STRUCTURE OF ROUND-OFF NOISE IN SINGLE-BIT 2ND-ORDER SIGMA-DELTA MODULATORS WITH ZERO INPUT

Single-bit sigma-delta modulators are used for A-D conversion in a wid e variety of systems. Analysis of first-order systems has made much pr ogress, but the analysis of second-order systems is conventionally bas ed on an approximate white-noise model of round-off noise. The paper a pplies a new method of analysing second-order systems. It shows that, with zero input, the behaviour for each sample is equivalent to a two- dimensional discontinuous mapping PHI. It derives an invariant form un der PHI and describes some of its properties. The motivation is the su ggestion that the invariant form is a useful approximation to the prob ability distribution of round-off noise.