Models of round-off noise in second-order sigma-delta modulators

Current theories of quantisation noise are approximate for second-order sigma-delta modulators which contain a one-bit A/D convertor. A method is suggested which gives a better approximation, based on the behaviour of the system in the absence of an input. In discrete variable systems, the output can follow one of a set of closed cycles, and the suggestion is that the average behaviour of the set of closed cycles in the required approximation. A two-dimensional invariant form is found for continuous variable systems, which gives the corresponding approximation.