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Application of Volterra-Wiener spline series for the analysis of nonlinear electric circuits

  • Theory of Radio Circuits
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Abstract

The functional atlas of the initial system of nonlinear differential equations is split into local charts with the help of a multidimensional Taylor series expansion. In each chart, the approximation with a weakly nonlinear Volterra-Wiener series up to the fourth order is used, where a chart is changed when its boundaries are crossed. It is established that the obtained approach allows one to increase the accuracy and reliability of the calculated output response of the nonlinear system as compared to the classical Volterra-Wiener series approach. The results of the numerical simulation of a nonlinear RC circuit are presented and the efficiency of the proposed method is shown.

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References

  1. S. A. Maas, Nonlinear Microwave and RF Circuit (Artech House, London, 2003).

    Google Scholar 

  2. E. A. Volkov, Nonlinear Characteristics of Electrical Devices: Calculation Methods. Educational Manual (UMK MPS Rossii, Moscow, 2000) [in Russian].

    Google Scholar 

  3. S. A. Maas, Microwaves RF 38(5), 55 (1999).

    Google Scholar 

  4. V. Wouw, H. Nijmeijer, D. Van Campen, Nonlinear Dynamics, 27, 397 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Zhu, J. Pedro, and T. Brazil, IEEE Trans. Microwave Theory Tech. 54, 4323 (2006).

    Article  Google Scholar 

  6. A. Zhu, J. Pedro, and T. Cunha, IEEE Trans. Micro-wave Theory Tech. 55, 813 (2007).

    Article  Google Scholar 

  7. N. Wiener, Nonlinear Problems in Random Theory (Technology, New York, 1958).

    MATH  Google Scholar 

  8. V. Volterra Theory of Functionals and of Integral and Integro-Differential Equations (Dover, New York, 1959).

    MATH  Google Scholar 

  9. Yu. S. Zav’yalov, B. I. Kvasov, and V. L. Miroshnichenko, Methods of Spline Functions (Nauka, Moscow, 1980) [in Russian].

    MATH  Google Scholar 

  10. B. A. Dubrovin, S. P. Novikov, A. T. Fomenko, Contemporary Geometry: Methods and Applications (Editorial URSS, Moscow, 1998), Vol. 2 [in Russian].

    Google Scholar 

  11. V. V. Khutortsev and V. N. Taran, Radiotekh. Elektron. (Moscow) 31, 2180 (1986).

    Google Scholar 

  12. H. Poincare, On Curves Defined by the Differential Equations (OGIZ, Moscow, 1947) [in Russian].

    Google Scholar 

  13. J. Bussgang, L. Ehraman, and J. Graham, Proc. IEEE 62, 1088 (1974).

    Article  Google Scholar 

  14. W. Rugh, Nonlinear System Theory. The Volterra/Wiener Approach (Web Version, 2002); http://reslib.com/book/

    Google Scholar 

  15. E. B. William and C. Richard, Elementary Differential Equations and Boundary Value Problems (Wiley, New York, 2000).

    Google Scholar 

  16. E. I. Yurevich, Automatic Control Theory (Energiya, Moscow, 1969) [in Russian].

    Google Scholar 

  17. Fundamentals of Automatic Control, Ed. by V. S. Pugachev (Nauka, Moscow, 1974) [in Russian].

    Google Scholar 

  18. I. I. Krinetskii, Computation of Nonlinear Automatic Systems. Textbook for Technological Institutes (Technika, Kiev, 1974).

    Google Scholar 

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Authors and Affiliations

  1. Moscow Technical University of Communications and Informatics, ul. Aviamotornaya 8a, Moscow, 111250, Russia

    A. N. Taran

  2. Rostov State University of Transport Communication Lines, pl. Rostovskogo Strelkovogo Polka Narodnogo Opolcheniya 2, Rostov-on-Don, 344038, Russia

    V. N. Taran

Authors
  1. A. N. Taran
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  2. V. N. Taran
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Correspondence to A. N. Taran.

Additional information

Original Russian Text © A.N. Taran, V.N. Taran, 2014, published in Radiotekhnika i Elektronika, 2014, Vol. 59, No. 7, pp. 702–710.

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Taran, A.N., Taran, V.N. Application of Volterra-Wiener spline series for the analysis of nonlinear electric circuits. J. Commun. Technol. Electron. 59, 758–766 (2014). https://doi.org/10.1134/S1064226914060199

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  • DOI: https://doi.org/10.1134/S1064226914060199

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