A Generic Model of Memristors With Parasitic Components
Abstract
In this paper, a generic model of memristive systems, which can emulate the behavior of real memristive devices is proposed. Non-ideal pinched hysteresis loops are sometimes observed in real memristive devices. For example, the hysteresis loops may deviate from the origin over a broad range of amplitude A and frequency f of the input signal. This deviation from the ideal case is often caused by parasitic circuit elements exhibited by real memristive devices. In this paper, we propose a generic memristive circuit model by adding four parasitic circuit elements, namely, a small capacitance, a small inductance, a small DC current source, and a small DC voltage source, to the memristive device. The adequacy of this model is verified experimentally and numerically with two thermistors (NTC and PTC) memristors.
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Pinched hysteresis loops provide the characteristic fingerprints of all memristors.
“Not only do pinched hysteresis loops provide the characteristic fingerprints of all memristors, they all behave in a similar fashion as a function of the frequency of the periodic excitations [21].”
From Everything You Wish to Know About Memristors But Are Afraid to Ask (2015) · cites this paper as [21]
At sufficiently high frequencies, the pinched hysteresis loops must tend to straight lines (whose slope depends on the amplitude of the exciting periodic waveform) for all Generic Memristors, or to a single-valued function (whose precise curve varies with the amplitude of the periodic input signals) in the v vs. i plane for all Extended Memristors.
“Moreover, at sufficiently high frequencies, the pinched hysteresis loops must tend to straight lines (whose slope depends on the amplitude of the exciting periodic waveform) for all Generic Memristors , or to a single-valued function (whose precise curve varies with the amplitude of the periodic input signals) in the v vs. i plane for all Extended Memristors [21], [5], [”
From Everything You Wish to Know About Memristors But Are Afraid to Ask (2015) · cites this paper as [21]
A voltage-controlled PTC thermistor can be modeled as a non-ideal Generic Memristor.
“Example 5.2 Positive-temperature coefficient (PTC) thermistor [6], [21] A voltage controlled PTC thermistor can be modeled as follow:”
From Everything You Wish to Know About Memristors But Are Afraid to Ask (2015) · cites this paper as [21]
Cites
Strukov, D. B., Snider, G. S., Stewart, D. R., & Williams, R. S. (2008) · Nature · doi:10.1038/nature06932 · Cited by 11,744 · see citing works
Memristor—The Missing Circuit Element
Chua, L. (1971) · IEEE Transactions on Circuit Theory · doi:10.1109/tct.1971.1083337 · Cited by 10,268 · cited 1× · see citing works
“The memristor was originally postulated by Leon Chua as the fourth basic circuit element in electrical circuits [2]–[4], and generalized in 1976 to a broader class of dynamical systems called memristive devices [5].”
BackgroundSelf-citationMemristive devices and systems
Chua, L. O., & Kang, S. M. (1976) · Proceedings of the IEEE · doi:10.1109/proc.1976.10092 · Cited by 2,604 · cited 2× · see citing works
“The memristor was originally postulated by Leon Chua as the fourth basic circuit element in electrical circuits [2]–[4], and generalized in 1976 to a broader class of dynamical systems called memristive devices [5].”
BackgroundSelf-citationResistance switching memories are memristors
Chua, L. (2011) · Applied Physics A · doi:10.1007/s00339-011-6264-9 · Cited by 1,434 · see citing works
Self-citationThree Fingerprints of Memristor
Adhikari, S. P., Sah, M. P., Kim, H., & Chua, L. O. (2013) · IEEE Transactions on Circuits and Systems I: Regular Papers · doi:10.1109/tcsi.2013.2256171 · Cited by 659 · cited 1× · see citing works
“The shape of the pinched hysteresis loop varies with frequency and shrinks to a single-valued function through the origin, as the frequency tends to infinity [6].”
BackgroundSelf-citationNanobatteries in redox-based resistive switches require extension of memristor theory
Valov, I., Linn, E., Tappertzhofen, S., Schmelzer, S., van den Hurk, J., Lentz, F., & Waser, R. (2013) · Nature Communications · doi:10.1038/ncomms2784 · Cited by 587 · see citing works
HODGKIN–HUXLEY AXON IS MADE OF MEMRISTORS
CHUA, L., SBITNEV, V., & KIM, H. (2012) · International Journal of Bifurcation and Chaos · doi:10.1142/s021812741230011x · Cited by 319 · see citing works
Self-citationDevice modeling via nonlinear circuit elements
Chua, L. (1980) · IEEE Transactions on Circuits and Systems · doi:10.1109/tcs.1980.1084742 · Cited by 277 · see citing works
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If it's pinched it's a memristor
Chua, L. (2014) · Semiconductor Science and Technology · doi:10.1088/0268-1242/29/10/104001 · Cited by 685 · see citing works
Self-citationEverything You Wish to Know About Memristors But Are Afraid to Ask
Chua, L. (2015) · Radioengineering · doi:10.13164/re.2015.0319 · Cited by 481 · see citing works
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- Authors
- Sah, M. P., Yang, C., Kim, H., Muthuswamy, B., Jevtic, J., & Chua, L.
- Affiliations
- University of Notre Dame (US)
- Jeonbuk National University (KR)
- Milwaukee School of Engineering (US)
- University of California, Berkeley (US)
- Venue
- IEEE Transactions on Circuits and Systems I: Regular Papers
- Published
- 2015-03
- Volume
- 62
- Issue
- 3
- Pages
- 891-898
- ISSN
- 1549-8328 (ISSN-L)
- 1558-0806
- OpenAlex
- W2033592371
- Cited by
- 98
- References
- 8
- Citations by year
- 2026: 3 · 2025: 10 · 2024: 8 · 2023: 12 · 2022: 10 · 2021: 7 · 2020: 5 · 2019: 8 · 2018: 12 · 2017: 8 · 2016: 8 · 2015: 6 · 2014: 1
- FWCI
- 5.46
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- IEEE Transactions on Circuits and Systems I Regular Papers (publishedVersion)
- Funders
- U.S. Air Force (FA9550-13-1-0136)
- Korean government (2013R1A2A2A01068683, 2012R1A1A2044078)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Memory and Neural Computing
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Electrical and Thermal Properties of Materials
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Ferroelectric and Negative Capacitance Devices
- Keywords
- memristors, parasitic components, NTC thermistor, PTC thermistors, small-signal modeling
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