Mathematical Analysis of a Prime Modulus Quantizer MASH Digital Delta–Sigma Modulator

A MASH digital delta-sigma modulator (DDSM) is analyzed mathematically. It incorporates first-order error feedback modulators (EFM) which include prime modulus quantizers to guarantee a minimum sequence length M. The purpose of this analysis is to calculate the exact sequence length of the aforementioned MASH DDSM. We show that the sequence length for an lth-order member of this modulator family M is for all constant inputs, and for all initial conditions, where M is the sequence length of the constituent first-order prime modulus quantizer EFMs.