Fourth Fundamental Circuit Element: SPICE Modeling and Simulation

Chapter

Abstract

This chapter deals with two possible stages of exploring the memristor as the fourth fundamental circuit element: (1) generation of the model and (2) simulation of the element behavior with the aid of the model. The initial stage, i.e. modeling of the two-terminal device, belonging to the family of memristors, should be based on the basic rules of a “correct modeling” as proposed by L. Chua. These rules are brought up in the introductory part of the chapter. The characteristics, defining the memristor, in particular the port and state equations, the constitutive relation, and the parameter-vs.-state-map, are the starting points of such a “correct modeling.” Several memristor fingerprints (FPs), which can be deduced from the above characteristics, are summarized. Their knowledge can be useful for determining whether the memristor model, irrespective of its nature (mathematical, software- or hardware-implemented) behaves correctly. Some methods for the implementation of memristor models in the SPICE-family programs are also described.

Keywords

TiO2 Platinum Sine 

Notes

Acknowledgments

This work was partially supported by the Czech Science Foundation under grant No P102/10/1614, and by the project for development of K217 Dept., UD Brno.

References

  1. 1.
    L.O. Chua, Memristor—the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519 (1971)CrossRefGoogle Scholar
  2. 2.
    G.F. Oster, D.M. Auslander, The memristor: a new bond graph element. J. Dyn. Syst. Meas. Control 94(3), 249–252 (1972)CrossRefGoogle Scholar
  3. 3.
    D.C. Mikulecky, Network thermodynamics and complexity: a transition to relational systems theory. Comput. Chem. 25(4), 369–391 (2001)CrossRefGoogle Scholar
  4. 4.
    D. Jeltsema, A.J. van der Schaft, Memristive port-Hamiltonian systems. Math. Comput. Model. Dyn. Syst. 16(2), 75–93 (2010)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    D. Jeltsema, A. Dòria-Cerezo, Port-Hamiltonian formulation of systems with memory. Proc. IEEE 100(6), 1928–1937 (2012)CrossRefGoogle Scholar
  6. 6.
    Z. Biolek, D. Biolek, V. Biolková, Analytical solution of circuits employing voltage- and current-excited memristors. IEEE Trans. Circuits Syst. Regul. Pap. 59(11), 2619–2628 (2012)CrossRefGoogle Scholar
  7. 7.
    Y.V. Pershin, S. Fontaine, M. Di Ventra, Memristive model of amoeba’s learning. Phys. Rev. E. 80, 021926/1–021926/6 (2009)Google Scholar
  8. 8.
    D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, The missing memristor found. Nature 453, 80–83 (2008)CrossRefGoogle Scholar
  9. 9.
    Y.V. Pershin, M. Di Ventra, Memory effects in complex materials and nanoscale systems. Adv. Phys. 60, 145–227 (2011)CrossRefGoogle Scholar
  10. 10.
    L.O. Chua, Resistance switching memories are memristors. Appl. Phys. A. 102, 765–783 (2011)CrossRefGoogle Scholar
  11. 11.
    L.O. Chua, S.M. Kang, Memristive devices and systems. Proc. IEEE 64(2), 209–223 (1976)MathSciNetCrossRefGoogle Scholar
  12. 12.
    S. Benderli, T.A. Wey, On SPICE macromodeling of TiO2 memristors. Electron. Lett. 45(7), 377–379 (2009)CrossRefGoogle Scholar
  13. 13.
    Z. Biolek, D. Biolek, V. Biolková, Spice model of memristor with nonlinear dopant drift. Radio Eng. 18(2), 210–214 (2009)Google Scholar
  14. 14.
    A. Rák, G. Cserey, Macromodeling of the memristor in SPICE. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 29(4), 632–636 (2010)CrossRefGoogle Scholar
  15. 15.
    L.O. Chua, Nonlinear circuit foundations for nanodevices, Part I: The four-element torus. Proc. IEEE 91(11), 1830–1859 (2003)CrossRefGoogle Scholar
  16. 16.
    Y.N. Joglekar, S.J. Wolf, The elusive memristor: properties of basic electrical circuits. Eur. J. Phys. 30(4), 661–675 (2009)CrossRefMATHGoogle Scholar
  17. 17.
    D. Biolek, Z. Biolek, V. Biolkova, Pinched hysteresis loops of ideal memristors, memcapacitors and meminductors must be ‘selfcrossing’. Electron. Lett. 47(25), 1385–1387 (2011)CrossRefGoogle Scholar
  18. 18.
    H. Kim, M. P. Sah, S. P. Adhikari, Pinched hysteresis loops is the fingerprint of memristive devices. arXiv:1202.2437v2 (2012)Google Scholar
  19. 19.
    L.O. Chua, in Hodgkin-Huxley, memristor and the edge of chaos, in Invited Lecture at the 3rd Memristor and Memristive Symposium, Turin, Italy, 2012Google Scholar
  20. 20.
    H.N. Huang, S.A.M. Marcantognini, N.J. Young, Chain rules for higher derivatives. Math. Intell. 28(2), 1–12 (2006)Google Scholar
  21. 21.
    E. Linn, R. Rosezin, C. Kügeler, R. Waser, Complementary resistive switches for passive nanocrossbar memories. Nat. Mater. 2010(9), 403–406 (2010)CrossRefGoogle Scholar
  22. 22.
    F. Corinto, A. Ascoli, A boundary condition-based approach to the modeling of memristor nano-structures. IEEE Trans. Circuits Syst. Regul. Pap. 59(11), 2713–2726 (2012)MathSciNetCrossRefGoogle Scholar
  23. 23.
    S. Shin, K. Kim, S.M. Kang, Compact models for memristors based on charge-flux constitutive relationships. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 29(4), 590–598 (2010)CrossRefGoogle Scholar
  24. 24.
    T. Prodromakis, B.P. Peh, C. Papavassiliou, C. Toumazou, A versatile memristor model with non-linear dopant kinetics. IEEE Trans. Electron Devices 58(99), 1–7 (2011)Google Scholar
  25. 25.
    S. Kvatinsky, E.G. Friedman, A. Kolodny, U.C. Weiser, TEAM: ThrEshold adaptive memristor model. IEEE Trans. Circuits Syst. Regul. Pap. 60(1), 211–221 (2013)Google Scholar
  26. 26.
    R. Kozma, R.E. Pino, G.E. Pazienza (eds.), Advances in Neuromorphic Memristor Science and Applications (Springer, New York, 2012)Google Scholar
  27. 27.
    E. Lehtonen, M. Laiho, CNN using memristors for neighborhood connections, in 12th International Workshop on Cellular Nanoscale Networks and Their Applications (CNNA), Berkeley, CA, 2010Google Scholar
  28. 28.
    K. Eshraghian, O. Kavehei, K.R. Cho, J.M. Chappell, A. Iqbal, S.F. Al-Sarawi, D. Abbott, Memristive device fundamentals and modeling: applications to circuits and systems simulation. Proc. IEEE 100(6), 1991–2007 (2012)Google Scholar
  29. 29.
    N.D. Manring, Hydraulic Control Systems (Wiley, USA, 2005), p. 464Google Scholar
  30. 30.
    A.L. Hodgkin, A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952)Google Scholar
  31. 31.
    L. Chua, V. Sbitnev, H. Kim, Hodgkin-Huxley axon is made of memristors. Int. J. Bifurcation Chaos 22(3), 1230011-1–1230011-48 (2012)Google Scholar
  32. 32.
    L. Chua, V. Sbitnev, H. Kim, Neurons are poised near the edge of chaos. Int. J. Bifurcation Chaos 22(4), 250098-1–250098-49 (2012)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Electrical Engineering/MicroelectronicsUniversity of Defence/Brno University of TechnologyBrnoCzech Republic
  2. 2.Department of MicroelectronicsBrno University of TechnologyBrnoCzech Republic

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