Bounding the integrator outputs of second-order sigma-delta modulators

The development to date of the bounds for the outputs of the integrators of second-order sigma-delta modulators has relied on a mixture of theoretical analysis and extensive use of simulation. This paper presents a new approach that analyzes the behavior of such systems, and identifies the external boundaries of the trapping region for the outputs of the integrators. With this approach, it is possible to develop tight results for the standard second-order modulator with constant input, without the need for simulation. This approach is flexible, and can be adapted for other second-order architectures, and gives strong insight into the behavior of these systems.