Modeling and Simulation of Memristor using SPICE Model

Asian Journal of Applied Science and Technology (AJAST)
Volume 1, Issue 2, Pages 31-35, March 2017
© 2017 AJAST All rights reserved. www.ajast.net
Page | 31
Modeling and Simulation of Memristor using SPICE Model
J.Jayarahini1
and M.Udhayavani2
1
PG Student, Department of ECE, Vivekanandha College of Engineering for Women, India. Email: rahinijai6@gmail.com
2
Assistant Professor, Department of ECE, Vivekanandha College of Engineering for Women, India. Email: udhayavani21@gmail.com
Article Received: 20 February 2017 Article Accepted: 28 February 2017 Article Published: 02 March 2017
1. INTRODUCTION
In circuit theory there are three basic two-terminal devices
namely-resistor, capacitor, and inductor. These elements are
defined by the relation between two of the four fundamental
circuit variables- current i, voltage v, charge q and fluxφ,
where the time derivative of charge q is current i and
according to Faradays laws voltage v is the time derivative of
fluxφ. The resistor is defined with the relation between the
voltage v and current i as dv = Rdi. The capacitor is defined
with the relation between the charge q and voltage v is
expressed as dq=Cdv. The inductor is defined with the
relation between the flux φ and current i as dφ = Ldi. The
discovery of the existence of the fourth fundamental circuit
element came to light in 1971 when Prof. Leon Chua
proposed the missing relation between charge q and the flux φ
through symmetry in figure 1 [1].
Fig.1. The four fundamental two-terminal circuit elements
Leon Chua named the element as memristor, which is the
short for memory resistor. The memristor has a memristance
M and the functional relation between flux φ and charge q is
given by dφ=Mdq. The already known passive two-terminal
devices are the basic building blocks of modern electronics
and are therefore ubiquitous in circuits. But we know that
though some elements store information they eventually
decay out. Even if the state of one element changes, the
information about the new state would be lost once the power
is turned on and wait sometime. This basic point may seem
irrelevant but fundamentally this is very crucial. The capacity
to store information without the need of a power source would
represent a paradigm change.
2. BASIC MEMRISTOR PROPERTIES
The memristor based on a lean film of titanium oxide has been
presented as an approximately ideal device. Since then a large
deal of efforts has been spent in the research community to
study the manufacture and characteristics of memristors. The
name Memristor itself indicates its functioning as a resistor
having memory of its previous condition. From the
circuit-theoretic top of view, the three basic two-terminal
circuit elements are defined in terms of a relationship between
two of the four fundamental circuit variables. Out of the six
possible combinations of these our variables, five have led to
well-known relationships. Three other relationships are given,
respectively, by the axiomatic definition of the three classical
circuit elements, namely, the resistor, the inductor and the
capacitor as stated in Table 1. Only one relationship remains
undefined, the relationship between φ and q. It is nothing but
the memristance.
Table 1. Fundamental Variables of Electrical Circuits
Sl. No. Definition Equation
1 Voltage (v) dφ = vdt
2 Current (i) dq = idt
3 Resistance (R) dv = Rdi
4 Capacitance (C) dq = Cdv
5 Inductance (L) dφ = Ldi
6 Memristance (M) dφ = Mdq
ABSTRACT
In evolution of memory technology the invention of memristor has colossal impact. It is the memory with resistor as its name indicates its function.
The development of memristor as the non-volatile memory device replaces the flash memory and for this reason it is compared to flash memory for
the better understanding of the memristor. The demand for high scalability, speed and endurance, the CMOS technology has limitation for the current
lithography technology. As the result it is hard to supply the increasing demand for the non-volatile memory with high density. The only hope for the
semiconductor industry is memristor by easier way to increase storage density. These larger storage density The increasing demand for high capacity
,high speed and lower priced acts as the force for the research in this field. The performance and the proposing innovation towards the development
of the memristor is simulated using the LTspice for new technology.
Keywords: Memristor and LTspice.

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3. ORIGIN OF MEMRISTORS
Leon Chua noted that there are six different mathematical
relations connecting pairs of the four fundamental circuit
variables current i, voltage v, charge q and flux φ. The relation
between these variable is deduced from Faradays law of
Induction. A resistor is defined by the relationship between
voltage v and current I (do = Rid), the capacitor is defined by
the relationship between charge q and voltage v (dq = Cdv)
and the inductor is defined by the relationship between flux φ
and current i dφ = Ldi. In addition, the current i is defined as
the time derivative of the charge q and according to Faradays
law, the voltage v is defined as the time derivative of the flux
φ. This relation is shown in the figure 2 [2].
According to this theory all matter consists of earth, water, air
and fire. Each of these elements exhibits two of the four
fundamental properties moistness, dryness, coldness and
hotness. So depending on the above theory he saw a striking
resemblance and predicted the existence of the fourth kind of
element and called it memristor. The physical memristor
device is essentially an a.c device, or else the d.c
electromagnetic fields would give rise to non-negligible
zero-order fields.
Fig.2.The Relation between the Circuit Elements
4. DEFINITION OF MEMRISTOR
Memristor is a contraction of memory resistor because its
main function is to remember its history. The memristor is a
two-terminal device whose resistance depends on the
magnitude and polarity of the voltage applied to it and the
length of the time that voltage has been applied. When this
voltage is turned off the memristor remembers its most recent
resistance until the next time you turn it on. The simple model
of this is as shown in figure3 [3].
Fig.3. Simple Model of Memristor
Memristor is either said to be a charge controlled or a flux
controlled depending upon the relation between the flux φ and
the charge q as a function of the other. For a charge controlled
memristor the relation between flux and charge is expressed
as a function of electric charge q [2],
) (1)
By differentiating (1) we get,
(2)
(3)
(4)
(5)
For a flux controlled memristor the relation between flux and
charge is expressed as a function of flux linkage φ [2],
(6)
(7)
(8)
5. CHARACTERISTICS OF MEMRISTORS
5.1 I-V characteristics
An important characteristic of a memristor is the pinched
hysteresis loop current- voltage characteristics [2]. For a
memristor excited by a periodic signal, when the voltage v(t)
is 0, the current i(t) is zero and vice versa. If any device has
the above characteristics, then the device is either a memristor
or a memristive device. The characteristics are as shown in
figure 4[7].
Fig.4. The Pinched Hysteresis Loop
5.2 φ-q Characteristics of Memristor
One of the main characteristics of φ-q of a memristor is it is
monotonically increasing. The memristance M(q) is the slope
of the φ-q curve. Prof. Leon Chua postulated a passivity
criterion, according to which a memristor is passive if and
only if the memristance M (q) is non-negative [5]. If M(q) 0,
then the instantaneous power dissipated by the memristor, p(i)
= M(q):[i(t)] 2, is always positive and so the memristor is a
passive device [6].The typical curves are as shown in figure 5.
Fig.5. The φ-q curve of Memristor

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6. LTSPICE MODEL OF MEMRISTOR
Biolek provided the Spice model of the memristor. Though
PSpice and LTSpice are similar in the nature of their analysis,
but even though there wasn’t any analysis done in LTSpice.
So I tried using LTSpice to be the basis of my simulation. The
listing for the LTSpice model is included in the appendix. The
model generated by me in LTSpice is as shown in figure 6.
The passing current from memristor in one way will increase
the resistance while changing the direction of the applied
current will decrease its memristance.
Fig.6. Symbol of the Memristor Model in LTSpice
The total resistance of the doped and undoped regions of a HP
memrister is given by,
(9)
(10)
Where x = w/D ε(0,1) is the thickness of the doped region,
referenced to the total length D of the TiO2 layer, and Roff
and Ron are the limit values of the memristor resistance for
w=0 and w=D. The ratio of the two resistances is given. The
speed of the movement of the boundary between the doped
and undoped regions depend on the resistance of the doped
area, on the passing current, and on other factors according to
the equation given by,
… (11)
… (12)
Where is the dopant mobility. As
mentioned in [9], in nanoscale devices, small voltages can
yield enormous electric fields, which can secondarily produce
significant nonlinearities in ionic transport. These non
linearities manifest themselves particularly at the thin film
edges, where the speed of boundary between the doped and
undoped regions gradually reduces to zero. This
phenomenon, called nonlinear dopant drift, can be modeled
by the so-called window function f(x).
6.1 Different Types of Window Function
1) Jogelkar window
2) Biolek window
3) Strukov window
4) Prodromakis window
5) Kvatinsky window
7. SIMULATION RESULTS-USING LTSPICE MODEL
For the simulation of the memristor for its desired
characteristics, the width D of the TiO2 film is considered to
be 10nm and the dopant mobility. The values assumed for
Ron = 100Ω, Roff = 16k Ω and the initial resistance Rinit =
11k ΩD=10N, uv=10F, p=10. The circuit symmetry is shown
in figure. The simulation results are shown in figure 10 and
figure 11 Parameter details for Transient Non-Linear Domain
Analysis Ron=100Ω, Roff=16KΩ, Rinit=11KΩ, D=10N,
uv=10F, p=10, Stop time = 3 seconds, Maximum time step =
3m.
Fig.7. Memristor Model Circuit
Fig.8. Input Voltage Applied to the Memristor
Input source voltage parameter details:
Ron=100Ω, Roff=16KΩ , Rinit=11KΩ, D=10N, uv=10F,
p=10, Sine wave with Amplitude = 1V, Frequency = 1Hz,
Time delay = 1 sec.
(a) (b)
Fig.9.(a) The Current through Memristor and (b)
Current-Verses-Voltage
Fig.10.Transient Non-Liner Time Domain Analysis Result of
a Memrister Model Using LT Spice

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Fig.11.Transient Non-Liner Analysis Result(a): F(1 Hz),
Td(0), A(1V)
Ron=100Ω, Roff=16KΩ , Rinit=11KΩ, D=10N, uv=10F,
p=10, Stop time = 3 seconds, maximum time step = 3m, Sine
wave with Amplitude = 1V, Frequency = 1Hz, with out any
time delay.
8. CONCLUSION
The impact that the memristor can have on the existing
technology is vast. This report presents the detail study of
memristors and also shows some worked out applications.
The memristor is modeled in LTSpice using the existing
model is proposed and plotted by the use of LTSpice.
Memristors has certainly showed a lot of promise and also has
the potential to be another milestone in the lane of evolution
of technology for superior. It was rightly said by Prof. Leon
Chua that all the engineering text books have to be re-written.
The future design of NV RAM design is implemented and
analyzed using LTSpice software.
Spice Model of a Non Linear Memristor Using LTspice
.SUBCKT memristor plus minus PARAMS
+ Ron=100 Roff=16K Rinit=11K D=10N uv=10F p=10
Differential Equation Modeling
Gx 0 x value={I(Emem)*uv*Ron/D**2*f(V(x),p)}
Cx x 0 1 IC={(Roff-Rinit)/(Roff-Ron)}
Raux x 0 1T
Resistive Port of The Memristor
Emem plus aux value={-I(Emem)*V(x)*(Roff-Ron)}
Roff aux minus {Roff}
Flux Computation
Eflux flux 0 value={SDT(V(plus,minus))}
Charge Computation
Echarge charge 0 value={SDT(I(Emem))}
For Non-Linear Drift Modeling
.func f(x,p)={1-(2*x-1)**(2*p)}
Proposed Jogelkar Window Function
.func f(x,i,p)={x(1-(2*x/(D-1))**(2*p))}
.ENDS memristor
//Another Reference Spice Model of a Mon Linear
Memrister with Various values of Ron, Roff and Window
Function codes using LTSpice
*Modified HP Memristor SPICE Model
**************************
* Ron, Roff - Resistance in ON / OFF States
* Rinit - Resistance at T=0
* D - Width of the thin film
* uv - Migration coefficient
* p - Parameter of the WINDOW-function
* for modeling nonlinear boundary conditions
REFERENCES
[1] Yasmin Halawani, Baker Mohammad, Dirar
Homouz,Mahmoud Al-Qutayri and Hani Saleh, “Modeling
and Optimization of Memristor and STT-RAM-Based
Memory for Low-Power Applications” June 2015 IEEE,
1063-8210.
[2] A.Kavehei.S. O, Kim.Y.S and Abbott.D, “The fourth
element: Characteristics, modelling, and electromagnetic
theory of the memristor”, in http:// arxiv.org/abs /1002.3210.
[3] Benderli.S and Wey.T.A, “On SPICE macromodelling of
TiO2 memristors”, in IET Electronics Lett., vol. 45, pp.
377-379, 2009.
[4] Biolek.D. B. Z and BiolkovaV, “Spice model of
memristor with nonlinear dopant drift”, in Radio engineering
J., vol. 18, 2009, pp. 210-214.
[5] Biolek.Z, Biolek.Dand Biolkova.V, “SPICE Model of
Memristor withNon-linear Dopant Drift”, in Radio
engineering, vol. 18, pp. 210-214, June 2009.
[6] Chua.L, “Memristor- the missing circiut element”, in
IEEE Trans. Circuit Theory, vol. CT-18, 1971, pp. 507519.
[7] Fano.L.C.R.M. (1960) and Adler.R, “Electromagnetic
fields, energy and forces”, in Proceedings of IEEE Congress
on Evolutionary Computation (CEC-2002), New York,
USA.,
[8] Joglekar.Y and Wolf.S, “The elusive memristor:
properties of basic electrical circuits”, in arXiv:0807.3994,
vol. 2, 2009, pp. 1-24.
[9] Joglekar.Y.Nand Wolf.S.J, “The Elusive Memristor:
Properties of Basic Electrical Circuits”, in European Journal
of Physics, vol. 30, pp. 661-675, 2009.
[10] Kvatinsky.A.K.S, Friedman.E.G and Weiser.U,
“Memristor and related application”.
[11] Mahuash.A.C.P.M, “A memristor spice model for
designing memristor circuits”.
[12] http://nature.berkeley.edu/Memristor.pdf.

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[13] Strukov.D.B, Snider.G.S, Stewart.D.R and
Williams.R.S, “The Missing Memristor Found”, in Nature,
vol. 453, pp. 83-86, May 2008.
[14] Strukov.D.S.D.B, SniderG.Sand Williams.R, “The
missing memristor found”, in Nature, vol. 453, 2008, pp.
80-83.
[15] Williams.R, (2008), “How we found the missing
memristor”, in IEEE Spectrum, vol. 45, pp. 2835.

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