An Exposition of Fractional Spurs Resulting From Nonlinear Distortion

The interaction between quantization noise intro-duced by the divider controller and memoryless nonlinearities in a fractional-N PLL causes fractional spurs to occur. This paper presents a comprehensive theory to explain why combinations of quantizers and memoryless nonlinearities produce fractional spurs. Necessary and sufficient conditions for spur-free behavior in the presence of an arbitrary memoryless nonlinearity or linear combinations of sets of arbitrary memoryless nonlinearities are derived. Finally, an upper limit on the number of nonlinearities for which a quantizer can exhibit spur-free performance is derived.