Influence of Initial Condition on Wandering Spur Pattern in a MASH-Based Fractional-N Frequency Synthesizer

A Multi-stAge noiSe sHaping Digital Delta-Sigma Modulator (MASH DDSM) is commonly employed as the divider controller in a fractional-N frequency synthesizer. Previous work has considered a time-varying pattern of spurious tones, called wandering spurs, which originate in the DDSM. Two cases have been considered, namely when the fractional part of the division ratio is (i) close to zero or (ii) close to a simple fraction. In both cases, the wandering spur pattern is independent of the initial state of the modulator. This brief considers a third case where the pattern of wandering spurs depends explicitly on the initial state. The phenomenon is explained analytically and simulation results are presented. Theoretical predictions are confirmed with spectral measurements from a representative commercial monolithic fractional-N frequency synthesizer.