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 modeling. In this paper, a quasi-linear model for Δ-Σ modulators with nonlinear feedback control analysis is presented that accurately predicts stability of single-loop 1-bit higher-order Δ-Σ modulators for multiple sinusoids. Theoretical values are shown to match closely with simulation results. The results of this paper would enable optimization of the design 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.