Nonlinear Model-Based Approach for Accurate Stability Prediction of One-Bit Higher-Order Delta-Sigma (Δ-Σ)Modulators

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. In this paper, a quasi-linear model for Δ-Σ modulators with nonlinear feedback control analysis is presented that accurately predicts the stability of higher-order single-loop 1-bit Δ-Σ modulators for various types of input signals such as single-sinusoids, dual-sinusoids, multiple-sinusoids and Gaussian. Theoretical values are shown to match closely with simulation results. The results of this paper would significantly speed up the design and evaluation of higher-order single-loop 1-bit Δ-Σ modulators for various applications including those that may require multiple-sinusoidal inputs or any general input composed of a finite number of sinusoidal components, circumventing the need to perform detailed time-consuming simulations to quantify stability limits. By using the proposed method, the difference between the predicted and the actual stable amplitude limits results in an error of less than 1 dB in the in-band Signal-to-Noise Ratio (SNR) for 3rd- and higher-order Δ-Σ modulators for single-sinusoidal inputs. For single-, dual-, multiple-sinusoidal and Gaussian inputs the error is less than 2 dB for the 5th-order and reduces to less than 1 dB for 6th- and higher-order Δ-Σ modulators.