DIRECT DIGITAL SYNTHESIZER IN A NEW MATHEMATICAL BASIS

Abstract

The principles of the construction and operation of a digital synthesizer for direct frequency synthesis with acceleration of computational operations by using a residual class system (RNS) are considered. The specifics of the implementation of the operation of direct and inverse transformations from the positional number system to the number system of the residual classes are described. A mathematical model of a synthesizer with a phase accumulator in the system of residual classes is considered. The ways of designing a digital synthesizer of direct synthesis with a phase accumulator in the RNS system and a sinusoidal DAC are considered. In traditional schemes, the conversion of residuals to the value of an analog signal occurs in several stages, where conversion to a binary system is one of the stages. This procedure degrades the speed of the RNS system, adding additional constraints and increasing the waiting time for the conversion result. Methods of converting from RNS to binary number system for basic operations are considered. A DDS design with a phase accumulator in the residual class system and a converter to an analog signal form without using a slow ROM is proposed. The problems of efficient use of the synthesizer crystal area and reduction of delays in the formation of the output signal are considered. A study of one of the main functional blocks of a direct digital frequency synthesizer, a digital-to-analog converter, has been carried out. The architecture of a direct digital frequency synthesizer with a DAC direct conversion from a non-positional number system to an analog signal is proposed. The main sources of noise generation in digital computational synthesizers of the proposed type are investigated. A mathematical model is proposed for calculating the power spectral density of phase noise, which will allow analyzing the noise characteristics in synthesizers built on the indicated principles