Nonlinear-Stability Analysis of Higher Order $\Delta$ – $\Sigma$ Modulators for DC and S

The present work that exists on predicting the stability of Delta-Sigma modulators is confined to DC input signals and unity quantizer gains. This poses a limitation for numerous Delta-Sigma 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 Delta-Sigma 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 Delta-Sigma 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.