Cordic Algorithm In Dds

Direct Digital Synthesis (DDS) is one of the dominating modern technologies for frequency synthesis. It possesses several advantages in producing high resolution frequency, fast frequency conversion and continuous phase change. Direct Frequency Synthesizer has been widely used in many fields. Traditional DDS applies a ROM look-up table to realize the phase-to-amplitude conversion.CORDIC algorithm calculates the rotation of vectors in an iterating manner and is mainly used in computing trigonometric, hyperbolic, exponential and logarithmic functions. The CORDIC algorithm only requires shifting operation, addition and subtraction on the data, which easies the hardware implementations. The pipelined version of CORDIC algorithm can be adopted to achieve greater computing speed.The main goal of this paper is to design a CORDIC algorithm to replace the ROM look-up table structure used by DDS. By applying the CORDIC algorithm, the hardware computational power and resources requirements could be greatly reduced compared to the traditional DDS. In addition, it could be easily implemented in FPGA chips. Nevertheless, the iterative nature of the CORDIC algorithm remains to be the bottleneck for speeding up DDS. To further improve the computational performance, this paper also carries out a detailed review of existing CORDIC algorithms and proposes a novel approach to calculate the direction of each rotation in advance. This approach reduces the computing time for the rotation direction on each iteration in the traditional CORDIC algorithm. Based on the different accuracy requirements, this paper designs two versions of this algorithm. The first version is targeted for the bit number lower than 24, that is the directions of rotation and reminding angles are obtained by referring to look-up table; the second version is used for the bit number more than 24, that is the directions of rotation and reminding angles are obtained in calculative way. Take 16 bits and 32 bits for examples,two versions of CORDIC algorithm are simulated on FPGA.More specifically, the proposed CORDIC algorithm is applied to phase conversion unit, and FPGA simulation is used to implement the digital circuit design for DDS. Lastly, the system errors produced by the CORDIC algothrim and the spurious ability of DDS design are discussed in the paper. Furthermore, a comparison between the traditional CORDIC algorithm and the improved one, a benchmark between ROM look-up table based DDS and proposed CORDIC algorithm based DDS are also provided.