# Seminar Report on Memristor

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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.

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 â€śmemrisrors are so significant that it would be mandatory to re-write the existing electronics engineering textbooks.â€ť

ACKNOWLEDGEMENT

I would like to express my immense gratitude to all those who have directly or indirectly helped me in completing my seminar on Memristor. I would like to thank them for their effective guidance & kind cooperation without which i would not have been able to introduce a good presentation and complete this seminar report.

I would like to thank the faculty members of Department of Electronics & Communication Engineering for their permission grant, constant reminders and much needed motivation, which helped me to extract maximum knowledge from the available sources.

Nipun Tandan

(ECE 4th Year )

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.

FUNDAMENTAL ELEMENTS OF ELECTRONICS

1 .RESISTOR

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohm’s law which states â€śVoltage (V) across a resistor is proportional to the current (I) through it where the constant of proportionality is the resistance (R)â€ť. V = IR

2. CAPACITOR

A capacitor or condenser is a passive electronic component consisting of a pair of conductors separated by a dielectric. When a voltage potential difference exists between the conductors, an electric field is present in the dielectric. This field stores energy and produces a mechanical force between the plates. The effect is greatest between wide, flat, parallel, narrowly separated conductors. An ideal capacitor is characterized by a single constant value, capacitance, which is measured in farads. This is the ratio of the electric charge on each conductor to the potential difference between them. In practice, the dielectric between the plates passes a small amount of leakage current. The conductors and leads introduce an equivalent series resistance and the dielectric has an electric field strength limit resulting in a breakdown voltage. Capacitors are widely used in electronic circuits to block the flow of direct current while allowing alternating current to pass, to filter out interference, to smooth the output of power supplies, and for many other purposes. They are used in resonant circuits in radio frequency equipment to select particular frequencies from a signal with many frequencies.

ELECTRONIC SYMBOL

CURRENT-VOLTAGE RELATION

The current i (t) through a component in an electric circuit is defined as the rate of change of the charge q (t ) that has passed through it. Physical charges cannot pass through the dielectric layer of a capacitor, but rather build up in equal and opposite quantities on the electrodes: as each electron accumulates on the negative plate, one leaves the positive plate. Thus the accumulated charge on the electrodes is equal to the integral of the current, as well as being proportional to the voltage (as discussed above). As with any antiderivative, a constant of integration is added to represent the initial voltage v (t0).

This is the integral form of the capacitor equation,

Taking the derivative of this, and multiplying by C, yields the derivative form, [pic]. The dual of the capacitor is the inductor, which stores energy in the magnetic field rather than the electric field. Its current-voltage relation is obtained by exchanging current and voltage in the capacitor equations and replacing C with the inductance L.

3. INDUCTOR

An inductor or a reactor is a passive electrical component that can store energy in a magnetic field created by the electric current passing through it. An inductor’s ability to store magnetic energy is measured by its inductance, in units of henries. Typically an inductor is a conducting wire shaped as a coil, the loops helping to create a strong magnetic field inside the coil due to Faraday’s law of induction. Inductors are one of the basic electronic components used in electronics where current and voltage change with time, due to the ability of inductors to delay and reshape alternating currents Inductance (L) (measured in henries) is an effect resulting from the magnetic field that forms around a current-carrying conductor that tends to resist changes in the current. 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, by Faraday’s law 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 example, an inductor with an inductance of 1 henry produces an EMF of 1 volt when the current through the inductor changes at the rate of 1 ampere per second. The number of loops, the size of each loop, and the material it is wrapped around all affect the inductance. An inductor opposes changes in current. An ideal inductor would offer no resistance to a constant direct current; however, only superconducting inductors have truly zero electrical resistance.

In general, the relationship between the time-varying voltage v(t) across an inductor with inductance L and the time-varying current i(t) passing through it is described by the differential equation:

Inductors are used extensively in analog circuits and signal processing. Inductors in conjunction with capacitors and other components form tuned circuits which can emphasize or filter out specific signal frequencies. Applications range from the use of large inductors in power supplies, which in conjunction with filter capacitors remove residual hums known as the Mains hum or other fluctuations from the direct current output, to the small inductance of the ferrite bead or torus installed around a cable to prevent radio frequency interference from being transmitted down the wire. Smaller inductor/capacitor combinations provide tuned circuits used in radio reception and broadcasting.

Two (or more) inductors which have coupled magnetic flux form a transformer, which is a fundamental component of every electric utility power grid. The efficiency of a transformer may decrease as the frequency increases due to eddy currents in the core material and skin effect on the windings. Size of the core can be decreased at higher frequencies and, for this reason, aircraft use 400 hertz alternating current rather than the usual 50 or 60 hertz, allowing a great saving in weight from the use of smaller transformers. An inductor is used as the energy storage device in some switched-mode power supplies.

The inductor is energized for a specific fraction of the regulator’s switching frequency, and de-energized for the remainder of the cycle. This energy transfer ratio determines the input-voltage to output-voltage ratio. This XL is used in complement with an active semiconductor device to maintain very accurate voltage control. Inductors are also employed in electrical transmission systems, where they are used to depress voltages from lightning strikes and to limit switching currents and fault current. In this field, they are more commonly referred to as reactors. Larger value inductors may be simulated by use of gyrator circuits.

Fig: An inductor with two 47mH windings, as may be found in a power supply

THE MISSING LINK :

There are six different mathematical relations connecting pairs of four fundamental circuit variables viz. current I, voltage v, charge q, and magnetic flux Î¦. One of these relation (the charge is time integral of current) is determined from the definition of two of the variables and another (the flux is the time integral of the electromotive force or voltage) is determined from faradayâ€™s law of induction. Thus there should be four basic circuit elements described by the remaining relation between the variables .

The relation between these fundamental elements can be shown as :

The relation between the charge and the flux was unknown, and so the device which describes it. This led to the discovery of the fourth fundamental element which describes the above missing relation between Charge And Flux.

THE 4TH NEW FUNDAMENTAL ELEMENT : MEMRISTOR

Memristor is one of four basic electrical circuit components, joining the resistor, capacitor, and inductor. The Memristor, short for â€śmemory resistorâ€ť 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.

Since, there is no proof of any practical device which shows memristance, according to Chuaâ€™s paper In the beginning of 2006, the group of researchers headed by R.Stanley Williams at HP labs, developed a simple model of binary switch based on the coupled movement of both charge dopants and electrons in the semiconductor and saw that the defining equations for this switch were identical to Chuaâ€™s mathematical definitions of memristor and they were able to write down a defining equation for memristance of this device interms of its physical and geometric properties

MEMRISTOR

FIG: A CROSSBAR ARRAY OF MEMRISTOR

NEED OF MEMRISTOR

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 element 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.

FIG: RELATION BETWEEN ALL FOUR FUNDAMENTAL ELEMENTS OF

ELECTRONICS

MEMRISTOR: THEORY AND PROPERTIES

âť– Definition of Memristor

o â€śThe Memristor is formally defined as a two-terminal element in which the magnetic flux Î¦m between the terminals is a function of the amount of electric charge q that has passed through the device.â€ť

âť– Electronic Symbol

âť– Chua defined the element as a resistor whose resistance level was based on the amount of charge that had passed through the Memristor

âť– MEMRISTANCE

o 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.

âť– Chuaâ€™s. Theory

o Each Memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge. [pic]

âť– As we know 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 [pic]

o It can be inferred from this that memristance is simply charge-dependent resistance. . i.e. , â–Ş V(t) = M(q(t))*I(t)

â–Ş 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 movementâ€”as long as the maximum change in q does not cause much change in M.

âť– CURRENT VS. VOLTAGE CHARACTERISTICS

o 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. o 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. It illustrates the current vs. voltage behavior of memristance.

Current vs. Voltage curve demonstrating hysteretic effects of memristance.

o 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. As observed above 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.

HYSTERESIS MODEL

Hysteresis model illustrates an idealized resistance behavior demonstrated in accordance with above current-voltage characteristic wherein the linear regions correspond to a relatively high resistance (RH) and low resistance (RL) and the transition regions are represented by straight lines. [pic]

Fig: Idealized hysteresis model of resistance vs. voltage for memristance switch.

Thus for voltages within a threshold region (-VL2