Maximum Sequence Length MASH Digital Delta–Sigma Modulators

Abstract

This paper presents a modified structure for the first-order digital delta-sigma modulator (DDSM) which yields the maximum sequence length (N) for all constant digital inputs and for all initial conditions. Using this structure, MultistAge noise-SHaping (MASH) DDSMs are developed which, for a constant input, always have a sequence length of N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sup> regardless of the initial conditions and input value, where N is the sequence length of each stage and l is the number of the first-order stages used in the MASH. The performance is confirmed mathematically, by simulation, and experimentally.