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### Some Contraction Methods for Locating and Finding All the DC Operating Points of Diode-Transistor Circuits

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Języki publikacji
EN
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EN
The paper is focused on the analysis of diodetransistor circuits having multiple DC solutions (operating points) and brings two methods enabling us to find all the solutions. The first method contracts and eliminates some hyperrectangular regions where the solutions are sought. It is based on the idea of framing of the nonlinear functions appearing in the mathematical description of the circuit by linear ones and exploits the Woodbury formula in matrix theory. The other method finds quickly and easily preliminary bounds on the location of all the solutions. The method employs some monotonic functions and generates convergent sequences leading to a shrinked hyperrectangle that contains all the solutions. Both the proposed methods are rigorously proved. They constitute the core of an algorithm which efficiently finds all the DC operating points of diode-transistor circuits. It is illustrated via numerical examples.
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EN
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331--338
Opis fizyczny
Bibliogr. 26 poz., rys., wykr.
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autor
• Department of Electrical, Electronic, Computer and Control Engineering, Technical University of Łódź, 90-924 Łódź, 18/22 Stefanowskiego Street, Poland, michal.tadeusiewicz@p.lodz.pl
Bibliografia
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• [4] L. V. Kolev and V. M. Mladenov, “An interval method for finding all operating points of non-linear resistive circuits,” International Journal of Circuit Theory and Applications, vol. 18, pp. 257-267, 1990.
• [5] M. Tadeusiewicz, “A method for finding bounds on the location of all the solutions of DC piecewise-linear circuits,” International Journal of Circuit Theory and Applications, vol. 18, pp. 165-174, 1990.
• [6] M. Tadeusiewicz, “A method for finding bounds on all the DC solutions of transistor circuits,” IEEE Transactions on Circuits and Systems, vol. 39, pp. 557-564, 1992.
• [7] S. Pastore and A. Premoli, “Polyhedral elements: A new algorithm for capturing all the equilibrium points of piecewise-linear circuits,” IEEE Transactions on Circuits and Systems, vol. 40, pp. 124-132, 1993.
• [8] M. Tadeusiewicz and K. Głowienka, “A contraction algorithm for finding all the DC solutions of piecewise-linear circuits,” Journal of Circuits, Systems and Computers, vol. 4, pp. 319-336, 1994.
• [9] S. Pastore and A.Premoli, “Finding all DC solutions of nonlinear resistive circuits by exploring both polyhedral and rectangular circuits,” in IEE: Proceedings, Circuits, Devices and Systems, vol. 144, no. 9, 1997, pp. 17-21.
• [10] M. Tadeusiewicz, “DC analysis of circuits with idealized diodes considering reverse bias breakdown phenomenon,” IEEE Transactions on Circuits and Systems, vol. 44, pp. 312-326, April 1997.
• [11] K. Yamamura and A. Machida, “An efficient algorithm for finding all DC solutions of piecewise-linear circuits,” International Journal of Circuit Theory and Applications, vol. 36, pp. 989-1000, 2008.
• [12] M. Tadeusiewicz and S. Hałgas, “A method for the analysis of transistor circuits having multiple DC solutions,” International Journal of Electronics and Communications, vol. 60, no. 8, pp. 582-589, 2006.
• [13] V. Fernandez, L. Martinez, A. Reyes, and M. Anda, “Finding all the operating points in piecewise-linear electrical networks: an iterative decomposed approach,” in Proceedings of the 15th IEEE International Conference on Electronics, Circuits and Systems, 2008, pp. 304-307.
• [14] S. Pastore, “Fast and efficient search for all DC solutions of PWL circuits by means of oversized polyhedra,” IEEE Transactions on Circuits and Systems, pp. 2270-2279, 2009.
• [15] A. Ushida, Y. Yamagami, Y. Nishio, I. Kinoichi, and Y. Inoue, “An efficient algorithm for finding multiple DC solutions based on the SPICE-oriented Newton homotopy method,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 21, pp. 337-348, 2002.
• [16] L. Kolev, “An interval method for global nonlinear analysis,” IEEE Transactions on Circuits and Systems, vol. 47, pp. 675-683, May 2000.
• [17] A. Reibiger, W. Mathis, T. Nahring, and L. Trajković, “Mathematical foundations of the TC-method for computing multiple DC-operating points,” International Journal of Applied Electromagnetics and Mechanics, vol. 17, pp. 169-191, 2003.
• [18] K. Yamamura and N. Igarashi, “An interval algorithm for finding all solutions of non-linear resistive circuits,” International Journal of Circuit Theory and Applications, vol. 32, pp. 47-55, 2004.
• [19] L. B. Goldgeisser and M. M. Green, “A method for automatically finding multiple operating points in nonlinear circuits,” IEEE Transactions on Circuits and Systems, vol. 52, pp. 776-784, April 2005.
• [20] M. Tadeusiewicz and S. Hałgas, “Finding all the DC solutions in circuits containing bipolar transistors,” in Proceedings of the International Conference on Signals and Electronic Systems, Łódź, 2006, pp. 361-365.
• [21] G. Gajani, A. Brambilla, and A. Premoli, “Numerical determination of possible multiple DC solutions of nonlinear circuits,” IEEE Transactions on Circuits and Systems, vol. 55, pp. 1074-1083, 2008.
• [22] M. Tadeusiewicz and S. Hałgas, “Finding all the DC solutions of circuits containing diodes and bipolar transistors,” Elektronika, vol. 12, pp. 39-42, 2009.
• [23] M.Tadeusiewicz and S.Hałgas, “Improved algorithm for computing all the DC operating points of diode-transistor circuits,” in European Conference on Circuit Theory and Design, Antalya, 2009, pp. 489-492, (CD-ROM).
• [24] A. Householder, The theory of matrices in numerical analysis. New York: Blaisded Publishing Company, 1965.
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Typ dokumentu
Bibliografia