Search

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 (\Delta-\Sigma) modulators. Analytical expressions using the nonlinear gains from the concept of modified nonlinearity in control theory are incorporated into the mathematical model of multibit \Delta-\Sigma 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 \Delta-\Sigma 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. [ABSTRACT FROM PUBLISHER]

The current approaches on predicting the stability of delta–sigma ( \Delta–\Sigma) modulators are mostly confined to dc inputs. This poses limitations as practical applications of \Delta–\Sigma modulators involve a wide range of signals other than dc. In this paper, a quasi-linear model for \Delta–\Sigma modulators with nonlinear feedback control analysis is presented, which accurately predicts the stability of higher-order single-loop 1-bit \Delta–\Sigma 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 \Delta–\Sigma 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 \Delta–\Sigma 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 \Delta–\Sigma modulators. [ABSTRACT FROM PUBLISHER]

The present work that exists on predicting the stability of Δ-Σ modulators is confined to DC input signals and unity quantizer gains. This poses a limitation for numerous Δ-Σ modulator applications. The proposed research work gives the stability curves for DC, sine, and dual sinusoidal inputs for any value of the quantizer gain. The maximum stable input limits for third-, fourth-, and fifth-order Chebyshev-Type-II-based Δ-Σ modulators are established using the describing-function method for DC and sinusoidal inputs. Closed-form mathematical expressions for the gains of the quantizer for higher order Δ-Σ modulators whose inputs are two concurrent sinusoids are derived from first principles. The derived stability curves are shown to agree reasonably well with the simulation results for different types of input signals and amplitudes. [ABSTRACT FROM AUTHOR]