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Informativity research of nonlinear continuous-discrete systems by the example sigma-delta ADC


I.A. Sidorova, A.V. Seleznev, B.V. Chuvykin

In this article research informativity of nonlinear continuous-discrete systems is carried out by the example of a sigma-delta ADC using the part of ADC - mathematical model of the third order sigma-delta modulator, which form provided in the system of difference equations. The main problem in designing this class of ADCs is calculation of the feedback coefficients in order to ensure stable operation of the modulator, while ensuring the maximum number of digits, and the minimum fluctuation noise in the output codes of the ADC. A method for calculating the maximum achievable bit sigma-delta ADC and methods of choosing the feedback coefficients of the criterion of maximum informativity of output codes sigma-delta modulator are given. We compared the results of the choice of feedback coefficients by the maximum informativity of output codes and the criterion of minimum medium-value kvadratichesoe quantization noise of sigma-delta ADC. The findings allow us to estimate the potential to improve the accuracy of the ADC by increasing the digital filtering algorithms for single-bit signal of the modulator, as well as to assess the stability boundary in the k-dimensional space of values of the feedback coefficients of the modulator for a variety of structural and algorithmic choices. The authors found that the most stable mode is a single ADC at a given time interval with zero initial conditions of integrators (digit gain in 16-bit ΣΔ-ADC is 2-4 third-order bits).

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