A novel technique to estimate the statistical properties of Σ-Δ A/D converters for the investigation of DC stability

Concerns the development of a novel technique for the determination of the moments of the quantizer input signal for Σ-Δ A/D converters. The starting point in this technique is the characterization of the quantizer output signal bit pattern. In the case of first-order Σ-Δ A/D converters this is facilitated by exploiting the fact that the spectrum of this bit pattern contains a dominant tone indicating that the bit pattern is almost periodic. In the case of higher-order A/D converters, this is achieved by taking into account that in stable Σ-Δ A/D converters, the constituent quantizer almost always operates in its overload-free region. Then, the quantizer input signal can be determined in terms of the DC input signal and in terms of the estimated quantizer output signal bit pattern. The desired quantizer input signal moments can then be obtained in a straightforward fashion. An application example is given to illustrate the accuracy of the proposed moment estimation technique.