Multiloop sigma-delta quantization

It is shown that, for a multiloop sigma-delta modulator driven by a DC input, the statistical behavior (described by long-term time averages) of the error process from an inner (multibit) quantizer is consistent with that of a signal-independent. white. uniform noise. The same result also holds for sinusoidal inputs, provided that the modulator has three or more loops. This behavior is exploited to obtain trade-offs between asymptotic system performances and oversampling ratios, for several sigma-delta modulator/decoding filter pairs. For an L-loop modulator with a simple sinc^L+1 decoding filter, it is shown that doubling the oversampling ratio can result in an improvement of 3.01(2L+1) dB in the signal-to-quantization-noise ratio