Spectral Shaping of Dithered Quantization Errors in Sigma–Delta Modulators

A well-known problem in sigma–delta $(\Sigma\Delta)$ modulators is limit cycle oscillations, which can cause unwanted tones of significant power to appear in the quantization error. This problem becomes more severe as the amplitude of an input signal is small. The unwanted tones can be eliminated from the quantization error by employing a properly chosen random sequence to break up the limit cycle oscillations. However, the injected random sequence inevitably raises the noise floor in the signal band of interest, and thus degrades the signal-to-quantization-noise ratio (SQNR). This paper first presents a spectrally shaped noise generator and the theoretical basis for the behavior of the proposed generator is explained. Then we introduce a class of pseudorandom noise sequences with least significant bit dithering. The effectiveness of this class of dither sequences is demonstrated through a $\Sigma\Delta$ modulator. Simulation results show that the proposed dither sequences improve the SQNR by more than 10 dB compared to the case wherein a white pseudorandom binary sequence is applied. Meanwhile, it is shown that the proposed sequences successfully break up the limit cycle oscillations for small input signals.