A Describing Function based method for predicting the stability of higher-order high-pass Σ-Δ modulators

This paper presents the stability analysis for higher-order single-loop high-pass Σ-Δ modulators based on a combination of the Describing Function (DF) method and the quasi-linear modeling of the quantizer. Closed form mathematical expressions are derived for the stability curves for different quantizer gain values. The stability prediction for the maximum stable input limits for third-, fourth-, and fifth-order Type-II-Chebyshev-based high-pass Σ-Δ modulators are established. The theoretical results are shown to be in good agreement with the simulation results for different sinusoidal input amplitudes. The proposed mathematical models of the quantizer will immensely help in speeding up the design of higher order high-pass Σ-Δ modulators.