Reconciliation of Statistical Approaches to Predicting Nonlinearity-Induced Spurs in Fractional-<i>N</i> Frequency Synthesizers

Fractional-N frequency synthesizers based on phase-locked loops exhibit spurious tones (spurs) that result from interactions between the accumulated output of the divider controller and nonlinearity in the loop. A number of methods have been proposed to modify the statistics of the divider controller signal so that interaction with a memoryless polynomial nonlinearity does not induce spurs. This tutorial paper reconciles two principal concepts in the literature: Familier and Galton’s mathematically rigorous fundamental limitation of DC-free quantization noise with respect to nonlinearity-induced spurious tones, and the heretofore empirical periodic nonlinearity noise function which has provided intuition and insight, as well as inspiring further innovation. It demonstrates the connection between the two concepts and highlights the strengths and limitations of the PNN as it relates to predicting the spur performance of fractional-N PLLs.