Equivalent open-loop system for a general class of sigma-delta modulator configurations

This paper presents an equivalent open-loop system for the exact analysis and characterization of a general class of sigma-delta (Σ-Δ) modulator configurations. This open-loop system is based on the exploitation of the closed-form solution of the granular error (i.e. the error under no-overload operation) associated with the constituent coarse quantizer. The proposed open-loop system is subsequently applied to the determination of the signal-to-quantization noise ratio for the class of Σ-Δ modulator configurations under consideration. The results are illustrated through their application to a triple-loop Σ-Δ modulator for DC as well as AC input signals