Skip to main content
SpringerLink
Log in

Fourth Fundamental Circuit Element: SPICE Modeling and Simulation

  • Chapter
  • First Online:
Memristors and Memristive Systems

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.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  Google Scholar 

  2. G.F. Oster, D.M. Auslander, The memristor: a new bond graph element. J. Dyn. Syst. Meas. Control 94(3), 249–252 (1972)

    Article  Google Scholar 

  3. D.C. Mikulecky, Network thermodynamics and complexity: a transition to relational systems theory. Comput. Chem. 25(4), 369–391 (2001)

    Article  Google Scholar 

  4. D. Jeltsema, A.J. van der Schaft, Memristive port-Hamiltonian systems. Math. Comput. Model. Dyn. Syst. 16(2), 75–93 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. D. Jeltsema, A. Dòria-Cerezo, Port-Hamiltonian formulation of systems with memory. Proc. IEEE 100(6), 1928–1937 (2012)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. Y.V. Pershin, M. Di Ventra, Memory effects in complex materials and nanoscale systems. Adv. Phys. 60, 145–227 (2011)

    Article  Google Scholar 

  10. L.O. Chua, Resistance switching memories are memristors. Appl. Phys. A. 102, 765–783 (2011)

    Article  Google Scholar 

  11. L.O. Chua, S.M. Kang, Memristive devices and systems. Proc. IEEE 64(2), 209–223 (1976)

    Article  MathSciNet  Google Scholar 

  12. S. Benderli, T.A. Wey, On SPICE macromodeling of TiO2 memristors. Electron. Lett. 45(7), 377–379 (2009)

    Article  Google Scholar 

  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. A. Rák, G. Cserey, Macromodeling of the memristor in SPICE. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 29(4), 632–636 (2010)

    Article  Google Scholar 

  15. L.O. Chua, Nonlinear circuit foundations for nanodevices, Part I: The four-element torus. Proc. IEEE 91(11), 1830–1859 (2003)

    Article  Google Scholar 

  16. Y.N. Joglekar, S.J. Wolf, The elusive memristor: properties of basic electrical circuits. Eur. J. Phys. 30(4), 661–675 (2009)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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. L.O. Chua, in Hodgkin-Huxley, memristor and the edge of chaos, in Invited Lecture at the 3rd Memristor and Memristive Symposium, Turin, Italy, 2012

    Google Scholar 

  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. E. Linn, R. Rosezin, C. Kügeler, R. Waser, Complementary resistive switches for passive nanocrossbar memories. Nat. Mater. 2010(9), 403–406 (2010)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

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

    Google Scholar 

  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, 2010

    Google Scholar 

  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. N.D. Manring, Hydraulic Control Systems (Wiley, USA, 2005), p. 464

    Google Scholar 

  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. 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. 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 

Download references

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.

Author information

Authors and Affiliations

  1. Department of Electrical Engineering/Microelectronics, University of Defence/Brno University of Technology, Brno, Czech Republic

    Dalibor Biolek

  2. Department of Microelectronics, Brno University of Technology, Brno, Czech Republic

    Zdenek Biolek

Authors
  1. Dalibor Biolek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zdenek Biolek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dalibor Biolek .

Editor information

Editors and Affiliations

  1. Faculty of Electrical and Computer Engineering, Institute of Circuits and Systems, Technische Universität Dresden, Dresden, Germany

    Ronald Tetzlaff

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

Biolek, D., Biolek, Z. (2014). Fourth Fundamental Circuit Element: SPICE Modeling and Simulation. In: Tetzlaff, R. (eds) Memristors and Memristive Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9068-5_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-9068-5_4

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-9067-8

  • Online ISBN: 978-1-4614-9068-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation