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Nonlinear signals distortions at sigma-delta converters

Keywords:

Y.A. Brykhanov – Dr. Sc. (Eng.), Professor, Head of Department of Electronic Systems Dynamics, Yaroslavl State University. E-mail: bruhanov@uniyar.ac.ru Y.A. Lukashevich – Electronic Engineer, Department of Electronic Systems Dynamics, Yaroslavl State University. E-mail: dcslab@uniyar.ac.ru


Work covers analysis of nonlinear signal distortions at sigma-delta analog-to-digital converters (ADC). In such type of the converters oversampling and negative feedback in low-frequency region with followed digital filtration of quantizer output signal are used for re-ducing of quantization effects. This combination provides reducing of quantization errors in working band of converted signals. Goal of this work is analysis of parameters of sigma-delta converter with arbitrary number of quantization levels on nonlinear distortions of harmonic signals. For finding of an output signal of ADC we use a method of calculation of the compelled fluctuations in nonlinear discrete time systems at periodic external influences according to which the established process (the compelled fluctuations) at the discrete time system exit under periodic external influence is presented in the form of sequence of invariant points of discrete transformation. For analysis of analog-to-digital conversion effect on nonlinear distortions of signals we use a method of calculation of distortions of har-monious signals on the basis of the nonlinear model of process of quantization applicable for any numbers of categories and ways of re-presentation of numbers. We define a signal spectrum at the exit of the converter and calculate coefficient of nonlinear distortions – КНИ. Calculation for the coefficient КНИ on the assumption that the ADC is used in fractional arithmetic, are used to represent numbers with direct code truncation or rounding, and as a digital filter using the lowpass filter tenth order is done. Calculations show that the amount of distortion reduction in the sigma-delta converters is dependent on the oversampling factor K and the time constant of the integrator-filter τц. For the case of truncation and K = 15, the increase of τц 4,46TД to 19,49TД where TД – signal oversampling period, depending on the number of bits reduces КНИ 4,4−8,2 times compared with the absence of negative feedback. And when K = 40 the same increase τц reduces КНИ 2,3−4,8 times. When the approximation is performed with estimation and K = 15, then increase τц in the same range of values depending on the number of bits reduces КНИ 3,1−6,1 times compared with the absence of the negative feedback. And when K = 40 the same increase τц reduces КНИ 4,5−76,0 times. Obtained dependences of nonlinear distortions coefficient from coefficient of redundancy, number of bits, constant of time of of filter integrator and method of number approximation let to choose sampling frequency, necessary parameters of sigma-delta converter for creation of message transmission systems with digital signal processing.
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