A new fractional spur modeling in fractional-N frequency synthesizers

In this paper, a new method of spur noise modeling in fractional-N synthesizers with closed form results is introduced. To achieve closed form and simple results, we used some simplifying assumptions on different parts of the system. The output of the synthesizer is assumed as a square waveform with constant frequency (fractionally proportional to the input frequency). In addition, the output of the sigma-delta modulator is assumed to have a specific pattern, a function of the fractional ratio. Having these assumptions, in order to determine frequency and power of fractional spur noise with acceptable accuracy, control voltage waveform is studied and examined. To evaluate the proposed model and analytical equations, using MATLAB and CppSim environments, a synthesizer for a global system for mobile communications (GSM) network is simulated. Simulations all show good conformity between simulation and analytical results.