability conditions of each of the low order modulators but shifted with respect to the origin of the quantizer function, because of the influence of all other low order modulators. The approach is generalized for the case of repeated poles of the loop filter transfer function