Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Time and frequency responses of non-integer order RLC circuits

Department of Mathematics, Ondokuz Mayis University, 55139 Atakum Samsun, Turkey

Special Issues: New trends of numerical and analytical methods with application to real world models for instance RLC with new nonlocal operators

By introducing an auxiliary parameter, the dynamic of RLC electrical circuits of non-integer order is described by a fractional order differential equation. The order of derivative in the component models is assumed to be $0<\gamma\leq 1$. The time and frequency domain characteristics of the circuit is investigated, and it is shown that three different filter characteristics of low-pass, high-pass and band-pass filters are obtained. The filter parameters are determined analytically, and the results are verified numerically.
  Figure/Table
  Supplementary
  Article Metrics

References

1. R. Metzler, J. Klafter, The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics, J. Phys. A: Math. Gen., 37 (2004), 161-208.    

2. O. Tokatlı , V. Patoglu, Using fractional order elements for haptic rendering, Springer Proceedings in Advanced Robotics, 2 (2018), 373-388.    

3. A. Karthikeyan, K. Rajagopal, FPGA implementation of fractional-order discrete memristor chaotic system and its commensurate and incommensurate synchronizations, Pramana-J. Phys., 90 (2018), 1-13.    

4. A. Pratap, R. Raja, C. Sowmiya, et al. Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses, Neural Networks, 103 (2018), 128-141.    

5. Q. Sun, M. Xiao, B-B. Tao, et al. Hopf bifurcation analysis in a fractional-order survival red blood cells model and PDα control, Adv Differ Equations, 10 (2018), 1-10.

6. J. Sabatier, F. Guillemard, L. Lavigne et al. Fractional models of lithium-ion batteries with application to state of charge and ageing estimation, Lecture Notes in Electrical Engineering, 430 (2018), 55-72.

7. K. Diethelm, D. Baleanu, E. Scalas, Fractional calculus: Models and numerical methods, Singapore: World Scientific, 2012.

8. M. A. E. Herzallahr, Notes on some fractional calculus operators and their properties, J. Fract. Calc. Appl., 5 (2014), 1-10.

9. J. Ma, P. Zhou, B. Ahmad et al. Chaos and multi-scroll attractors in RCL-shunted junction coupled Jerk circuit connected by memristor, PloS One, 13 (2018), 1-21.

10. S. Bhalekar, V. D. Gejji, D. Baleanu, et al. Transient chaos in fractional Bloch equations, Comput. Math. Appl., 64 (2012), 3367-3376.    

11. A. Razminia, D. Baleanu, Fractional synchronization of chaotic systems with different orders, P. Romanian Acad. A, 13 (2012), 314-321.

12. A. Jakubowska-Ciszek, J. Walczak, Analysis of the transient state in a parallel circuit of the class RLβCα, Appl. Math. Comput., 319 (2018), 287-300.

13. A. Buscarino, R. Caponetto, G. D. Pasquale, et al. Carbon black based capacitive fractional order element towards a new electronic device, AEU-Int. J. Electron C., 84 (2018), 307-312.    

14. P. Bertsias, C. Psychalinos, Differentiator based fractional-order high-pass filter designs, 7th International Conference on Modern Circuits and Systems Technologies, 7-9 May 2018, (2018), 1-4.

15. A. Obeidat, M. Gharibeh, et al. Fractional calculus and applied analysis, 14, Springer, 2011.

16. J. F. Gomez-Aguilar, J. J. Rosales-Garcia, J. J. Bernal-Alvarado, et al. Fractional mechanical oscillators, Rev. Mex. Fis., 58 (2012), 348-352.

17. F. Gomez, J. Rosales, M. Guia, RLC electrical circuits of non-integer orders, Cent. Eur. J. Phys., 11 (2013), 1361-1365.

18. C. Alexander, M. Sadiku, Fundamentals of electric circuits, 5 Eds., New York: Mc Graw Hill, 2013.

19. A. Tepljakov, E. Petlenkov, J. Belikov, et al. Fractional-order controller design and digital implementation using FOMCON toolbox for MATLAB, 2013 IEEE Conference on Computer Aided Control System Design, 28-30 Aug 2013, Hyderabad, India, (2013), 340-345.

Copyright Info: © 2019, Mehmet Emir Koksal, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved