1/f fluctuations sources in direct digital frequency synthesizers and their contribution to the output oscillations power spectral density

An analysis of 1/f noise transformation at the output of a direct digital frequency synthesizer (DDS) is presented. Basic 1/f noise sources located in the digital-to-analog converter (DAC) are taken into consideration. Using theory of the periodically nonstationary random processes, general formulae for power spectral densities (SDs), both noise at the DDS output and 1/f type amplitude and phase fluctuations, are obtained. They are simplified for two particular cases: noise sources located in bit current generators and noise sources located in the biasing circuit. It is shown that these noise sources usually cause only amplitude fluctuations. The main causes of 1/f type phase fluctuations contributed by the DAC are fluctuations of bit currents switching times. An approximate analysis of these fluctuations is also presented. Some results of DAC 1/f noise currents measurements are given and based on them quantitative estimations of DDS output noise are obtained.