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Method of Direct Digital Synthesis of the Harmonious Signal. The Analysis and Mathematical Modelling


A.I. Smekalov

In tasks of generation of a sine wave signal of the precision form the choice of a concrete digital synthesizer which parameters of realization provide required quality of an output signal is still difficult. Especially it is actual at use of a synthesizer for generation of a wide range of frequencies, for example at designing low-frequency generators of sine wave signals where the use of the band pass filter for a filtration of harmonics is impossible. In the article, models of a digital synthesizer and DAC which us allow us to receive approached to practice the time diagram and a spectrum of an output signal are resulted. It is shown that on the basis of the received spectrum it is possible to calculate total harmonic distortion KГ and a peak level of the spurious spectral components PLSH determined by a synthesizer and LPF on its output. Dependence of parameters KГ and PLSH on a frequency word of a synthesizer is determined. Feature of the frequency word corresponding to frequency of equal 25 % from clock frequency of a synthesizer is allocated and explained. Influence of LPF on an output signal and its spectrum, and on parameters KГ and PLSH is described. The reasons of deterioration of spectral purity of the output signal, the realizations of chip of digital synthesizers caused by features, such as phase truncation, finite resolution of the phase-amplitude converter and DAC, nonlinearity of the DAC transfer function are in detail considered. Influence of each of them on total harmonic distortion and peak level of the spurious spectral components which is submitted as graphics is revealed. By the example of 14-bit DAC microcircuits AD9952 for Chebyshev type I filter the graphic is received, allowing determination of the greatest possible percentage ratio of the maximal frequency of a required range of frequencies to clock frequency of a digital synthesizer at concrete realization of the filter at which requirements to spectral purity of the output signal are carried out. The result of the analysis and modelling is the developed technique of calculation of such values of parameters of a digital synthesizer and characteristics LPF on its output which allow us to receive the set range and step of frequency, nonlinear distortion factor and a peak level of spurious spectral components. Results of modelling and the developed technique of calculations are used for designing low-frequency generators of high-precision signals G3-135 and G3-136, having a total harmonic distortion no more than 0,003 % in a range of frequencies from 200 Hz up to 20 kHz and a peak level of spurious components no more than 70 dB.

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