Fundamental noise in direct digital frequency synthesizers

An analysis of fundamental noise at the output of direct digital frequency synthesizer (DDS) due to noise sources in the digital-to-analog converter (DAC) is presented. Based on the periodically nonstationary random processes theory, general formulae for spectral densities (SDs) of both noise floor and amplitude and phase fluctuations are obtained. These formulae are simplified for the case of δ-correlated noises and for the noise sources that have SDs proportional to the output signal value and to the square of the signal value. For the particular example of a DDS, having a high speed ECL type DAC, detailed investigation is carried out. Using noise models of bipolar transistors and other components, simple formulae for two groups of noise sources are derived. Noise sources of the first group are located in the DAC bit currents generators. Noise sources of the second group are in the circuit for biasing and temperature stabilization of bit currents generators. Using these formulae and real values of supply voltages, currents, transistor parameters and resistors, some calculations are made, and quantitative estimations of the output noise SD and both amplitude and phase fluctuations SDs are obtained and discussed