Invariant sets for general second-order low-pass delta-sigma modulators with DC inputs

An invariant set, S, is a set of points in state space which has the property that all trajectories emanating from points in S remain in S. Such sets are useful in the context of delta-sigma modulation as they yield rigorous theoretical bounds on the state variables. This paper describes analytic and algorithmic methods for finding invariant sets of second-order delta-sigma modulators with DC inputs. The noise transfer functions of the modulators studied have two zeros near z=1 and arbitrary poles. The state-variable bounds which result are quite tight, with the algorithmic method providing the tightest bounds.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>