Practical Synthesis Of Irrational Impedance Based On Solutions Of The Quadratic Equation

Öz

Abstract: This article presents the rational approximations of recursively obtained solutions of the quadratic equation which lead to networks with lattice or tree structure. The impedance of a similar electrical circuit, composed of resistors and capacitors, has a module, depending on the square root of the frequency and its phase is equivalent to -45º. After considering the effect that the number of elements and their tolerances have on the accuracy of the impedance function of the networks, an eight section lattice cascade was constructed. The deviation between the theoretically and experimentally obtained magnitude and phase characteristics of such a device in the frequency interval 0,05÷1MHz did not exceed -1,2% and -1,3º respectively. Furthermore, it was found that the lattice network performance had impedance close to the expected one but in parallel with a capacity. Keywords: Circuit, Irrational impedance, Synthesis, Continued fraction, Lattice structure, Tree structure.

Anahtar Kelimeler

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Kaynakça

1. B. Vinagre, I. Podlubny, A. Hernandez, "Some approximations of fractional order operators used in control theory and applications", Fractional Calculus and Applied Analysis, Vol. 3, No. 3, pp.231–248, 2000.
2. A. Djouambi, A. Charef, A. Besançon1, "Approximation and synthesis of non integer order systems", 2nd IFAC Workshop on Fractional Differentiation and its Applications, Porto, Portugal, pp.1-4, 2006.
3. B. Krishna, Reddy K., "Active and passive realization of fractance device of order 1/2", Journal of Active and Passive Electronic Components, vol. 2008, p.5, 2008.
4. L. Dorčák1, J. Terpák1, I. Petráš1, F. Dorčáková, "Electronic realization of the fractional-order systems", Acta Montanistica Slovaca, vol.12, pp.231-237, 2007.
5. A. Djouambi, A. Charef, A. Besançon1, "Optimal approximation, simulation and analog realization of the fundamental fractional order transfer function", Int. J. Appl. Math. Comput. Sci., vol.17, No.4, p.455–462, 2007.
6. A. Charef, "Modeling and analog realization of the fundamental linear fractional order differential equation", Nonlinear Dynamics, vol.46, pp.195-210, 2006.
7. P. Sotiriadis, Y. Tsividis, "Integrators using a single distributed Symposium on Circuits and Systems, Arizona, USA, vol.2, pp.21-24, 2002. IEEE International
8. A. Radwan, A. Soliman, A. Elwakil, "First order filters generalized to the fractional domain", Journal of Circuits Systems & Computers, vol.17, pp.55-66, 2008. [9] M. Lima, J. Machado, "Experimental signal analysis of robot impacts in a fractional Advanced Computational Intelligence and Intelligent Informatics, vol.11, No.9, pp.1079–1085, 2007. of [10] I. Podlubny, "Fractional-order

9. fractional-order controllers", Slovak Academy of
10. Sciences, Slovakia, UEF-02-94, 1994. and
11. F. Soulier, P. Lagonotte, "Modeling distributed parameter systems with discrete element networks", Proceedings of 15th International Symposium on the Mathematical Theory of Networks and Systems, University of Notre Dame, Indiana, USA, p.7, 2002.
12. R. Burden, J. Faires, Numerical analysis, 8th edition, Cengage Learning, USA, p.864, 2005.
13. W. Press, S. Teukolsky, W. Vetterling, B. Flannery, Numerical Recipes in C: The Art of Scientific Computing, Second Edition, Cambridge University Press, USA, p.994, 2002.
14. J. Stoer, R. Bulirsch, Introduction to numerical analysis, Springer, USA, p.744, 2002.
15. A. Sudhakar, S. Palli, Circuits and Networks, Tata McGraw-Hill Education, India, p.965, 2006.
16. J. Chitode, Dr. Jalnekar, Network Analysis and Synthesis, Technical Publications, India, p.853, 2009.
17. O. Wing, Chitode, Dr. Jalnekar, Network Analysis Classical Circuit Theory, Springer, USA, p.296, 2008.
18. T. Iyer, Circuit theory, McGraw-Hill, p.520, 2006.
19. Pl. Nikovski, N. Katrandziev, "Modelling of phase- constant element in PSpice environment", Scientific conference with international participation – Food science, Engineering and Technologies, Plovdiv, Bulgaria, pp. 430-435, 2009. [20] Pl. Nikovski, "Improving the metrological characteristics of capacitive charge transfer