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The spectrum of the quantization error in a dithered sigma-delta modulator is derived under the constraint that the dithering signal does not cause overload. The results apply to DC, sinusoidal, and more general quasi-stationary signals. It is shown in the case of a simple sigma-delta modulation that no-overload dithering can smooth the error spectrum and can make the quantization error asymptotically uncorrelated with the input. It does not, however, make the quantization error white. In the case of multistage sigma-delta modulation with the appropriate dithering, the quantization error becomes white, even for a system with only two stages. The signal-to-quantization-noise ratio (SQNR) 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.