Magnitude-only modeling for sigma-delta modulator characterization

Abstract

Abstract Sigma delta modulators importance is unambiguous in many applications. Since they are inherently non-linear systems, they are often approximately linearized to allow for the derivation of their theoretical Noise-Transfer-Function (NTF). SDM NTF is used for both analyzing and synthesizing them. Although linearization is the standard approach for its derivation, there do exist SDM architectures to which it cannot be applied. The aim of this paper is twofold: To provide a general framework for deriving the NTF for all SDM architectures, and, to use it to evaluate the accuracy of the standard theoretical NTF approximation for those SDM architectures accepting linearization. To this end, we introduce a new magnitude-only transfer-function modeling framework for SDM architectures, which is based on output noise spectrum and produces a stable LTI NTF approximation model. This framework is based on a phase reconstruction and a rational transfer-function fitting step, using the Vector Fitting algorithm. To show its applicability, we used it to derive NTF models for SDMs at system level and at RTL. Finally, the generality of our approach is demonstrated by deriving experimental NTF for a class of SDMs without standard linearized models.