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Phase locked loops for fractional frequency synthesis typically use Digital <inline-formula> <tex-math notation="LaTeX">$\Delta \Sigma $ </tex-math></inline-formula> Modulators (DDSMs) as their divider controllers. Different types and configurations of DDSMs have been presented in the past which have distinctive characteristics in terms of spectral shaping of their quantization errors, spur immunity and implementation costs. This paper presents a family of DDSMs that have provably high spur immunity and low folded noise when used in fractional-<inline-formula> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> frequency synthesizers with polynomial nonlinearities.

ieee transactions on circuits and systems i: regular papers

A Family of &#x0394;&#x03A3; Modulators With High Spur Immunity and Low Folded Nonlinearity Noise When Used in Fractional- Frequency Synthesizers<italic/>