Predicting ΣΔ frequency synthesizer performance

This paper describes a nonlinear mathematical model which can be used to predict ΣΔ frequency synthesizer fractional spur and phase noise levels. The model applies to ideal circuits or circuits with nonlinearity, such as mismatch of the phase detector and charge pump. This model was first established based on an ideal circuit and nonlinearity was added next. The model based predictions were compared against circuit-equivalent simulation results and measurement data from a commercial IC. Excellent correlation was achieved. The model also shows that the phase noise is not sensitive to the mismatch while the fractional spur is.