Analysis and Design of Low-Complexity Stochastic DEM Encoder for Reduced-Distortion Multi-bit DAC in Sigma-Delta Modulators


A low-complexity stochastic dynamic element matching (DEM) technique to mitigate the distortions caused by the nonlinearity of multi-bit digital-to-analog converters (DACs) in sigma-delta modulator is proposed. Multi-bit DAC noise is analyzed in detail from a signal processing point-of-view in this research, and then implementation of the basic stochastic unit named swapper cell which includes bar state and cross state controlled by a 1-bit pseudo-random noise signal, is illustrated. To reduce the hardware complexity, a multi-layer scheme for multi-input multi-output stochastic encoder is presented and demonstrated based on rigorous mathematical derivation. For a n-input n-output version, the number of the switch elements employed in the proposed encoder is reduced to 2nlog2n from the conventional n!. Simulation results show that, with the use of the stochastic encoder, severe harmonic distortions resulted by the DAC elements mismatch errors are suppressed effectively. When the proposed encoders are applied to the internal multi-bit DACs in sigma-delta (ΣΔ) modulators, large improvements of the linearity performance of the modulators are achieved. Additionally, the analyses and explanations for this stochastic scheme provide a theoretical foundation for the future development of noise shaping DEM.

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This research is supported by National Natural Science Foundation of China (Grant Nos. 61504102 and 11604251) and the National Key Project of Intergovernmental Cooperation in International Scientific and Technological Innovation (2016YFE0107900).

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Correspondence to Di Li.

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Li, D., Fei, C. & Zhang, Q. Analysis and Design of Low-Complexity Stochastic DEM Encoder for Reduced-Distortion Multi-bit DAC in Sigma-Delta Modulators. Circuits Syst Signal Process (2020).

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  • Sigma-delta ADC
  • Multi-bit DAC
  • Mismatch noise
  • Mixed analog–digital integrated circuits
  • Dynamic element matching (DEM)