Accurate stability prediction of one-bit higher-order delta-sigma modulators for multiple-sinusoidal inputs

The present approaches on predicting stability of delta-sigma (Δ-Σ) modulators are mostly confined to DC inputs. This poses limitations as practical applications of Δ-Σ modulators involve a wide range of signals other than DC such as multiple-sinusoidal inputs for speech modelling. In this study, a quasi-linear model for Δ-Σ modulators with non-linear feedback control analysis is presented that accurately predicts stability of single-loop one-bit higher-order Δ-Σ modulators for multiple sinusoids. Theoretical values are shown to match closely with the simulation results. The results of this study would significantly speed up the design and evaluation of higher-order single-loop Δ-Σ modulators with increased dynamic ranges for various applications that require multiple-sinusoidal inputs or any general input composed of a finite number of sinusoidal components.