New stability criteria for the design of low-pass sigma-delta modulators

This paper describes a new model for the stability analysis of low-pass Sigma-Delta modulators (/spl Sigma//spl Delta/Ms) using the describing function method. The transfer of a single-bit quantizer is represented by a global signal gain and a phase uncertainty. This phase uncertainty arises from the limited accuracy in time with which the quantizer can detect the quantization-level crossings. This new model allows for a better prediction of possible idle patterns (important for the in-band signal-to-quantization error ratio), and calculation of zero-input stability boundaries for loop-filter parameters in higher order low-pass /spl Sigma//spl Delta/Ms.