Closed form solution of granular quantization error for multi-loop sigma-delta modulator configurations

This paper undertakes an investigation of the closed-form solution of the quantization error for the conventional multi-loop sigma-delta (Σ-Δ) modulator configurations. The underlying assumption in this investigation is that the constituent coarse quantizer operates in its no-overload region. The required overload-free quantizer operation is achieved by placing an appropriate bound on the Σ-Δ modulator input signal. The main results are illustrated through their application to the determination of the quantization error for a number of multi-loop Σ-Δ modulator configurations for both DC as well as AC input signals