Maximum Sequence Length MASH Digital Delta–Sigma Modulators

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^l 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.