Direct digital frequency synthesizers: Complete analysis and design guidelines

This dissertation is intended to serve as an essential guide for anyone designing and/or evaluating the performance of Direct Digital Frequency Synthesizers (DDS). To date, the presence of a complete, exact, general, and efficient DDS characterization algorithm is absent.; The new theoretical basis, developed in this dissertation, gives rise to a key “windowing function,” and an algorithm that enables the exact analysis of DDS output spectra in the presence of phase truncation and arbitrary approximations and errors in the implementation of the sine/cosine mapping function (SCMF). As an input, the algorithm accepts the SCMF contents, the “signature sequence,” which includes all relevant information regarding specific non-idealities due to the actual DDS implementation. The new theory makes evident that the set of spurs from phase truncation and the set resulting from SCMF imprecision are effectively disjoint. Phase-truncation spurs are shown to have distinct magnitudes and their spectral locations, ordered from worst to best, are easily ascertained.; Without computing all spur magnitudes, the algorithm supported by the new theory determines the magnitudes and locations of N worst spurs due to phase truncation and arbitrary SCMF imprecision (where N is a user-specified integer), or all spurs above some specified threshold. An efficient method of accounting for the effects of phase accumulator initial conditions and their influence on DDS spurs is given.; The “windowing function” and SCMF “signature sequence” yield a simple and exact calculation for DDS output Signal-to-Noise Ratio (SNR) in the presence of phase truncation and arbitrary SCMF imprecision. The resulting expressions produce very tight upper and lower bounds for the SNR. The asymptotic behavior of the SNR curves and a method for computing the asymptote levels is discussed.; A common phase mapping technique is analyzed and shown to degrade the DDS performance. A new modified mapping technique is introduced, one that completely eliminates all phase-mapping errors. It is also shown that the use of 2's complement negation for reconstruction at the DDS output, instead of 1's complement negation, yields significantly better DDS performance and, the magnitudes of all spurs located in even DFT frequency bins can easily be made zero by careful DDS design.