Abstract
With the use of a linear approximation, the quantizer characteristics are defined by the stability conditions of the discrete models of the first- and second-order sigma‒delta analog-to-digital converters. The processes occurring in the nonlinear converter models are discussed at an arbitrary amount of digit positions in the representation of numbers under periodic external actions. An investigation method whereby stationary oscillations are represented as an invariant set of nonlinear discrete point mappings is employed. The spectral composition of the converter response and nonlinear signal distortions with an arbitrary period are calculated using the classical and modified discrete Fourier transformations. The dependences of the nonlinear- distortion coefficient of harmonic signals in the first- and second-order converters on the oversampling coefficient, the approximation method, the amount of digits in the representation of numbers, and the time constant of an integrating filter are presented.
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References
Analog-to-Digital Conversion, Ed. by W. Kester (Analog Devices, 2004; Tekhnosfera, Moscow, 2007) [in Russian].
W. Max, “Hauser. Principles of Oversampling A/D Conversation,” J. Audio Eng. Soc. 39 (1/2), 3 (1991).
Delta-Sigma Data Converters: Theory, Design and Simulation, Ed. by R. S. Norsworthy, R. Schreier, and G. C. Temes (IEEE Computer Soc., New York, 1996).
E. K. Shakhov, Datchiki i Sistemy, No. 11, 50 (2006).
B. V. Chuvykin, E. K. Shakhov, and V. N. Ashanin, Izv. Vyssh. Uchebn. Zaved., Povolzh. Region, Tekh. Nauki, No. 1, 91 (2007).
V. Cappellini, A. G. Constantinides, and P. Emiliani, Digital Filters and Their Applications (Academic Press, London, 1981; Energoatomizdat, Moscow, 1983).
Yu. A. Bryukhanov and Yu. A. Lukashevich, Radiotekhnika, No. 10, 57 (2009).
L. R. Rabiner and B. Gold, Theory and Applications of Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N. J., 1975; Mir, Moscow, 1981).
Yu. A. Bryukhanov and Yu. A. Lukashevich, Radiotekhnika, No. 12, 30 (2014).
A. V. Oppenheim and R. W. Schafer, Digital Signal Processing, (Englewood Cliffs, New York, 1979; Tekhnosfera, Moscow, 2006).
Yu. A. Bryukhanov, Izv. Vyssh. Uchebn. Zaved., Radioelektron., No. 11, 37 (1996).
Yu. A. Bryukhanov, J. Commun. Technol. Electron. 53, 807 (2008).
Yu. A. Bryuhanov, Radiophys. Quant. Electron. 53, 207 (2010).
Yu. I. Neimark, The Method of Point Mappings in the Theory of Nonlinear Oscillations (Nauka, Moscow, 1972) [in Russian].
Yu. A. Bryukhanov, J. Commun. Technol. Electron. 51, 186 (2006).
S. I. Baskakov, Radio Circuits and Signals (Vysshaya Shkola, Moscow, 2003) [in Russian].
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Original Russian Text © Yu.A. Bryukhanov, Yu.A. Lukashevich, 2017, published in Radiotekhnika i Elektronika, 2017, Vol. 62, No. 3, pp. 224–233.
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Bryukhanov, Y.A., Lukashevich, Y.A. Nonlinear distortions caused by sigma‒delta analog-digital conversion of signals. J. Commun. Technol. Electron. 62, 219–228 (2017). https://doi.org/10.1134/S1064226917030044
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DOI: https://doi.org/10.1134/S1064226917030044