Stability predictions for higher-order Band-Pass Σ-Δ modulators for dual sinusoidal inputs

The stability boundaries of higher-order Band-Pass (BP) Σ-Δ modulators for dual sinusoidal inputs based on a combination of the Describing Function (DF) method and the quasi-linear modeling of the quantizer are determined in this paper. 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 eighth- and tenth-order Type-II-Chebyshev-based BP Σ-Δ modulators for different stop-band attenuations and bandwidths are established. The theoretical results are shown to be in good agreement with the simulation results for different input amplitudes and modulator orders. The proposed mathematical models of the quantizer will immensely help in speeding up the design of higher order BP Σ-Δ modulators.