Fast detection of instability in sigma-delta modulators based on unstable embedded limit cycles

As a sequel to a previous study (Wong and Ng) on the nonlinear dynamical behavior of low-pass, high-order (order > 2), single-bit ΣΔ modulators with distinct unit-circle noise transfer function zeros, this paper proposes a novel scheme for the fast detection of unstable operation in these modulators under general time-varying input. The scheme is based on the variation of unstable embedded limit-cycle fixed points (which form the bounds beyond which the modulator becomes unstable) versus modulator input amplitude. Deployment of the detection scheme requires simple analog components with possible simplification. The effectiveness of the scheme is demonstrated with numerical examples.