Nonlinear Stability Prediction of Multibit Delta–Sigma Modulators for Sinusoidal Inputs

This paper proposes a novel algorithm that can be integrated with various design and evaluation tools, to more accurately and rapidly predict stability in multibit delta-sigma (Δ-Σ) modulators. Analytical expressions using the nonlinear gains from the concept of modified nonlinearity in control theory are incorporated into the mathematical model of multibit Δ-Σ modulators to predict the stable amplitude limits for sinusoidal input signals. The nonlinear gains lead to a set of equations, which can numerically estimate the quantizer gain as a function of the input sinusoidal signal amplitude. This method is shown to accurately predict the stable amplitude limits of sinusoids for second-sixth-order three- and five-level midtread quantizer-based Δ-Σ modulators. The algorithm is simple to apply and can be extended to midrise quantizers or to any number of quantizer levels. The only required input parameters for this algorithm are the number of quantizer levels and the coefficients of the noise transfer function.