Arbitrary Frequency, Ultra Low Phase Noise DDS

Direct Digital Synthesizers use a phase accumulator to form the argument of a complex sinusoid and a phase-to-amplitude conversion mechanism to form the samples of continuous phase, and arbitrary frequency sinusoids. The most common conversion process is a look-up-table addressed by the M-Most significant bits of the phase accumulator. The M-bit address is a quantized approximation to the desired phase, which leads to incidental phase modulation with spurious spectral lines at levels -6 dB per bit of address width. To obtain lower levels of phase noise with a small look-up table the DDS often employs a two-pass algorithm in which the quadrature samples formed from high order phase bits are corrected by post processing with terms derived from low order phase bits. We demonstrate how this technique is further improved by a gain correction term related to the low order phase bits. We then review the next most common phase to amplitude conversion process, the iterative CORDIC algorithm. We show how to embed the look-up table corrections to a version of the CORDIC based DDS. This variation in turn leads to a stable fully recursive version of the DDS.