Designs of angle-rotation in digital frequency synthesizer/mixer using multi-stage architectures

The key operation of the quadrature digital frequency synthesizer/mixer (QDFS/M) in many communication systems is the rotation of an input vector in the complex plane. In this paper, we propose three multi-stage architectures for the design of the angle rotation in QDFS/M, targeting for different precision requirements. The rotation is decomposed into three sub-rotations, each implemented by ROM-based multiplication-addition, linear approximation, or CORDIC operations. The major design consideration is to choose the proper architecture for a particular precision so that we can reduce the size of the required look-up table (LUT) and the bit widths of the corresponding arithmetic operations. Implementation results of various bit accuracies show that the best design choice depends on the desired precision.