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Cited by 639Advanced Memory and Neural ComputingAnalog and Mixed-Signal Circuit DesignFerroelectric and Negative Capacitance Devices

Practical Approach to Programmable Analog Circuits With Memristors

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Pershin, Yuriy V., Di Ventra, Massimiliano·2010·IEEE Transactions on Circuits and Systems I: Regular Papers
DOI 10.1109/tcsi.2009.2038539
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Abstract

We suggest an approach to use memristors (resistors with memory) in programmable analog circuits. Our idea consists in a circuit design in which low voltages are applied to memristors during their operation as analog circuit elements and high voltages are used to program the memristor's states. This way, as it was demonstrated in recent experiments, the state of memristors does not essentially change during analog mode operation. As an example of our approach, we have built several programmable analog circuits demonstrating memristor-based programming of threshold, gain and frequency. In these circuits the role of memristor is played by a memristor emulator developed by us.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper proposes using memristors in programmable analog circuits by keeping analog-operation voltages below a threshold and using high-voltage pulses to program memristance. It demonstrates the idea with a memristor emulator in programmable threshold, gain, Schmitt-trigger, and relaxation-oscillator circuits.

Key findings

  • Low-voltage analog operation plus high-voltage programming makes a memristor behave like a digital potentiometer: below the threshold \(V_T\), memristance changes extremely slowly, while above \(V_T\) it changes quickly.
  • The authors built a memristor emulator with resistance range \(50\ \Omega < R < 10\ \text{k}\Omega\), 256 steps, characteristic frequency \(\lesssim 50\ \text{Hz}\), and maximum continuous current \(\pm 11\ \text{mA}\); its I-V curves show pinched hysteresis and frequency-dependent hysteresis.
  • In a programmable threshold comparator, each 10 ms programming pulse changed \(R_M\) by approximately \(430\ \Omega\), lowering the comparator threshold and widening output pulses.
  • In a programmable gain amplifier, the gain changed approximately from 2 to 11; 10 ms pulses gave finer control and 20 ms pulses gave coarser control. Programming also changed Schmitt-trigger switching thresholds and relaxation-oscillator frequency.

Methods

  • Circuit design: a memristor-based digital potentiometer uses two FETs and external control signals \(V_{pp}\), \(V_{pn}\) to apply programming voltages \(\pm V_{pr}\) above the memristor threshold \(V_T\); during analog operation the FETs are off and voltages are kept below \(V_T\).
  • Emulator implementation: a digital potentiometer AD5206 (256 positions, \(10\ \text{k}\Omega\)) is updated by a dsPIC30F2011 microcontroller with internal 12-bit ADC, implementing a voltage-controlled memristive model with \(\alpha=0\), \(\beta=62\ \text{k}\Omega/\text{V}\cdot\text{s}\), \(V_T=1.75\ \text{V}\), \(R_{\min}=1\ \text{k}\Omega\), and \(R_{\max}=10\ \text{k}\Omega\).
  • Validation and demonstrations: I-V curves were obtained with \(V(t)=V_0\sin(2\pi ft)\), \(V_0=2.3\ \text{V}\), and \(R_0=100\ \Omega\); the analog circuits used an operational amplifier TLV2770 powered by \(\pm 2.5\ \text{V}\), with \(R_1=10\ \text{k}\Omega\), \(C_1=0.1\ \mu\text{F}\), and \(C=10\ \mu\text{F}\) in the relaxation oscillator.

Limitations

  • Stated: at low voltages the memristance can still drift over long times; this is difficult to estimate because of limited experimental data, but can be reduced by lower voltages and corrected by periodic resetting or circuit calibration.
  • Stated: programming precision requires sufficient knowledge of the memristor model and parameters, reproducibly operating memristors, or precise pulse amplitude/duration and calibration; TiO\(_2\) thin films show significant noise in hysteresis curves, and colossal magnetoresistive films may be more suitable for analog-mode applications.
  • Stated/evident: the demonstrations use a memristor emulator, not a solid-state memristor, because memristors were not yet available on the market; the emulator itself is limited to \(50\ \Omega\)–\(10\ \text{k}\Omega\), 256 steps, \(\lesssim 50\ \text{Hz}\), and \(\pm 11\ \text{mA}\).

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1109/tcsi.2009.2038539

Cites

37 of 37 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 6 cited sources checked · 0 supported · 0 flagged

  • Findingown data
    § D. Programmable frequency relaxation oscillator · p. 6

    In the programmable frequency relaxation oscillator, a decrease of the memristor resistance R_M results in an increase of the relaxation oscillator frequency.

    “Fig. 7b demonstrates that a decrease of the memristor resistance R M results in an increase of the relaxation oscillator frequency.”
    Quote in the paperSubstantial claim
  • Findingown data
    § B. Programmable gain amplifier · p. 5

    Longer programming pulses produce larger changes in R_M, allowing for coarser control of the gain.

    “We demonstrate in Fig. 5c that longer pulses produce larger changes in R M allowing for coarser control of the gain.”
    Quote in the paperSubstantial claim
  • Findingreasoning
    § III. MEMRISTOR EMULATOR · p. 4

    The ADC sampling frequency of 1 kHz limits the characteristic frequency of signals applied to the memristor emulator to approximately 50 Hz.

    “The ADC sampling frequency of 1kHz limits the characteristic frequency of signals applied to memristor to approximately 50Hz (20 points per period are reasonably enough to simulate a real memristor response).”
    Quote in the paperNot a substantial claim
  • Findingown data
    § B. Programmable gain amplifier · p. 5

    In the programmable gain amplifier experiment, the circuit gain changes approximately from 2 to 11 for the selected memristor parameters.

    “For the selected memristor parameters, the circuit gain changes approximately from 2 to 11.”
    Quote in the paperSubstantial claim
  • Findingown data
    § A. Programmable threshold comparator · p. 5

    Each 10 ms voltage pulse changes R_M by approximately 430 Ω in the programmable threshold comparator experiment.

    “Each 10ms voltage pulse changes R M by approximately 430 Ω causing a gradual decrease of the comparator threshold.”
    Quote in the paperNot a substantial claim
  • May combine two claims. 10
  • Classified as probably not a substantial claim. 2
  • The quote only partly states this claim. 1

  • May combine two claims.

    Findingown data
    § A. Programmable threshold comparator · p. 4

    In the programmable threshold comparator experiment, application of a train of negative pulses between 4 and 8 seconds re-programs the memristor state by lowering the comparator threshold, observed as smaller V- and wider output pulses.

    “The application of a train of negative pulses in the time interval between 4 and 8 seconds re-programs the memristor state by lowering the comparator threshold. This can be observed in a smaller V -and wider output pulses starting at t = 8 s.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § V. DISCUSSION AND CONCLUSION · p. 7

    This parasitic drift effect becomes less important at low voltages applied to the memristor and can be corrected by periodic re-setting of R_M or/and circuit calibration.

    “However, this parasitic effect becomes less important at low voltages applied to the memristor and, in practice, can be corrected by periodic re-setting of R M or/and circuit calibration.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationcitation
    § V. DISCUSSION AND CONCLUSION · p. 7

    The rate of memristance change at low voltages is very small as observed in certain experiments, but it can eventually lead to a drift of R_M at long times.

    “although the rate of memristance change at low voltages is very small as observed in certain experiments [10], it can eventually lead to a drift (increase or decrease depending on particular application scheme) of R M at long times.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [10] [10] J. J. Yang, M. D. Pickett, X. Li, D. A. A. Ohlberg, D. R. Stewart, and R. S. Williams, 'Memristive switching mechanism for metal/oxide/metal nanodevices,' Nat. Nanotechnol. , vol. 3, no. 7, pp. 429-433, 2008. -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Interpretationown data
    § V. DISCUSSION AND CONCLUSION · p. 7

    A memristor with a control scheme provides a simple realization of digital potentiometers and can find useful and broad-range applications in electronics.

    “We have thus shown that a memristor with a control scheme provides a simple realization of digital potentiometers and, therefore, can find useful and broad-range applications in electronics.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § V. DISCUSSION AND CONCLUSION · p. 7

    The memristor emulator uses inexpensive off-the-shelf components and can be built easily in any electronic lab.

    “The latter is a scheme that uses inexpensive off-the-shelf components and can, therefore, be built quite easily in any electronic lab.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § B. Programmable gain amplifier · p. 5

    In the programmable gain amplifier, the gain is determined by the value of memristance R_M, which can be programmed between R_min and R_max.

    “is determined by the value of memristance R M which can be selected (programmed) between two limiting values R min and R max using two field-effect transistors (FETs).”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductnone given
    § A. Programmable threshold comparator · p. 4

    In all practical examples, the maximum voltage drop on the memristor is always smaller than the threshold voltage of the memristor, selected to be 1.75 V.

    “In all our practical examples we build a scheme in such a way that the maximum voltage drop on memristor is always smaller than the threshold voltage of memristor which was selected to be equal to 1.75V.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § B. Memristors in programmable analog circuits · p. 2

    The rate of memristance change depends essentially on the magnitude of applied voltage: below a threshold it is extremely slow, above the threshold it is fast.

    “the rate of memristance change depends essentially on the magnitude of applied voltage [9], [10]. At voltages below a certain threshold, the change of memristance is extremely slow, whereas at voltages above the threshold, V T , it is fast.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [9] [9] S. Liu, N. Wu, and A. Ignatiev, 'Electric-pulse-induced reversible resistance change effect in magnetoresistive films,' Appl. Phys. Lett. , vol. 76, no. 19, pp. 2749-2751, 2000. -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [10] [10] J. J. Yang, M. D. Pickett, X. Li, D. A. A. Ohlberg, D. R. Stewart, and R. S. Williams, 'Memristive switching mechanism for metal/oxide/metal nanodevices,' Nat. Nanotechnol. , vol. 3, no. 7, pp. 429-433, 2008. -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Premisecitation
    § I. INTRODUCTION · p. 1

    Experimentally realizable memristors are not ideal; they belong to the general class of memristive systems.

    “However, experimentally realizable memristors [10] are not ideal. In fact, these devices belong to the much more general class of memristive systems [3]”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [10] [10] J. J. Yang, M. D. Pickett, X. Li, D. A. A. Ohlberg, D. R. Stewart, and R. S. Williams, 'Memristive switching mechanism for metal/oxide/metal nanodevices,' Nat. Nanotechnol. , vol. 3, no. 7, pp. 429-433, 2008. -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [3] [3] L. O. Chua and S. M. Kang, 'Memristive devices and systems,' Proc. IEEE , vol. 64, no. 2, pp. 209-223, 1976. -

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims. The quote only partly states this claim.

    Interpretationreasoning
    § A. Programmable threshold comparator · p. 4

    In the programmable threshold comparator, the comparator threshold is determined by the voltage on the memristor, which depends on R_M and R1.

    “In the programmable threshold comparator circuit, the comparator threshold is determined by the voltage on the memristor given by”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given
    § III. MEMRISTOR EMULATOR · p. 4

    The model given by Eq. (8) contains all important physics of solid-state memristive devices whose behavior derives from activation-type processes.

    “The model we employ (given by Eq. (8)) is quite simple. However, it contains all important physics of solid-state memristive devices whose behavior derives from activation-type processes.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning
    § D. Programmable frequency relaxation oscillator · p. 6

    The decrease of the switching threshold results in a faster capacitor charging time, and via this mechanism the memristor-based digital potentiometer determines the frequency of oscillations.

    “As it is demonstrated in the upper panel of Fig. 7b, the decrease of the switching threshold results in a faster capacitor charging time (because now the capacitor has to charge to a smaller voltage). Via this mechanism, the memristorbased digital potentiometer then determines the frequency of oscillations.”
    Quote in the paperSubstantial claim
12 of 12

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The hysteresis curves demonstrate non-linear dependencies at lower frequencies, pinched hysteresis loops at intermediate frequencies, and linear behavior at higher frequencies.

    “The hysteresis curves demonstrate typical behavior of memory elements 1 : non-linear dependencies at lower frequencies, pinched hysteresis loops at intermediate frequencies and linear behavior at higher frequencies.”

    From Bistable Nonvolatile Elastic-Membrane Memcapacitor Exhibiting a Chaotic Behavior (2011) · cites this paper as [1]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Input variable is called the initial state

    Minor

    The paper defines u(t) as an input variable and x as the internal state variables, but then calls u(t=t0) the initial state for Eq. (2).

1 of 1

Cites

Flagged first, then by citations

Research works printed but not linked: 1

  1. biolek, 2009, spice model of memristor with nonlinear dopant drift, Radioengineering, 18, 210

Cited by

Sorted by citations

Authors
Pershin, Y. V., & Di Ventra, M.
Affiliations
University of South Carolina (US)
ORCID
Pershin, Yuriy V.
Venue
IEEE Transactions on Circuits and Systems I: Regular Papers
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Published
2010-08
Volume
57
Issue
8
Pages
1857-1864
ISSN
  • 1549-8328 (ISSN-L)
  • 1558-0806
DOI
10.1109/tcsi.2009.2038539
OpenAlex
W2141071915
Semantic Scholar
91684011ce1f18ad6774cac7e21f9a87197d07da
Cited by
639
References
37
Citations by year
2026: 12 · 2025: 18 · 2024: 29 · 2023: 27 · 2022: 47 · 2021: 32 · 2020: 31 · 2019: 41 · 2018: 45 · 2017: 49 · 2016: 44 · 2015: 42 · 2014: 63 · 2013: 55 · 2012: 51
FWCI
40.09
Type
journal article
Language
en
Open access
Licence
ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html (vor)
Locations
  • IEEE Transactions on Circuits and Systems I Regular Papers (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Memory and Neural Computing
  • Physical Sciences › Engineering › Biomedical Engineering › Analog and Mixed-Signal Circuit Design
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Ferroelectric and Negative Capacitance Devices
Keywords
memristors, programmable analog circuits, memristor emulator, threshold control, gain control, frequency regulation, resistive switching

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