Dithering and its effects on sigma delta and multi-stage sigma delta modulation

The spectrum of quantization noise in a dithered sigma-delta modulator and multistage sigma-delta modulator is derived under the constraint that the dithering signal does not cause overload. It is shown in the case of a simple sigma-delta modulation that no-overload dithering can smooth the noise spectrum and can make the binary quantization noise asymptotically uncorrelated with the input. It does not, however, make the noise white. In the case of multistage sigma-delta modulation with the appropriate dithering, the binary quantization noise becomes asymptotically white, even for a system with only two-stages. The signal-to-quantization-noise ratio is derived for sigma-delta and multistage sigma-delta oversampled analog-to-digital conversion with additive dithering. Simulation results are presented to support the theoretical analysis