Nonlinear Model-Based Approach for Accurate Stability Prediction of One-Bit Higher-Order Delta–Sigma Modulators

Abstract

The current approaches on predicting the 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, which 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 for the third-order and higher-order Δ-Σ modulators for single-sinusoidal inputs. For single-sinusoidal, dual-sinusoidal, multiple-sinusoidal, and Gaussian inputs, the error is less than 2 dB for the fifth-order modulator and reduces to less than 1 dB for the sixth-order and higher-order Δ-Σ modulators.