Skip to main content
SpringerLink
Log in

Fractional-order Memristor Response Under DC and Periodic Signals

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

Recently, there is an essential demand to extend the fundamentals of the conventional circuit theory to include the new generalized elements, fractional-order elements, and mem-elements due to their unique properties. This paper presents the relationships between seven different elements based on the four physical quantities and the fractional-order derivatives. One of them is the Fractional-order memristor, where the memristor dynamic is expressed by fractional-order derivative. This element merge the memristive and fractional-order concepts together where the conventional modeling becomes a special case. Moreover, the mathematical modeling of the fractional-order memristor is introduced. In addition, the response of applying DC, sinusoidal, and nonsinusoidal periodic signals is discussed. Finally, different numerical simulations are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. K. Biswas, S. Sen, P.K. Dutta, Modeling of a capacitive probe in a polarizable medium. Sens. Actuators A: Phys. 120(1), 115–122 (2005)

    Article  Google Scholar 

  2. J. Borghetti, G.S. Snider, P.J. Kuekes, J.J. Yang, D.R. Stewart, R.S. Williams, Memristive switches enable stateful logic operations via material implication. Nature 464(7290), 873–876 (2010)

    Article  Google Scholar 

  3. R. Caponetto, Fractional Order Systems: Modeling and Control Applications, vol. 72 (World Scientific, Singapore, 2010)

    Google Scholar 

  4. L. Chua, Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519 (1971)

    Article  Google Scholar 

  5. L. Chua, Device modeling via nonlinear circuit elements. IEEE Trans. Circuits Syst. 27(11), 1014–1044 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  6. A.S. Elwakil, Fractional-order circuits and systems: an emerging interdisciplinary research area. IEEE Circuits Syst. Mag. 10(4), 40–50 (2010)

    Article  Google Scholar 

  7. A.S. Elwakil, M.E. Fouda, A.G. Radwan, A simple model of double-loop hysteresis behavior in memristive elements. IEEE Trans. Circuits Syst. 60(8), 487–491 (2013)

    Article  Google Scholar 

  8. M. Faryad, Q.A. Naqvi, Fractional rectangular waveguide. Prog. Electromagn. Res. 75, 383–396 (2007)

    Article  Google Scholar 

  9. M.E. Fouda, A.G. Radwan, Resistive-less memcapacitor-based relaxation oscillator. Int. J. Circuit Theory Appl. (2014). doi:10.1002/cta.1984

  10. M.E. Fouda, M. Khatib, A. Mosad, A.G. Radwan, Generalized analysis of symmetric and asymmetric memristive two-gate relaxation oscillators. Circuits and Systems I: IEEE Trans. Regul. Pap. 60(10), 2701–2708 (2013). doi:10.1109/TCSI.2013.2249172

    Article  MathSciNet  Google Scholar 

  11. M.E. Fouda, A.G. Radwan, On the fractional-order memristor model. J. Fract. Calc. Appl. 4(1), 1–7 (2013)

    Google Scholar 

  12. T.C. Haba, G.L. Loum, J.T. Zoueu, G. Ablart, Use of a component with fractional impedance in the realization of an analogical regulator of order â\(1/2\). J. Appl. Sci. 8, 59–67 (2008)

    Article  Google Scholar 

  13. R. Kozma, R.E. Pino, G.E. Pazienza, Advances in Neuromorphic Memristor Science and Applications, vol. 4 (Springer, New York, 2012)

    Book  Google Scholar 

  14. K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (Wiley, New York, 1993)

    MATH  Google Scholar 

  15. A.G. Radwan, M.A. Zidan, K. Salama, Hp memristor mathematical model for periodic signals and dc. in 2010 53rd IEEE International Midwest Symposium on Circuits and Systems (MWSCAS), (IEEE, 2010), pp. 861–864

  16. A.G. Radwan, A.S. Elwakil, A.M. Soliman, Fractional-order sinusoidal oscillators: design procedure and practical examples. Circuits Syst. I: IEEE Trans. Regul. Pap. 55(7), 2051–2063 (2008)

    Article  MathSciNet  Google Scholar 

  17. A.G. Radwan, A. Shamim, K. Salama, Theory of fractional order elements based impedance matching networks. IEEE Microw. Wirel. Compon. Lett. 21(3), 120–122 (2011)

    Article  Google Scholar 

  18. A.G. Radwan, K.N. Salama, Fractional-order RC and RL circuits. Circuits Syst. Signal Process. 31(6), 1901–1915 (2012)

    Article  MathSciNet  Google Scholar 

  19. A.G. Radwan, M.E. Fouda, Optimization of fractional-order rlc filters. Circuits Syst. Signal Process. 32(5), 2097–2118 (2013)

    Article  MathSciNet  Google Scholar 

  20. I. Schäfer, K. Krüger, Modelling of lossy coils using fractional derivatives. J. Phys. D: Appl. Phys. 41(4), 045,001 (2008)

    Article  Google Scholar 

  21. M. Sivarama Krishna, S. Das, K. Biswas, B. Goswami, Fabrication of a fractional order capacitor with desired specifications: a study on process identification and characterization. IEEE Trans. Electron Devices 58(11), 4067–4073 (2011)

    Article  Google Scholar 

  22. A. Soltan, A.G. Radwan, A.M. Soliman, Fractional order filter with two fractional elements of dependant orders. Microelectron. J. 43(11), 818–827 (2012)

    Article  Google Scholar 

  23. D. Strukov, G. Snider, D. Stewart, R. Williams, The missing memristor found. Nature 453(7191), 80–83 (2008)

    Article  Google Scholar 

  24. J. Tenreiro Machado, Fractional generalization of memristor and higher order elements. Commun. Nonlinear Sci. Numer. Simul. 18(2), 264–275 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  25. Y.B. Zhao, C.K. Tse, J.C. Feng, Y.C. Guo, Application of memristor-based controller for loop filter design in charge-pump phase-locked loops. Circuits Syst. Signal Process. 32(3), 1013–1023 (2013)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Engineering Mathematics and Physics Department, Cairo University, Giza, 12613, Egypt

    Mohamed E. Fouda & Ahmed G. Radwan

Authors
  1. Mohamed E. Fouda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahmed G. Radwan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ahmed G. Radwan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fouda, M.E., Radwan, A.G. Fractional-order Memristor Response Under DC and Periodic Signals. Circuits Syst Signal Process 34, 961–970 (2015). https://doi.org/10.1007/s00034-014-9886-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-014-9886-2

Keywords

Search

Navigation