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21-02-2010, 01:44 PM



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Memristor “ The Fourth Fundamental Circuit Element

Introduction

Currently known fundamental passive elements “ Resistors, Capacitors & Inductors.
Does a 4th passive element exist..
Leon O. Chua formulated Memristor theory in his paper Memristor-The Missing Circuit Element in 1971.
Memistors are passive two terminal circuit elements.
Behaves like a nonlinear resistor with memory.

History Of Memristor

Four fundamental circuit variables- current i, voltage v, charge q, and flux linkage f
Six possible combinations of these four variables
Five already defined as
Resistor(dv=Rdi), Capacitor(dq=Cdv), Inductor(df=Ldi), q(t)=i(T)dT, f(t)=v(T)dT
The 6th relation defines memristance as df=Mdq

So what is Memristance

Memristance is a property of an electronic component.
When charge flows in one direction, its resistance increases, and if direction is reversed, resistance decreases.
When v=0, charge flow stops & component will Ëœrememberâ„¢ the last resistance it had.
When the flow of charge regains, the resistance of the circuit will be the value when it was last active.

Memristor Theory

Two terminal device in which magnetic flux Fm between its terminals is a function of amount of electric charge q passed through the device.
M(q) = dFm/dq
M(q) = [dFm/dt] / [dq/dt] = V/I
V(t) = M(q(t))I(t)
The memristor is static if no current is applied.
If I(t)=0, then V(t)=0 and M(t) is a constant. This is the essence of the memory effect.

Physical analogy for a memristor

Resistor is analogous to a pipe that carries water.
Water(charge q), input pressure(voltage v), rate of flow of water(current i).
In case of resistor, flow of water is faster if pipe is shorter and/or has a larger diameter.
Memristor is analogous to a special kind of pipe that expands or shrinks when water flows through it
The pipe is directive in nature.
If water pressure is turned off, pipe will retain its most recent diameter, until water is turned back on.

Titanium dioxide memristor

On April 30, 2008, a team at HP Labs led by the scientist R. Stanley Williams announced the discovery of a switching memristor.
It achieves a resistance dependent on the history of current using a chemical mechanism.
The HP device is composed of a thin (5nm) Titanium dioxide film between two Pt electrodes.
Initially there are two layers, one slightly depleted of Oxygen atoms, other non-depleted layer.
The depleted layer has much lower resistance than the non-depleted layer.

Conclusion

The rich hysteretic v-i characteristics detected in many thin film devices can now be understood as memristive behaviour.
This behaviour is more relevant as active region in devices shrink to nanometer thickness.
It takes a lot of transistors and capacitors to do the job of a single memristor.
No combination of R,L,C circuit could duplicate the memristance.
So the memristor qualifies as a fundamental circuit element.
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25-03-2010, 08:53 AM

MEMRISTOR


ABSTRACT:


We are familiar with circuit elements which are three important elements
named as resistor, capacitor, and inductor. In 1971 leon chua developed a fourth fundamental element which is called MEMRISTOR.

MEMRISTOR is a short for memory resistor (memory + resistor).It is a two terminal passive circuit element maintain relationship between integral current and voltage and it saves the power too .The device is based on nanoscale systems to enable coupling between solidstate electronic and ionic transport under external bias voltage. Single MEMRISTOR can perform the same logic functions as multiple transistors, making them promise way to increase computer power. A single MEMRISTOR takes atleast dozen of transistors.

Implementation of MEMRISTOR can dramatically change the size and perform of existing circuits. It also reduce the booting time of pc .It can change resistance depending on amount and direction of the voltage applied and can remember its resistance even voltage is turned off. It is faster, smaller, more energy efficient alternative to flash storage.



By:
P.RAJITHA G.SHALINI
CSE 3RD YEAR CSE 3RD YEAR
ACE ENGG.COLLEGE ACE ENGG.COLLEGE
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INTRODUCTION

Generally when most people think about electronics, they may initially think of products such as cell phones, radios, laptop computers, etc. others, having some engineering background, may think of resistors, capacitors, etc. which are the basic components necessary for electronics to function. Such basic components are fairly limited in number and each having their own characteristic function.
Memristor theory was formulated and named by Leon Chua in a 1971 paper. Chua strongly believed that a fourth device existed to provide conceptual symmetry with the resistor, inductor, and capacitor. This symmetry follows from the description of basic passive circuit elements as defined by a relation between two of the four fundamental circuit variables. A device linking charge and flux (themselves defined as time integrals of current and voltage), which would be the memristor, was still hypothetical at the time. However, it would not be until thirty-seven years later, on April 30, 2008, that a team at HP Labs led by the scientist R. Stanley Williams would announce the discovery of a switching memristor. Based on a thin film of titanium dioxide, it has been presented as an approximately ideal device.
The reason that the memristor is radically different from the other fundamental circuit elements is that, unlike them, it carries a memory of its past. When you turn off the voltage to the circuit, the memristor still remembers how much was applied before and for how long. That's an effect that can't be duplicated by any circuit combination of resistors, capacitors, and inductors, which is why the memristor qualifies as a fundamental circuit element.
The arrangement of these few fundamental circuit components form the basis of almost all of the electronic devices we use in our everyday life. Thus the discovery of a brand new fundamental circuit element is something not to be taken lightly and has the potential to open the door to a brand new type of electronics. HP already has plans to implement memristors in a new type of non-volatile memory which could eventually replace flash and other memory systems.

HISTORY

The transistor was invented in 1925 but lay dormant until finding a corporate champion in BellLabs during the 1950s. Now another groundbreaking electronic circuit may be poised for the same kind of success after laying dormant as an academic curiosity for more than three decades. Hewlett-Packard Labs is trying to bring the memristor, the fourth passive circuit element after the resistor, and the capacitor the inductor into the electronics mainstream. Postulated in 1971, the memory resistor represents a potential revolution in electronic circuit theory similar to the invention of transistor.
The history of the memristor can be traced back to nearly four decades ago when in 1971, Leon Chua, a University of California, Berkeley, engineer predicted that there should be a fourth passive circuit element in addition to the other three known passive elements namely the resistor, the capacitor and the inductor. He called this fourth element a memory resistor or a memristor. Examining the relationship between charge, current, voltage and flux in resistors, capacitors, and inductors in a 1971 paper, Chua postulated the existence of memristor. Such a device, he figured, would provide a similar relationship between magnetic flux and charge that a resistor gives between voltage and current. In practice, that would mean it acted like a resistor whose value could vary according to the current passing through it and which would remember that
value even after the current disappeared.
Fig1. The Simplest Chuaâ„¢s Circuit. Fig2. Realization of Four Element Chuaâ„¢s Circuit, NR is Chua Diode. Fig3. Showing Memristor as Fourth Basic Element. But the hypothetical device was mostly written off as a mathematical dalliance. However, it took more than three decades for the memristor to be discovered and come to life. Thirty years after Chuaâ„¢s Proposal of this mysterious device, HP senior fellow Stanley Williams and his group were working on molecular electronics when they started to notice strange behavior in their devices. One of his HP collaborators, Greg Snider, then rediscovered Chua's work from 1971. Williams spent several years reading and rereading Chua's papers. It was then that Williams realized that their molecular devices were really memristors.

Fig1. The Simplest Chuaâ„¢s Circuit
Fig2. Realization of Four Element Fig3. Showing Memristor as Fourth
Chuaâ„¢s Circuit Basic Element

NEED FOR MEMRISTOR

A memristor is one of four basic electrical circuit components, joining the resistor, capacitor, and inductor. The memristor, short for memory resistor was first theorized by student Leon Chua in the early 1970s. He developed mathematical equations to represent the memristor, which Chua believed would balance the functions of the other three types of circuit elements.
The known three fundamental circuit elements as resistor, capacitor and inductor relates four fundamental circuit variables as electric current, voltage, charge and magnetic flux. In that we were missing one to relate charge to magnetic flux. That is where the need for the fourth fundamental element comes in. This element has been named as memristor.
Memristance (Memory + Resistance) is a property of an Electrical Component that describes the variation in Resistance of a component with the flow of charge. Any two terminal electrical component that exhibits Memristance is known as a Memristor. Memristance is becoming more relevant and necessary as we approach smaller circuits, and at some point when we scale into nano electronics, we would have to take memristance into account in our circuit models to simulate and design electronic circuits properly. An ideal memristor is a passive two-terminal electronic device that is built to express only the property of memristance (just as a resistor expresses resistance and an inductor expresses inductance). However, in practice it may be difficult to build a 'pure memristor,' since a real device may also have a small amount of some other property, such as capacitance (just as any real inductor also has resistance).A common analogy for a resistor is a pipe that carries water. The water itself is analogous to electrical charge, the pressure at the input of the pipe is similar to voltage, and the rate of flow of the water through the pipe is like electrical current. Just as with an electrical resistor, the flow of water through the pipe is faster if the pipe is shorter and/or it has a larger diameter. An analogy for a memristor is an interesting kind of pipe that expands or shrinks when water flows through it. If water flows through the pipe in one direction, the diameter of the pipe increases, thus enabling the water to flow faster. If water flows through the pipe in the opposite direction, the diameter of the pipe decreases, thus slowing down the flow of water. If the water pressure is turned off, the pipe will retain it most recent diameter until the water is turned back on. Thus, the pipe does not store water like a bucket (or a capacitor) “ it remembers how much water flowed through it.
Possible applications of a Memristor include Nonvolatile Random Access
Memory (NVRAM), a device that can retain memory information even after being switched off, unlike conventional DRAM which erases itself when it is switched off. Another interesting application is analog computation where a memristor will be able to deal with analog values of data and not just binary 1s and 0s.

Figure 4. Fundamental circuit Elements and Variables.

Types of Memristors:

¢ Spintronic Memristor
¢ Spin Torque Transfer Magneto resistance
¢ Titanium dioxide memristor
¢ Polymeric memristor
¢ Spin memristive systems
¢ Magnetite memristive systems
¢ Resonant tunneling diode memristor
Titanium Dioxide Memristor It is a solid state device that uses nano scale thin-ilms to produce a Memristor. The device consists of a thin titanium dioxide film (50nm) in between two electrodes (5nm) one Titanium and the other latinum. Initially, there are two layers to the titanium dioxide film, one of which has a slight depletion of oxygen atoms. The oxygen vacancies act as charge carriers and this implies that the depleted layer has a much lower resistance than the no depleted layer. When an electric field is applied, the oxygen vacancies drift, changing the boundary between the high-resistance and low-resistance layers. Thus the resistance of the film as a whole is dependent on how much charge has been passed through it in a particular direction, which is reversible by Changing the direction of current.


MEMRISTOR THEORY AND ITS PROPERTIES:
Definition of Memristor

The memristor is formally defined as a two-terminal element in which the magnetic flux Φm between the terminals is a function of the amount of electric charge q that has passed through the device.

Figure 5. Symbol of Memristor.
Chua defined the element as a resistor whose resistance level was based on the amount of charge that had passed through the memristor
Memristance
Memristance is a property of an electronic component to retain its resistance level even after power had been shut down or lets it remember (or recall) the last resistance it had before being shut off.
Theory
Each memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge.

Noting from Faraday's law of induction that magnetic flux is simply the time integral of voltage, and charge is the time integral of current, we may write the more convenient form

It can be inferred from this that memristance is simply charge-dependent resistance. . i.e. ,
V(t) = M(q(t))*I(t)
3
This equation reveals that memristance defines a linear relationship between current and voltage, as long as charge does not vary. Of course, nonzero current implies instantaneously varying charge. Alternating current, however, may reveal the linear dependence in circuit operation by inducing a measurable voltage without net charge movement as long as the maximum change in q does not cause much change in M.

Current vs. Voltage characteristics
This new circuit element shares many of the properties of resistors and shares the same unit of measurement (ohms). However, in contrast to ordinary resistors, in which the resistance is permanently fixed, memristance may be programmed or switched to different resistance states based on the history of the voltage applied to the memristance material. This phenomena can be understood graphically in terms of the relationship between the current flowing through a memristor and the voltage applied across the memristor.
In ordinary resistors there is a linear relationship between current and voltage so that a graph comparing current and voltage results in a straight line. However, for memristors a similar graph is a little more complicated as shown in Fig. 3 illustrates the current vs. voltage behavior of memristance.
In contrast to the straight line expected from most resistors the behavior of a memristor appear closer to that found in hysteresis curves associated with magnetic materials. It is notable from Fig. 3 that two straight line segments are formed within the curve. These two straight line curves may be interpreted as two distinct resistance states with the remainder of the curve as transition regions between these two states.

Figure-6. Current vs. Voltage curve demonstrating hysteretic effects of memristance.
Fig. 6 illustrates an idealized resistance behavior demonstrated in accordance
with Fig.7 wherein the linear regions correspond to a relatively high resistance (RH) and lowresistance (RL) and the transition regions are represented by straight lines.

Figure 7. Idealized hysteresis model of resistance vs. voltage for memristance switch.
Thus for voltages within a threshold region (-VL2<V<VL1 in Fig. 4) either a high or low resistance exists for the memristor. For a voltage above threshold VL1 the resistance switches from a high to a low level and for a voltage of opposite polarity above threshold VL2 the resistance switches back to a high resistance.

WORKING OF MEMRISTOR


Figure 8(a). Al/TiO2 or TiOX /Al Sandwich
The memristor is composed of a thin (5 nm) titanium dioxide film between two electrodes as shown in figure 5(a) above. Initially, there are two layers to the film, one of which has a slight depletion of oxygen atoms. The oxygen vacancies act as charge carriers, meaning that the depleted layer has a much lower resistance than the non-depleted layer. When an electric field is applied, the oxygen vacancies drift changing the boundary between the high-resistance and low-resistance layers.


POTENTIAL APPLICATIONS


Figure8(b).showing 17 memristors in a row
Thus the resistance of the film as a whole is dependent on how much charge has been passed through it in a particular direction, which is reversible by changing the direction of current. Since the memristor displays fast ion conduction at nanoscale, it is considered a nanoionic device .Figure 5(b) shows the final memristor component
Williams' solid-state memristors can be combined into devices called crossbar latches, which could replace transistors in future computers, taking up a much smaller area. They can also be fashioned into non-volatile solid-state memory, which would allow greater data density than hard drives with access times potentially similar to DRAM, replacing both components. HP prototyped a crossbar latch memory using the devices that can fit 100 gigabits in a square centimeter. HP has reported that its version of the memristor is about one-tenth the speed of DRAM. The devices' resistance would be read with alternating current so that they do not affect the stored value. Some patents related to memristors appear to include applications in programmable logic, signal processing, neural networks, and control systems. Recently, a simple electronic circuit consisting of an LC contour and a memristor was used to model experiments on adaptive behavior of unicellular organisms. It was shown that the electronic circuit subjected to a train of periodic pulses learns and anticipates the next pulse to come, similarly to the behavior of slime molds Physarum polycephalum subjected to periodic changes of environment. Such a learning circuit may find applications, e.g., in pattern recognition.


MEMRISTOR-THE FOURTH BASICCIRCUIT ELEMENT

From the circuit-theoretic point of view, the three basic two-terminal circuit elements are defined in terms of a relationship between two of the four fundamental circuit variables, namely;the current i, the voltage v, the charge q, and the flux-linkage cp.Out of the six possible combinations of these four variables, five have led to well-known relationships . Two of these relationships are already given by 9 Q(t) = ò ˆž
I (t) dt and O (t) = ò ˆž v(t) dt.
. Three other relationships are given, respectively, by the axiomatic definition of the three classical circuit elements, namely, the resistor (defined by a relationship between v and i), the inductor (defined by a relationship between cp and i), and the capacitor defined by a relationship between q and v). Only one relationship remains undefined, the relationship between o and q. From the logical as well as axiomatic points of view, it is necessary for the sake of completeness to postulate the existence of a fourth basic two-terminal circuit element which is characterized by a o-q curve. This element will henceforth be called the memristor because, as will be shown later, it behaves somewhat like a nonlinear resistor with memory. The proposed symbol of a memristor and a hypothetical o-q curve are shown in Fig. l(a). Using a ,mutated , a memristor with any prescribed o-q curve can be realized by connecting an appropriate nonlinear resistor, inductor, or capacitor across port 2 of an M-R mutated, an M-L mutated, and an M-C mutated, as shown in Fig. l(b), ©, and (d), respectively. These mutators, of which there are two types of each, are defined and characterized in Table I.3
Hence, a type-l M-R mutated would transform the VR -IR< curve of the nonlinear resistor f(VR, IR)=O into the corresponding o-q curve f(o,q)=O of a memristor. In contrast to this, a type-2 M-R mutated would transform the IR,VR curve of the nonlinear resistor f(IR,VR)=O into the corresponding o-q curve f(o,q) = 0 of a memristor. An analogous transformation is realized with an M-L mutated (M-C mutated) with respect to the ((oL,iL) or (iL, oL) [(vC, qC) or (qC, vC)] curve of a nonlinear inductor (capacitor).10 t
(a) Memristor and its o-q curve.
(b). Memristor basic realization 1: M-R mutated terminated by nonlinear Resistor R.
© Memristor basic realization 2: M-L mutated terminated by nonlinear inductor L
(d) Memristor basic realization M-C mutated
terminated by nonlinear capacitor C

FEATURES

The reason that the memristor is radically different from the other fundamental
circuit elements is that, unlike them, it carries a memory of its past. When you turn off the voltage to the circuit, the memristor still remembers how much was applied before and for how long. That's an effect that can't be duplicated by any circuit combination of resistors, capacitors, and inductors, which is why the memristor qualifies as a fundamental circuit element.
New 'Memristor' Could Make Computers Work like Human Brains
After the resistor, capacitor, and inductor comes the memristor. Researchers at HP Labs have discovered a fourth fundamental circuit element that can't be replicated by a11 combination of the other three. The memristor (short for "memory resistor") is unique because of its ability to, in HP's words, "[retain] a history of the information it has acquired." HP says the discovery of the memristor paves the way for anything from instant on computers to systems that can "remember and associate series of events in a manner similar to the way a human brain recognizes patterns." Such brain-like systems would allow for vastly improved facial or biometric recognition, and they could be used to make appliances that "learn from experience."
In PCs, HP foresees memristors being used to make new types of system memory that can store information even after they lose power, unlike today's DRAM. With memristor-based system RAM, PCs would no longer need to go through a boot process to load data from the hard drive into the memory, which would save time and power especially since users could simply switch off systems instead of leaving them in a "sleep" mode

Memristors Make Chips Cheaper

The first hybrid memristor-transistor chip could be cheaper and more energy efficient. Entire industries and research fields are devoted to ensuring that, every year,computers continue getting faster. But this trend could begin to slow down as the components used in electronic circuits are shrunk to the size of just a few atoms.Researchers at HP Labs in Palo Alto, CA, are betting that a new fundamental electronic component--the memristor--will keep computer power increasing at this rate for years to come.
They are nanoscale devices with unique properties: a variable resistance and the ability to remember the resistance even when the power is off.Increasing performance has
usually meant shrinking components so that more can be packed onto a circuit. But instead, Williams's team removes some transistors and replaces them with a smaller number of memristors. "We're not trying to crowd more transistors onto a chip or into a particular circuit," Williams says. "Hybrid memristor-transistor chips really have the promise for delivering a lot more performance."12 A memristor acts a lot like a resistor but with one big difference: it can change resistance depending on the amount and direction of the voltage applied and can remember its resistance even when the voltage is turned off. These unusual properties make them interesting from both a scientific and an engineering point of view. A single memristor can perform the same logic functions as multiple transistors, making them a promising way to increase computer power. Memristors could also prove to be a faster, smaller, more energy-efficient alternative to flash storage.

Memristor as Digital and Analog

A memristive device can function in both digital and analog forms, both having very diverse applications. In digital mode, it could substitute conventional solid-state memories (Flash) with high-speed and less steeply priced nonvolatile random access
memory (NVRAM). Eventually, it would create digital cameras with no delay between photos or computers that save power by turning off when not needed and then turning
back on instantly when needed.

No Need of Rebooting

The memristor's memory has consequences:The reason computers have to be rebooted every time they are turned on is that their logic circuits are incapable of holding their bits after the power is shut off. But because a memristor can remember voltages, a memristor-driven computer would arguably never need a reboot. You could leave all your Word files and spreadsheets open, turn off your computer, and go get a cup of coffee or go on vacation for two weeks, says Williams. When you come back, you turn on your computer and everything is instantly on the screen exactly the way you left it.that keeps memory powered. HP says memristor-based RAM could one day replace DRAM altogether.

FUTURE OF MEMRISTOR

Although memristor research is still in its infancy, HP Labs is working on a handful of practical memristor project and implimentations. And now Williams's team has demonstrated a
working memristor-transistor hybrid chip. "Because memristors are made of the same materials used in normal integrated circuits," says Williams, "it turns out to be very easy to integrate them with transistors." His team, which includes HP researcher Qiangfei Xia, built a field-programmable gate array (FPGA) using a new design that includes memristors made of the semiconductor titanium dioxide and far fewer transistors than normal.Engineers commonly use FPGAs to test prototype chip designs because they can
be reconfigured to perform a wide variety of different tasks. In order to be so flexible,
however, FPGAs are large and expensive. And once the design is done, engineers
generally abandon FPGAs for leaner "application-specific integrated circuits." "When
you decide what logic operation you want to do, you actually flip a bunch of switches and
configuration bits in the circuit," says Williams. In the new chip, these tasks are
performed by memristors. "What we're looking at is essentially pulling out all of the
configuration bits and all of the transistor switches," he says. According to Williams, using memristors in FPGAs could help significantly lower costs. "If our ideas work out, this type of FPGA will completely change the balance," he says. Ultimately, the next few years could be very important for memristor research.
Right now, "the biggest impediment to getting memristors in the marketplace is having [so few] people who can actually design circuits [using memristors]," Williams says. Still, he predicts that memristors will arrive in commercial circuits within the next three years.
When is it coming?
Researchers say that no real barrier prevents implementing the memristor in circuitry immediately. But it's up to the business side to push products through to commercial reality. Memristors made to replace flash memory (at a lower cost and lower 14 power consumption) will likely appear first; HP's goal is to offer them by 2012. Beyond that, memristors will likely replace both DRAM and hard disks in the 2014-to-2016 time frame. As for memristor-based analog computers, that step may take 20-plus years.

CONCLUSION

By redesigning certain types of circuits to include memristors, it is possible to obtain the same function with fewer components, making the circuit itself less expensive and significantly decreasing its power consumption. In fact, it can be hoped to combine memristors with traditional circuit-design elements to produce a device that does computation. The Hewlett-Packard (HP) group is looking at developing a memristor-based nonvolatile memory that could be 1000 times faster than magnetic disks and use much less power.
As rightly said by Leon Chua and R.Stanley Williams (originators of memristor), memrisrors are so significant that it would be mandatory to re-write the existing electronics engineering textbooks.
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ABSTRACT

Typically electronics has been defined in terms of three fundamental elements such as resistors, capacitors and inductors. These three elements are used to define the four fundamental circuit variables which are electric current, voltage, charge and magnetic flux. Resistors are used to relate current to voltage, capacitors to relate voltage to charge, and inductors to relate current to magnetic flux, but there was no element which could relate charge to magnetic flux.

This paper analyzes the fourth fundamental circuit element named ˜Memristor™ which had been proposed by a University of California, Berkeley engineer, Leon Chua in 1971, and has recently been developed by a group of researchers at Hewlett“Packard led by Stanley Williams. The paper studies the implications of the discovery of this new element and highlights its potential applications in the circuit design and computer technology.

To overcome this missing link, scientists came up with a new element called Memristor. These Memristor has the properties of both a memory element and a resistor (hence wisely named as Memristor). Memristor is being called as the fourth fundamental component, hence increasing the importance of its innovation.

Its innovators say memrisrors are so significant that it would be mandatory to re-write the existing electronics engineering textbooks.
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This article is presented by:
PRESENTED BY
Varun Thomas
S7 R
MEMRISTOR


INTRODUCTION
A fundamental circuit
A two terminal device
Relates to charge and flux

BASIC MEMRISTOR MODEL

Doped: region of low resistance
Undoped: region of high resistance
R off : Resistance when w/d=0
R on: Resistance when w/d=1

TYPES OF MEMRISTOR

Spintronic Memristor
Titanium dioxide Memristor

WORKING OF MEMRISTOR
Spintronic Memristor
Spin of electrons
Magnetism
Magneto resistance principal
Electrons flow alters the magnetization state

WORKING OF MEMRISTOR


Titanium dioxide Memristor
Two thin layer sandwich
First layer oxygen deficient
Oxygen vacancies control resistance














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Memristor – The Fourth Fundamental Circuit Element


Presented by :
Arun Kuriakose
Roll No : 11
S7-EE



Introduction

Currently known fundamental passive elements – Resistors, Capacitors & Inductors.
Does a 4th passive element exist..?
Leon O. Chua formulated Memristor theory in his paper “Memristor-The Missing Circuit Element” in 1971.
Memistors are passive two terminal circuit elements.
Behaves like a nonlinear resistor with memory.
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ABSTRACT
Typically electronics has been defined in terms of three fundamental elements such as resistors and inductors. These three elements are used to define the four fundamental circuit variables which are electrical current, voltage, charge and magnetic flux. Resistors are used to relate current to voltage, capacitors to relate voltage and charge, and inductor to relate current to magnetic flux, but there was no element which could relate charge to magnetic flux.
To overcome this missing link, scientists came up with a new element called Memristor. These Memristor has the properties of both a memory and a resistor (hence named as Memristor). Memristor is being called as the fourth fundamental component, hence increasing the importance of its innovation.
Its innovators say “Memristor are so significant that it would be mandatory to re-write the existing electronics textbooks”.
INTRODUCTION
Generally when most people think about electronics, they may initially think of products such as cell phones, radios, laptops, computes etc., others, having some electronics background, may think of resistors, capacitors etc., which are the basic components necessary for electronics function. Such basic components are fairly limited in number and each having their own characteristic function.
Memristor theory was formulated and named y Leon Chua in a 1971 paper. Chua strongly believed that a fourth device existed to provide conceptual symmetry with the resistor, inductor and capacitor. This symmetry follows from the description of basic passive circuit elements as defined by a relation between two of the four fundamental circuit variables. A device liking charge and flux (they defined as time integrals of current and voltage), which would be the memristor, was still hypothetical at the time. However, it would be until thirty- seven years later, on April 30, 2008, that a team at HP Labs led by the scientist R. Stanley Williams would announce the discovery of the switching memristor. Based on a thin film of titanium dioxide, it has been presented as an approximately ideal device.
The reason that the memristor is radically different from the other fundamental circuit elements is that, unlike them it carries a memory of its past. When you turn off the voltage to the circuit, the memristor still remembers how much was applied before and for how long. That’s an effect that can’t be duplicated by any circuit combination of resistors, capacitors, and inductors, which is why the memristor qualifies as a fundamental circuit element.
The arrangement of these few fundamental circuit components form the basis of almost all of the electronic devices we use in our everyday life. Thus the discovery of the brand new fundamental circuit element is something not to be taken lightly and has the potential to open the door to a brand new type of electronics. HP already has plans to implement memristor in a new type of non-volatile memory which could eventually replace flash and other memory systems.
NEED FOR MEMRISTOR
A memristor is one of four basic electrical components, joining the resistor, capacitor and inductor. The memristor short for “memory resistor” was first theorized by student Leon Chua in the early 1970s. He developed mathematical equations to represent the memristor, which Chua believed would balance the function of the other three types of circuit elements.
The known three fundamental circuit elements as resistor, capacitor and inductor relates four fundamental circuit variables as electric current, voltage, charge and magnetic flux. In that we were missing one to relate charge to magnetic flux. That is where the need for the fourth fundamental element comes in. This element has been named as memristor.
MEMRISTOR THEORY AND ITS APPLICATIONS
DEFINITION OF MEMRISTOR
“The memristor is formally defined as a two terminal element in which the magnetic flux ф¬¬m between the terminals is a function of the amount of electric charge q that has passed through the device.”


FIGURE 2 : MEMRISTOR SYMBOL
Chua defined the element as a resistor whose resistance level was based on the amount of charge that had passed through the memristor.
MEMRISTANCE
Memristance is a property of an electronic component to retain its resistance level even after power had been shut down or lets if remember (or recall) the last resistance it had before being shut off.
THEROY
Each memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge.


Noting from Faraday’s law of induction that magnetic flux is simply the time integral of voltage, and charge is the time integral of current, we may write the more convenient form



It can be inferred from this that memristance is simply charge-dependent resistance i.e.,


This equation reveals that memristance defines a linear relationship between current and voltage, as long as charge does not vary. Of course, nonzero current implies instantaneously varying charge. Alternating current however may reveal the linear dependence in circuit operation by inducing a measurable voltage without net charge movement – as the maximum change in q does not cause much change in M.
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Introduction
Memristor is a two terminal passive element which provide a similar relationship between magnetic flux and charge that a resistor gives between voltage and current. The magnetic flux Φm between the terminals is a function of the amount of electric charge q that has passed through the device.

It is characterized by its memristance function describing the charge-dependent rate of change of flux with charge. Memristance is a property of an electronic component. If charge flows in one direction through a circuit, the resistance of that component of the circuit will increase, and if charge flows in the opposite direction in the circuit, the resistance will decrease. If the flow of charge is stopped by turning off the applied voltage, the component will 'remember' the last resistance that it had, and when the flow of charge starts again the resistance of the circuit will be what it was when the voltage is turned off.

Memristors can be combined into devices called crossbar latches, which could replace transistors in future computers, taking up a much smaller area. They can also be fashioned into non-volatile solid-state memory, which would allow greater data density than hard drives with access times potentially similar to DRAM, replacing both components.

Passive Elements

Passive elements are those elements which are themselves not able to make any difference in signals applied to them. They are;

2.1 Resistor

A resistor is a two-terminal electronic component that opposes an electric current by producing a voltage drop between its terminals in proportion to the current, that is, in accordance with Ohm’s law:

V = IR.

The electrical resistance R is equal to the voltage drop V across the resistor divided by the current I through the resistor. The power dissipated by a resistor is the voltage across the resistor multiplied by the current through the resistor.

2.2Capacitor

A capacitor is an electrical/electronic device that can store energy in the electric field between a pair of conductors. The process of storing energy in the capacitor is known as "charging", and involves electric charges of equal magnitude, but opposite polarity, building up on each plate.

2.3 Inductor

An "ideal inductor" has inductance, but no resistance or capacitance, and does not dissipate energy. Inductance is an effect which results from the magnetic field that forms around a current-carrying conductor. Electric current through the conductor creates a magnetic flux proportional to the current. A change in this current creates a change in magnetic flux that, in turn, generates an electromotive force (EMF) that acts to oppose this change in current. Inductance is a measure of the amount of EMF generated for a unit change in current.


Memristor

Memristor is the fourth passive element which has created recently. It is characterized by its memristance function describing the charge-dependent rate of change of flux with charge. When the voltage to the circuit is turned off, the Memristor still remembers how much was applied before and for how long.


History of Memristor
We are aware of over 100 published papers going back to at least the early 1960's in which researchers observed and reported unusual 'hysteresis' in their current-voltage plots of various devices and circuits based on many different types of materials and structures. In retrospect, we can understand that those researchers were actually seeing memristance, but they were apparently not aware of it. Memristor postulated in a seminal 1971 paper in the IEEE Transactions on Circuit Theory by an Electrical Engineer Professor Leon Chua at the University of California, Berkeley. The hold-up over the last 37 years, according to professor Chua, has been a misconception that has pervaded electronic circuit theory. That misconception is that the fundamental relationship in passive circuitry is between voltage and charge.

Anyone familiar with electronics knows the trinity of fundamental components: the resistor, the capacitor, and the inductor. Professor Chua predicted that there should be a fourth element: a memory resistor, or Memristor. Such a device, he figured, would provide a similar relationship between magnetic flux and charge that a resistor gives between voltage and current. In practice, it will act like a resistor whose value could vary according to the current passing through it and which would remember that value even after the current disappeared. As, Professor Leon Chua pointed out in 1971, for the sake of the logical completeness of circuit theory; a fourth passive element should in fact be added to the list. He named this hypothetical element, linking flux and charge, the ‘Memristor’. But no one knew how to build one.

Building on their groundbreaking research in nanoelectronics, Stanley Williams (Senior Fellow, Information and Quantum Systems lab, HP Labs), and team are the first to prove the existence of the Memristor. They were the first to understand that the hysteresis that was being observed in the I-V curves of a wide variety of materials and structures was actually the result of memristance and something more general that can be called 'memristive behavior'. Then they went on to create an elementary circuit model that was defined by exactly the same mathematical equations as those predicted by Professor Chua for the Memristor, with the exception that this model had an upper bound to the resistance (which means that at large bias or long times, it is a memristive device).

Now, 37 years later, electronics have finally gotten small enough to reveal the secrets of that fourth element within the electrical characteristics of certain nanoscale devices.
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Introduction
Memristor is a two terminal passive element which provide a similar relationship between magnetic flux and charge that a resistor gives between voltage and current. The magnetic flux Φm between the terminals is a function of the amount of electric charge q that has passed through the device.

It is characterized by its memristance function describing the charge-dependent rate of change of flux with charge. Memristance is a property of an electronic component. If charge flows in one direction through a circuit, the resistance of that component of the circuit will increase, and if charge flows in the opposite direction in the circuit, the resistance will decrease. If the flow of charge is stopped by turning off the applied voltage, the component will 'remember' the last resistance that it had, and when the flow of charge starts again the resistance of the circuit will be what it was when the voltage is turned off.

Memristors can be combined into devices called crossbar latches, which could replace transistors in future computers, taking up a much smaller area. They can also be fashioned into non-volatile solid-state memory, which would allow greater data density than hard drives with access times potentially similar to DRAM, replacing both components.

Passive Elements

Passive elements are those elements which are themselves not able to make any difference in signals applied to them. They are;
Resistor

A resistor is a two-terminal electronic component that opposes an electric current by producing a voltage drop between its terminals in proportion to the current, that is, in accordance with Ohm’s law:

V = IR.

The electrical resistance R is equal to the voltage drop V across the resistor divided by the current I through the resistor. The power dissipated by a resistor is the voltage across the resistor multiplied by the current through the resistor.

Capacitor

A capacitor is an electrical/electronic device that can store energy in the electric field between a pair of conductors. The process of storing energy in the capacitor is known as "charging", and involves electric charges of equal magnitude, but opposite polarity, building up on each plate. When a capacitor is connected to a current source, charge is transferred between its plates at a rate:

i (t) = dq (t) / dt.

Inductor

An "ideal inductor" has inductance, but no resistance or capacitance, and does not dissipate energy. Inductance is an effect which results from the magnetic field that forms around a current-carrying conductor. Electric current through the conductor creates a magnetic flux proportional to the current. A change in this current creates a change in magnetic flux that, in turn, generates an electromotive force (EMF) that acts to oppose this change in current. Inductance is a measure of the amount of EMF generated for a unit change in current. For an inductor

v (t) =L di/dt



There are four fundamental circuit variables: electric current, voltage, charge, and magnetic flux. For these variables, we have resistors to relate current to voltage, capacitors to relate voltage to charge, and inductors to relate current to magnetic flux, but we were missing one to relate charge to magnetic flux. That is where the Memristor comes in.

Memristor

Memristor is the fourth passive element which has created recently. It is characterized by its memristance function describing the charge-dependent rate of change of flux with charge. When the voltage to the circuit is turned off, the Memristor still remembers how much was applied before and for how long.

M (q) = dΦm/dq

History of Memristor
We are aware of over 100 published papers going back to at least the early 1960's in which researchers observed and reported unusual 'hysteresis' in their current-voltage plots of various devices and circuits based on many different types of materials and structures. In retrospect, we can understand that those researchers were actually seeing memristance, but they were apparently not aware of it. Memristor postulated in a seminal 1971 paper in the IEEE Transactions on Circuit Theory by an Electrical Engineer Professor Leon Chua at the University of California, Berkeley. The hold-up over the last 37 years, according to professor Chua, has been a misconception that has pervaded electronic circuit theory. That misconception is that the fundamental relationship in passive circuitry is between voltage and charge.

Anyone familiar with electronics knows the trinity of fundamental components: the resistor, the capacitor, and the inductor. Professor Chua predicted that there should be a fourth element: a memory resistor, or Memristor. Such a device, he figured, would provide a similar relationship between magnetic flux and charge that a resistor gives between voltage and current. In practice, it will act like a resistor whose value could vary according to the current passing through it and which would remember that value even after the current disappeared. As, Professor Leon Chua pointed out in 1971, for the sake of the logical completeness of circuit theory; a fourth passive element should in fact be added to the list. He named this hypothetical element, linking flux and charge, the ‘Memristor’. But no one knew how to build one.

Building on their groundbreaking research in nanoelectronics, Stanley Williams (Senior Fellow, Information and Quantum Systems lab, HP Labs), and team are the first to prove the existence of the Memristor. They were the first to understand that the hysteresis that was being observed in the I-V curves of a wide variety of materials and structures was actually the result of memristance and something more general that can be called 'memristive behavior'. Then they went on to create an elementary circuit model that was defined by exactly the same mathematical equations as those predicted by Professor Chua for the Memristor, with the exception that this model had an upper bound to the resistance (which means that at large bias or long times, it is a memristive device).

Now, 37 years later, electronics have finally gotten small enough to reveal the secrets of that fourth element within the electrical characteristics of certain nanoscale devices.

Evolution
Many researchers observed and reported unusual 'hysteresis' in their current-voltage plots of various devices and circuits based on many different types of materials and structures. They were actually seeing memristance, but apparently not aware of it.

All electronic textbooks have been teaching using the wrong variables - voltage and charge - explaining away inaccuracies as anomalies. What they should have been teaching is the relationship between changes in voltage, or flux, and charge.

Without Professor Chua's circuit equations, making use of this device is not possible. It's such a funky thing. People were using all the wrong circuit equations.

The fact that the magnetic field does not play an explicit role in the mechanism of memristance is one possible reason why the phenomenon has been hidden for so long. Those interested in memristive devices were searching in the wrong places. The mathematics simply require there to be a nonlinear relationship between the integrals of the current and voltage. Another significant issue that was not anticipated by Chua is that the state variable w, which in this case specifies the distribution of dopants in the device, is bounded between zero and D. The state variable is proportional to the charge q that passes through the device until its value approaches D; this is the condition of ‘hard’ switching (large voltage excursions or long times under bias). As long as the system remains in the Memristor regime, any symmetrical alternating-current voltage bias results in double-loop i–v hysteresis that collapses to a straight line for high frequencies (Fig. 2b). Multiple continuous states will also be obtained if there is any sort of asymmetry in the applied bias (Fig. 2c).

The proof of its existence remained elusive - in part because memristance is much more noticeable in nanoscale devices. The crucial issue for memristance is that the device's atoms need to change location when voltage is applied, and that happens much more easily at the nanoscale.




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27-02-2011, 04:40 PM

SIR,
I WANT MORE INFO.. ABOUT MEMRISTOR WOULD U SEND THAT TO ME...
THAT SHOULDEXCEPT THE MATTER PRESENT IN THIS SITE
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SUBMITTED BY:
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PANKAJ


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MEMRISTOR: THE MISSING LINK DISCOVERED
ABSTRACT
This paper analyzes the fourth fundamental circuit element named ‘Memristor’ which had been proposed by a University of California, Berkeley engineer, Leon Chua in 1971, and has recently been developed by a group of researchers at Hewlett–Packard led by Stanley Williams. The paper studies the implications of the discovery of this new element and highlights its potential applications in the circuit design and computer technology.
INTRODUCTION
In the last few decades, the age old dream of building an artificial brain, i.e. using biological cognitive systems as a benchmark and inspiration to fabricate complex material assemblies which can learn, make decisions, analyze information in a highly parallel way: in other words, highly efficient bio-inspired information processors, has acquired the concreteness of real life research. Many programs and project and implimentations in materials science, nanotechnologies, ICT, biosciences use the relevant biological systems and processes as the basic paradigm for the research. However the enormous complexity of even the simplest brains still puts a barrier to the realization of such ambitions. Hence most of the current research (apart from theoretical modelling and simulations) deals with the fabrication and characterization of specific components which are expected to mimic in their functional behaviour neurons, synapses, or use biological molecules to build innovative sensing or electronic components. Recently a non-linear inorganic thin film two electrode device has been reported which the authors claim to be the very first memristor, i.e. a resistor with memory or which can learn.
When studying circuit theory we learn that there are three fundamental circuit elements the resistor, the capacitor and the inductor. The first element determines the relation between current and voltage, the second between charge and voltage, and the third between current and magnetic flux (or the time integral of the voltage). These passive two-terminal devices are basic building blocks of modern electronics and are therefore ubiquitous in circuits. However, we are also taught that they do not store information. Even if the state of one of the above elements changes, the information about the new state will be lost once we turn off the power source and wait some time. This point may seem irrelevant but it is instead fundamentally crucial: storing information without the need of a power source would represent a paradigm change in electronics. For instance, we would need many less active elements (like transistors) to perform any type of computation or processing.
HISTORY
The transistor was invented in 1925 but lay dormant until finding a corporate champion in Bell Labs during the 1950s. Now another groundbreaking electronic circuit may be poised for the same kind of success after laying dormant as an academic curiosity for more than three decades.
Hewlett-Packard Labs is trying to bring the memristor, the fourth passive circuit element after the resistor, and the capacitor the inductor into the electronics mainstream. Postulated in 1971, the “memory resistor” represents a potential revolution in electronic circuit theory similar to the invention of transistor.
The history of the memristor can be traced back to nearly four decades ago when in 1971, Leon Chua, a University of California, Berkeley, engineer predicted that there should be a fourth passive circuit element in addition to the other three known passive elements namely the resistor, the capacitor and the inductor. He called this fourth element a “memory resistor” or a memristor. Examining the relationship between charge, current, voltage and flux in resistors, capacitors, and inductors in a 1971 paper, Chua postulated the existence of memristor. Such a device, he figured, would provide a similar relationship between magnetic flux and charge that a resistor gives between voltage and current. In practice, that would mean it acted like a resistor whose value could vary according to the current passing through it and which would remember that value even after the current disappeared.
But the hypothetical device was mostly written off as a mathematical dalliance. However, it took more than three decades for the memristor to be discovered and come to life. Thirty years after Chua’s Proposal of this mysterious device, HP senior fellow Stanley Williams and his group were working on molecular electronics when they started to notice strange behavior in their devices. One of his HP collaborators, Greg Snider, then rediscovered Chua's work from 1971. Williams spent several years reading and rereading Chua's papers. It was then that Williams realized that their molecular devices were really memristors.
MEMRISTOR FUNDAMENTALS
Chua noted that there are six different mathematical relations connecting pairs of the four fundamental circuit variables: electric current i, voltage v, charge q and magnetic flux ɸ. One of these relations ,the charge is the time integral of the current, is determined from the definitions of two of the variables, and another, the flux is the time integral of the electromotive force, or voltage, is determined from Faraday’s law of induction. Thus, there should be four basic circuit elements described by the remaining relations between the variables. The three known circuit elements are described by the following equations
dv/di = r incremental resistance
dɸ/di = L inductance
dv/dq = 1/C inverse capacitance
The ‘missing’ element—the memristor, with memristance M, provides a functional relation between charge and flux as given under
dɸ/dq = M(q) memristance
The above equation can also be written in the following form
(dɸ/dt)/(dq/dt) = M(q(t)), or
v(t)/i(t) = M(q(t)) (1)
Thus, it can be clearly seen from equation (1) that memristor is basically a charge dependent resistor. The expression for voltage is given as
v(t) = M(q(t)) i(t) (2)
This equation reveals that memristance defines a linear relationship between current and voltage, as long as charge does not vary. Of course, nonzero current implies time varying charge. Furthermore, the memristor is static if no current is applied. If i(t) = 0, we find v(t) = 0 and M(q(t)) is constant. This is the essence of the memory effect. The power consumption characteristics are comparable to resistor and the power consumed is given by i2r. This is expressed in the relations that follow where power depends on the memristance.
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15-03-2011, 08:58 AM

Memristor
P.Balamurali Krishna & Rajesh.R
Department of Electronics and Communication Engineering
M.G. College of Engineering


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Abstract
A memristor is a passive two-terminal circuit element in which the resistance is a function of the history
of the current through and voltage across the device. Memristor theory was formulated and named
by Leon Chua in a 1971 paper. Chua strongly believed that a fourth device existed to provide conceptual
symmetry with the resistor, inductor, and capacitor. This symmetry follows from the description of basic
passive circuit elements as defined by a relation between two of the four fundamental circuit variables. A
device linking charge and flux (themselves defined as time integrals of current and voltage), which would
be the memristor, was still hypothetical at the time. However, it would not be until thirty-seven years
later, on April 30, 2008, that a team at HP Labs led by the scientist R. Stanley Williams would announce
the discovery of a switching memristor. Based on a thin film of titanium dioxide, it has been presented as
an approximately ideal device.

Introduction
A memristor is a passive two-terminal electronic
component for which the resistance (dV/dI) depends
in some way on the amount of charge that has flowed
through the circuit. When current flows in one
direction through the device, the resistance increases;
and when current flows in the opposite direction, the
resistance decreases, although it must remain
positive. When the current is stopped, the component
retains the last resistance that it had, and when the
flow of charge starts again, the resistance of the
circuit will be what it was when it was last active.
[8]
More generally, a memristor is a two-terminal
component in which the resistance depends on the
integral of the input applied to the terminals (rather
than on the instantaneous value of the input as in
a varistor). Since the element "remembers" the
amount of current that has passed through it in the
past, it was tagged by Chua with the name
"memristor." Another way of describing a memristor
is that it is any passive two-terminal circuit elements
that maintains a functional relationship between
the time integral of current (called charge) and the
time integral of voltage (often called flux, as it is
related to magnetic flux). The slope of this function is
called the memristance M and is similar to variable
resistance. Batteries can be considered to have
memristance, but they are not passive devices. The
definition of the memristor is based solely on the
fundamental circuit variables of current and voltage
and their time-integrals, just like
the resistor, capacitor, and inductor


Need For Memristor
Memristance (Memory + Resistance) is a property
of an Electrical Component that describes the
variation in Resistance of a component with the flow
of charge. Any two terminal electrical component
that exhibits Memristance is known as a Memristor.
Memristance is becoming more relevant and
necessary as we approach smaller circuits, and at
some point when we scale into nano electronics, we
would have to take memristance into account in our
circuit models to simulate and design electronic
circuits properly. An ideal memristor is a passive
two-terminal electronic device that is built to express
only the property of memristance (just as a resistor
expresses resistance and an inductor expresses
inductance). However, in practice it may be difficult
to build a 'pure memristor,' since a real device may
also have a small amount of some other property,
such as capacitance (just as any real inductor also has
resistance).A common analogy for a resistor is a pipe
that carries water. The water itself is analogous to
electrical charge, the pressure at the input of the pipe
is similar to voltage, and the rate of flow of the water
through the pipe is like electrical current. Just as with
an electrical resistor, the flow of water through the
pipe is faster if the pipe is shorter and/or it has a
larger diameter. An analogy for a memristor is an
interesting kind of pipe that expands or shrinks when
water flows through it. If water flows through the
pipe in one direction, the diameter of the pipe
increases, thus enabling the water to flow faster. If
water flows through the pipe in the opposite
direction, the diameter of the pipe decreases, thus
slowing down the flow of water. If the water pressure
is turned off, the pipe will retain it most recent
diameter until the water is turned back on. Thus, the
pipe does not store water like a bucket (or a
capacitor) – it remembers how much water flowed
through it.
Possible applications of a Memristor include
Nonvolatile Random Access
Memory (NVRAM), a device that can retain memory
information even after being switched off, unlike
conventional DRAM which erases itself when it is
switched off. Another interesting application is analog computation where a memristor will be able
to deal with analog values of data and not just binary
1s and 0s.


Memristor Theory And Its Properties:

Definition of Memristor
“The memristor is formally defined as a
two-terminal element in which the magnetic flux Φm
between the terminals is a function of the amount of
electric charge q that has passed through the device.”
Figure 5. Symbol of
Memristor.
Chua defined the element as a resistor whose
resistance level was based on the amount of charge
that had passed through the memristor
Memristance
Memristance is a property of an electronic
component to retain its resistance level even after
power had been shut down or lets it remember (or
recall) the last resistance it had before being shut off.

Conclusion
By redesigning certain types of circuits to include
memristors, it is possible to obtain the same function
with fewer components, making the circuit itself less
expensive and significantly decreasing its power
consumption. In fact, it can be hoped to combine
memristors with traditional circuit-design elements to
produce a device that does computation. The
Hewlett-Packard (HP) group is looking at developing
a memristor-based nonvolatile memory that could be
1000 times faster than magnetic disks and use much
less power.

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1. INTRODUCTION
Memristor is a contraction of “memory resistor,” because that is exactly its function: to remember its history. A memristor is a two-terminal device whose resistance depends on the magnitude and polarity of the voltage applied to it and the length of time that voltage has been applied. When you turn off the voltage, the memristor remembers it’s most recent resistance until the next time you turn it on, whether that happens a day later or a year later.
DEFINITION:
A memristor is a resistor with memory; it’s a device which changes its resistance depending upon how much electrical charge flow through them.
What is it?
As its name implies, the memristor can "remember" how much current has passed through it. And by alternating the amount of current that passes through it, a memristor can also become a one-element circuit component with unique properties. Most notably, it can save its electronic state even when the current is turned off, making it a great candidate to replace today's flash memory.
Memristors will theoretically be cheaper and far faster than flash memory, and allow far greater memory densities. They could also replace RAM chips as we know them, so that, after you turn off your computer, it will remember exactly what it was doing when you turn it back on, and return to work instantly. This lowering of cost and consolidating of components may lead to affordable, solid-state computers that fit in your pocket and run many times faster than today's PCs.
Someday the memristor could spawn a whole new type of computer, thanks to its ability to remember a range of electrical states rather than the simplistic "on" and "off" states that today's digital processors recognize.
By working with a dynamic range of data states in an analog mode, memristor-based computers could be capable of far more complex tasks than just shuttling ones and zeroes around.
An array of 17 purpose-built oxygen-doped titanium dioxide memristors built at HP Labs, imaged by an atomic force microscope, the wires are about 50 nm, or 150 atoms, wide. Electric current through the memristors shifts the oxygen ions, causing a gradual and persistent change in electrical resistance
2. MEMRISTOR THEORY
History

Memristor theory was formulated and named by Leon Chua in a 1971 paper. Chua extrapolated the conceptual symmetry between the resistor, inductor, and capacitor, and inferred that the memristor is a similarly fundamental device. Other scientists had already used fixed nonlinear flux-charge relationships, but Chua's theory introduces generality.
Life Cycle of Memristor
The memristor is formally defined as a two-terminal element in which the magnetic flux Φm between the terminals is a function of the amount of electric charge q that has passed through the device. Each memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge.
Noting from FARADAY'S LAW OF INDUCTION that magnetic flux is simply the time integral of voltage, and charge is the time integral of current, we may write the more convenient form
It can be inferred from this that memristance is simply charge-dependent resistance. If M(q(t)) is a constant, then we obtain OHM'S LAW R(t) = V(t)/ I(t). If M(q(t)) is nontrivial, however, the equation is not equivalent because q(t) and M(q(t)) will vary with time. Solving for voltage as a function of time we obtain
This equation reveals that memristance defines a linear relationship between current and voltage, as long as charge does not vary. Of course, nonzero current implies time varying charge. Alternating Current, however, may reveal the linear dependence in circuit operation by inducing a measurable voltage without net charge movement—as long as the maximum change in q does not cause much change in M.
Furthermore, the memristor is static if no current is applied. If I(t) = 0, we find V(t) = 0 and M(t) is constant. This is the essence of the memory effect
The power consumption characteristic recalls that of a resistor, I2R.
As long as M(q(t)) varies little, such as under alternating current, the memristor will appear as a resistor. If M(q(t)) increases rapidly, however, current and power consumption will quickly stop.
Magnetic Flux in a Passive Device
In circuit theory, magnetic flux Φm typically relates to FARADAY'S LAW OF INDUCTION, which states that the voltage in terms of energy gained around a loop (electromotive force) equals the negative derivative of the flux through the loop:
This notion may be extended by analogy to a single passive device. If the circuit is composed of passive devices, then the total flux is equal to the sum of the flux components due to each device. For example, a simple wire loop with low resistance will have high flux linkage to an applied field as little flux is "induced" in the opposite direction. Voltage for passive devices is evaluated in terms of energy lost by a unit of charge:
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11-04-2011, 04:37 PM


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MEMRISTOR
An array of 17 purpose-built oxygen-depleted titanium dioxide memristors built at HP Labs, imaged by an atomic force microscope. The wires are about 50 nm, or 150 atoms, wide. Electric current through the memristors shifts the oxygen vacancies, causing a gradual and persistent change in electrical resistance.
Memristor (pronounced "memory resistor") is a name of passive two-terminal circuit elements in which the resistance is a function of the history of the current through and voltage across the device and is expressable in terms of a functional relationship between charge and magnetic flux linkage. Memristor theory was formulated and named by Leon Chua in a 1971 paper.
On April 30, 2008, a team at HP Labs announced the development of a switching memristor based on a thin film of titanium dioxide[It has a regime of operation with an approximately linear charge-resistance relationship as long as the time-integral of the current stays within certain bounds. These devices are being developed for application in nanoelectronic memories, computer logic, and neuromorphic computer architectures.
2. BACKGROUND
A memristor is a passive two-terminal electronic component whose present resistance depends in some way on the amount of charge that has flowed through the circuit. When current flows in one direction through the device, the resistance increases; and when current flows in the opposite direction, the resistance decreases, although it must remain positive. When the current is stopped, the component retains the last resistance that it had, and when the flow of charge starts again, the resistance of the circuit will be what it was when it was last active.
More generally, a memristor is a two-terminal component in which the resistance depends on the integral of the input applied to the terminals (rather than on the instantaneous value of the input as in a varistor). Since the element "remembers" the amount of current that has passed through it in the past, it was tagged by Chua with the name "memristor." Another way of describing a memristor is that it is any passive two-terminal circuit elements that maintains a functional relationship between the time integral of current (called charge) and the time integral of voltage (often called flux, as it is related to magnetic flux). The slope of this function is called the memristance M and is similar to variable resistance. Batteries can be considered to have memristance, but they are not passive devices. The definition of the memristor is based solely on the fundamental circuit variables of current and voltage and their time-integrals, just like the resistor, capacitor, and inductor. Unlike those three elements however, which are allowed in linear time-invariant or LTI system theory, memristors of interest have a nonlinear function and may be described by any of a variety of functions of net charge. There is no such thing as a standard memristor. Instead, each device implements a particular function, wherein the integral of voltage determines the integral of current, and vice versa. A linear time-invariant memristor is simply a conventional resistor.
In his 1971 paper, memristor theory was formulated and named by Leon Chua, extrapolating the conceptual symmetry between the resistor, inductor, and capacitor, and inferring the memristor was a similarly fundamental device. (However, as mentioned above, if it has no non-linearity then it is the same as a standard resistor. It is more meaningful to compare it with a varistor, which has a non-linear relationship between current and voltage.) Other scientists had already proposed fixed nonlinear flux-charge relationships, but Chua's theory introduced generality.
Like other two-terminal components (e.g., resistor, capacitor, inductor), real-world devices are never purely memristors ("ideal memristor"), but will also exhibit some amount of capacitance, resistance, and inductance. Note however that a "memristor" with constant M and a resistor with constant R (i.e. not a varistor) are the same thing.
3. THEORY
The memristor is essentially a two-terminal variable resistor, with resistance dependent upon the amount of charge q that has passed between the terminals.
To relate the memristor to the resistor, capacitor, and inductor, it is helpful to isolate the term M(q), which characterizes the device, and write it as a differential equation.
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