Prediction of Phase Noise and Spurs in a Nonlinear Fractional- ${N}$ Frequency Synthesizer

Integer boundary spurs appear in the passband of the loop response of fractional-N phase lock loops and are, therefore, a potentially significant component of the phase noise. In spite of measures guaranteeing spur-free modulator outputs, the interaction of the modulation noise from a divider controller with inevitable loop nonlinearities produces such spurs. This paper presents analytical predictions of the locations and amplitudes of the spurs and accompanying noise floor levels produced by interaction between a divider controller output and a PLL loop with a static nonlinearity. A key finding is that the spur locations and amplitudes can be estimated by using only the knowledge of the structure and pdf of the accumulated modulator noise and the nonlinearity. These predictions also offer new insights into why the spurs appear.