Nonlinear dynamics of sigma-delta modulation

It is shown how a rigorous application of the theory of nonlinear dynamics can explain the behavior of the single-loop sigma-delta system in the presence of such common circuit nonidealities as integrator leak, integrator gain mismatch, and comparator offset with bilevel or multilevel quantization. The results provide circuit designers with qualitative insights into the behavior of these commonly used systems as well as quantitative information for use in system design. The extension of the map describing the leaky system into the parameter region p >1 is also examined, and the chaotic nature of the ensuing motion is discussed