J. Semicond. > Volume 38 > Issue 11 > Article Number: 114008

Electro-magnetic interpretation of four-element torus

Wei Wu and Ning Deng ,

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Abstract: The concept of the memristor was proposed by Leon Chua in 1971, along with some electro-magnetic interpretations according to quasi-static expansion of Maxwell’s equations. In 2003, Chua included the memristor into a four-element torus that has infinite circuit elements. This paper uses the quasi-static method to interpret every circuit element in the torus. Two examples are also provided to show how topologic structure of an element affects its electrical properties by affecting the dominant electro-magnetic field components. Additionally, it is proved that the circuit elements in the torus, except the resistive, capacitive and inductive elements, cannot exist independently. Moreover, the incorrectness in Chua’s interpretation of the memristor, that the memristor cannot be interpreted with the transient quasi-static method due to its memory property, is pointed out. Finally, the limitations of the electro-magnetic interpretation method are discussed.

Key words: electro-magnetic interpretationfour-element torusmemristorquasi-static expansion of Maxwell’s equations

Abstract: The concept of the memristor was proposed by Leon Chua in 1971, along with some electro-magnetic interpretations according to quasi-static expansion of Maxwell’s equations. In 2003, Chua included the memristor into a four-element torus that has infinite circuit elements. This paper uses the quasi-static method to interpret every circuit element in the torus. Two examples are also provided to show how topologic structure of an element affects its electrical properties by affecting the dominant electro-magnetic field components. Additionally, it is proved that the circuit elements in the torus, except the resistive, capacitive and inductive elements, cannot exist independently. Moreover, the incorrectness in Chua’s interpretation of the memristor, that the memristor cannot be interpreted with the transient quasi-static method due to its memory property, is pointed out. Finally, the limitations of the electro-magnetic interpretation method are discussed.

Key words: electro-magnetic interpretationfour-element torusmemristorquasi-static expansion of Maxwell’s equations



References:

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[2]

Ho P W C, Almurib H A F, Kumar T N. Memristive SRAM cell of seven transistors and one memristor[J]. J Semicond, 2016, 37(10): 104002. doi: 10.1088/1674-4926/37/10/104002

[3]

You Z, Hu F, Huang L. A long lifetime, low error rate RRAM design with self-repair module[J]. J Semicond, 2016, 37(11): 115004. doi: 10.1088/1674-4926/37/11/115004

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Jo S H, Chang T, Ebong I. Nanoscale memristor device as synapse in neuromorphic systems[J]. Nano Lett, 2010, 10(4): 1297. doi: 10.1021/nl904092h

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Kim H, Sah M P, Yang C. Neural synaptic weighting with a pulse-based memristor circuit[J]. IEEE Trans Circuits Syst I, 2012, 59-I(1): 148.

[7]

Shinde S S, Dongle T D. Modelling of nanostructured TiO2-based memristors[J]. J Semicond, 2015, 36(3): 034001.

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Biolek Z, Biolek D, Biolkova V. SPICE Model of Memristor with Nonlinear Dopant Drift[J]. Radioengineering, 2009, 18(2): 210.

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Kumar A, Baghini M S. Experimental study for selection of electrode material for ZnO-based memristors[J]. Electron Lett, 2014, 50(21): 1547. doi: 10.1049/el.2014.1491

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Ho P W C, Hatem F O, Almurib H A F. Comparison between Pt/TiO2/Pt and Pt/TaOX/TaOY/Pt based bipolar resistive switching devices[J]. J Semicond, 2016, 37(6): 064001. doi: 10.1088/1674-4926/37/6/064001

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Chua L O. Device modeling via nonlinear circuit elements[J]. IEEE Trans Circuits Syst, 1980, 27(11): 1014. doi: 10.1109/TCS.1980.1084742

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Chua L O. Resistance switching memories are memristors[J]. Appl Phys A, 2011, 102(4): 765.

[1]

Chua L O. Memristor—the missing circuit element[J]. IEEE Trans Circuit Theory, 1971, 18(5): 507. doi: 10.1109/TCT.1971.1083337

[2]

Ho P W C, Almurib H A F, Kumar T N. Memristive SRAM cell of seven transistors and one memristor[J]. J Semicond, 2016, 37(10): 104002. doi: 10.1088/1674-4926/37/10/104002

[3]

You Z, Hu F, Huang L. A long lifetime, low error rate RRAM design with self-repair module[J]. J Semicond, 2016, 37(11): 115004. doi: 10.1088/1674-4926/37/11/115004

[4]

Kokate P P. Memristor-based chaotic circuits[J]. IETE Techn Rev, 2009, 26(6): 417. doi: 10.4103/0256-4602.57827

[5]

Jo S H, Chang T, Ebong I. Nanoscale memristor device as synapse in neuromorphic systems[J]. Nano Lett, 2010, 10(4): 1297. doi: 10.1021/nl904092h

[6]

Kim H, Sah M P, Yang C. Neural synaptic weighting with a pulse-based memristor circuit[J]. IEEE Trans Circuits Syst I, 2012, 59-I(1): 148.

[7]

Shinde S S, Dongle T D. Modelling of nanostructured TiO2-based memristors[J]. J Semicond, 2015, 36(3): 034001.

[8]

Biolek Z, Biolek D, Biolkova V. SPICE Model of Memristor with Nonlinear Dopant Drift[J]. Radioengineering, 2009, 18(2): 210.

[9]

Kumar A, Baghini M S. Experimental study for selection of electrode material for ZnO-based memristors[J]. Electron Lett, 2014, 50(21): 1547. doi: 10.1049/el.2014.1491

[10]

Ho P W C, Hatem F O, Almurib H A F. Comparison between Pt/TiO2/Pt and Pt/TaOX/TaOY/Pt based bipolar resistive switching devices[J]. J Semicond, 2016, 37(6): 064001. doi: 10.1088/1674-4926/37/6/064001

[11]

Ventra M D, Pershin Y V, Chua L O. Circuit elements with memory: memristors, memcapacitors, andmeminductors[J]. Proc IEEE, 2009, 97(10): 1717. doi: 10.1109/JPROC.2009.2021077

[12]

Wang F Z. A triangular periodic table of elementary circuit elements[J]. IEEE Trans Circuits Syst I, 2013, 60(3): 616. doi: 10.1109/TCSI.2012.2209734

[13]

Chua L O. Nonlinear circuit foundations for nanodevices I: the four-element torus[J]. Proc IEEE, 2003, 9(11): 1830. doi: 10.1109/JPROC.2003.818319

[14]

Chua L O. Device modeling via nonlinear circuit elements[J]. IEEE Trans Circuits Syst, 1980, 27(11): 1014. doi: 10.1109/TCS.1980.1084742

[15]

Fano R M, Chu L J, Adler R B. Electromagnetic fields, energy, and forces[J]. Wiley, 1960: 122.

[16]

Chua L O. Resistance switching memories are memristors[J]. Appl Phys A, 2011, 102(4): 765.

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W Wu, N Deng. Electro-magnetic interpretation of four-element torus[J]. J. Semicond., 2017, 38(11): 114008. doi: 10.1088/1674-4926/38/11/114008.

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History

Manuscript received: 24 February 2017 Manuscript revised: 08 May 2017 Online: Uncorrected proof: 30 October 2017 Accepted Manuscript: 13 November 2017 Published: 01 November 2017

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