Improved Direct Stability Analysis of High-Order Continuous-Time Sigma-Delta Modulators

Direct stability analysis for continuous-time (CT) sigma-delta modulators (SDM) in s-domain requires an accurate system model to ensure the reliability of the analysis. This paper presents an extended s-domain stability model for high-order single-bit CT SDMs including an improved quantizer model and an added delay element in the feedback path to represent the nonzero excess loop delay. An algorithm is also presented to generate the root-locus diagram of CT SDM systems with time delay elements. As an example stability of a class of third-order CT SDMs is analyzed and the stability boundary of the loop filter parameters is derived. Extensive time-domain simulations are conducted to verify the method