A novel approach to bounding the integrator outputs of second order sigma-delta converters

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 uses a combination of geometrical techniques and the characterization of the trajectories of the system in state space. With this approach it is possible to develop flexible but 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