Stability of single-stage single-bit ∑Δ modulator. (August 2021) - Khokhryakov, Evgeny I.
Abstract: A feedback loop of sigma-delta modulator (∑ΔM) is analysed, including the following parameters: operational amplifier gain factor, leakages of integrators, internal scale coefficients. The aspects of stability were presented for both chaotic and non-chaotic ∑ΔM mode. A criterion close to the Tsypkin absolute stability criterion was obtained for the chaotic mode. This criterion provides a system of inequalities of internal parameters for the ∑ΔM configuration. The coefficients down to the 5th order, satisfying the criterion, are given. A stability bound, according to which different configurations of the same order are compared to one another, appears as a useful innovation. The bound is also compared to a common non-invertible area. Based on the non-invertible area for non-chaotic case and ADC (analog-to-digital converter), the ranges were found for internal integrators and input, sufficient for smooth operation. In discrete-time systems, the role of necessary criterion for absolute stability in respect to both chaotic and non-chaotic cases is under discussion. Highlights: Absolute stability is inherent in chaotic systems. Integrators' scales and input constraints of non-chaotic ADC case are sufficient. Stability of chaotic DAC imposes constraints on the feedback loop configuration. Extension of stability bound helps in selecting configuration.