An approach for stability analysis of a single-bit high-order digital sigma-delta modulator

In this work we considered the stability of a single-bit high-order sigma-delta modulator under dc input. A new approach for stability analysis is proposed. A nonlinear circle map is suggested to model the dynamics of the modulator. An analogy between the dynamics of the sigma-delta modulator and the sinusoidal digital phase-locked loop (DPLL) is studied and an approximate fixed point solution is presented with stability criteria. Suggestions for designing stabilized high-order systems are presented.