Limit cycles in embedded high-order, lowpass sigma-delta modulators with distinct NTF zeros

In a related work by the authors, high-order sigma-delta (ΣΔ) modulators with distinct noise transfer function (NTF) zeros are decomposed into second-order and first-order subsystems, whose state-trajectories are then investigated by continuous-time embedding. This paper, based on the properties of these subsystems, furthers the study by introducing a scalable numerical method to locate the fixed-points on the generalized Poincare sections. A closed-form tangent linear manifold matrix for an arbitrary order modulator is derived, enabling the stability determination of the fixed-points and the accompanying limit cycles. Numerical examples show that the estimated DC input bound based on the boundary transition flow assumption cannot be relied on for modulators of order greater than four.