Direct Digital Frequency Synthesizer in the Residue Number System

Abstract

The principles of construction and operation of direct digital frequency synthesizers are considered in order to speed up computational operations using Residue Number System. The problems of forming the output signals are considered. The specifics of the implementation of the operation of direct and reverse transformations from positional to non-positional number systems are described. A mathematical model of a synthesizer with a phase accumulator in a Residue Number System is considered. Methods for converting from RNS (Residue Number System) to binary system for problematic operations are considered. The design of a DDS (Direct Digital Synthesizer) with a phase accumulator in a Residue Number System and a converter to an analogue signal form is proposed without the use of slow ROM (Read Only Memory). The article deals with the issues of efficiency of the crystal area of the synthesizer and the reduction of the delays in the formation of the output signal.