Wandering Spurs in MASH 1-1 Delta-Sigma Modulators

Wandering spurs are a little-studied phenomenon seen in MASH and SQ-digital delta-sigma modulators. They take the form of frequency-modulated spurs which periodically appear in-band. Since modulators are often employed as divide ratio controllers in fractional-N phase lock loops, these spurs can feed into the output phase noise spectrum. In this paper, we explain the mechanism which creates the wandering spurs and offer a prediction for the behavior of these spurs in the MASH 1-1 modulator. Simulation results are presented which confirm our theoretical predictions.