LAUSR

Phase locked loops for fractional frequency synthesis typically use Digital $\Delta \Sigma $ 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- ${N}$ frequency synthesizers with polynomial nonlinearities.