Folded Noise Prediction in Nonlinear Fractional-N Frequency Synthesizers

The presence of nonlinearities in a fractional-N frequency synthesizer leads to the generation of an additional component of noise that appears in the output phase noise spectrum. This nonlinearity-induced noise component manifests itself as spurious tones and an elevated noise floor, also known as folded noise. This paper presents a mathematical analysis of the folded noise generated in fractional-N phase locked loops (PLL) by the interaction between the quantization noise introduced by the divider controller and a nonlinearity. The analysis is performed for different digital
$\Delta \Sigma $
modulators (DDSM) and nonlinearities, providing expressions that allow one to predict the folded noise. These are compared with state-of-the-art predictions and simulation results.