An element rotation algorithm for multi-bit DAC nonlinearities in complex bandpass ΔΣAD modulators

This paper presents a technique for improving the resolution of complex bandpass ΔΣADCs which are used for wireless communication systems. Oversampling and noise-shaping are used to achieve high accuracy of a ΔΣAD modulator. However when a multi-bit DAC is used inside a modulator, nonlinearities of the DAC are not noise-shaped and the SNR of the ΔΣADC degrades. For the conversion of complex intermediate frequency (IF) input signals, a complex bandpass ΔΣAD modulator can provide superior performance to a pair of real bandpass ΔΣAD modulators of the same order. This paper proposes a new noise-shaping algorithm-implemented by adding simple digital circuitry-to reduce the effects of nonlinearities in multi-bit DACs of complex bandpass ΔΣAD modulators. We have performed simulation with MATLAB to verify the effectiveness of the algorithm, and the results show that the proposed algorithm can improve the SNR of a complex bandpass ΔΣADC with nonlinear internal multi-bit DACs.