Stability Analysis of Incremental ΣΔ Modulators using Mixed-Logic Dynamical Systems and Optimal Control Theory

In this paper, we present a mixed-logic dynamical (MLD) system model that allows for an iron-clad prediction of the stability of Incremental Sigma Delta (I-ΣΔ) modulators. The model extends the mixed logic dynamical description of freely-running Sigma-Delta (ΣΔ) modulators with single-bit quantizers presented in [1] to the multibit case. Moreover, we use the derived model to compare I-ΣΔs with different loop filter orders and different number of quantizer levels concerning their stability.