ROLE OF MEMRISTORS IN ADVANCED ELECTRONIC CIRCUIT THEORY
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 “Memristor
are so significant that it would be mandatory to re-write the existing
electronics engineering textbooks. “In this paper the introduction of Memristor
and its role in advanced electronic circuits required to involved in processors,
memory units and so on is presented
1.
Definition of a Memristor
It is a two terminal passive
element flux produced by it is proportional to charge flowing in it. The symbol
of Memristor is given below.
So Memristor
is a passive element which shoes fundamental relation between charge and flux
2. Flux –Charge Curve of a Memristor
Its φ-q curve is monotonically increasing.
The slope of the φ–q
curve is called Memristance M (q). Memristor is passive if and only if Memristance
is non-negative. (M (q) ≥
0).
Memristance is a transfer property of Memristor so
it is simply impedance offered by Memristor. The current is defined as the time derivative of the
charge and the voltage is defined as the time derivative of the flux.
Memristance
is a property of the Memristor. When charge flows in a direction through a
circuit, the resistance of the Memristor increases. When it flows in the
opposite direction, the resistance of the Memristor decreases. If the applied
voltage is turned off, thus stopping the flow of charge, the Memristor
remembers the last resistance that it had. When the flow of charge is started
again, the resistance of the circuit will be what it was when it was last
active. So the Memristor is essentially a two-terminal variable resistor.
3.
MODEL OF THE MEMRISTOR FROM HP LABS
In 2008, thirty-seven years after Chua proposed the
Memristor, Stanley Williams and his group at HP Labs realized the Memristor in
device form. To realize a Memristor, they used a very thin film of titanium
dioxide (TiO2). The thin film is sandwiched between two platinum (Pt) contacts
and one side of TiO2 is doped with oxygen vacancies. The oxygen vacancies are
positively charged ions. Thus, there is a TiO2 junction where one side is doped
and the other side is undoped. The device established by HP is shown in Fig.
D is the device length and w is the length of the doped region. Pure TiO2 is a
semiconductor and has high resistivity. The doped oxygen vacancies make the
TiO2-x material conductive. When a positive voltage is applied, the positively
charged oxygen vacancies in the TiO2-x layer are repelled,
Moving
them towards the undoped TiO2 layer. As a result, the boundary between the two
materials moves, causing an increase in the percentage of the conducting TiO2-x
layer. This increases the conductivity of the whole device. When a negative
voltage is applied, the positively charged oxygen vacancies are attracted,
pulling them out of TiO2 layer. This increases the amount of insulating TiO2,
thus increasing the resistivity of the whole device. When the voltage is turned
off, the oxygen vacancies do not move. The boundary between the two titanium
dioxide layers is frozen. This is how the Memristor remembers the voltage last
applied.
The
simple mathematical model of the HP Memristor is given by
Roff = High resistance state
Ron = Low resistance state
W =
width of doped region
D = Thickness of semiconductor film
sandwiched between two metal contacts.
4. Current–Voltage Curve of a Memristor
Memristor
has the pinched hysteresis loop current voltage characteristic.
Another
signature of the Memristor is that the pinched hysteresis loop shrinks
with the increase in the excitation frequency. Figure shows the pinched
hysteresis loop‖ and an example
of the loop shrinking with the increase in frequency. In fact, when the
excitation frequency increases towards infinity, the Memristor behaves as a
normal resistor.
DC response:
This example shows a Memristor, a recently
discovered device. It acts as a resistor, but the resistance varies depending
on the current over time. In this example, use the slider at right to select
the input voltage. The Memristor has a high resistance at first, but current
flow causes the resistance to decrease over time until it hits a minimum value.
If you set the input voltage to a negative value, then the resistance will
gradually increase until it hits a maximum value. A graph of the memristors
voltage, current, and resistance is shown below the circuit.
The graphs below the circuit show the memristors
voltage (in green), current (in yellow), and resistance (in white). A graph of
voltage versus current is also shown. Note that the voltage has a nonlinear
relationship to current.
The graphs below the circuit show the memristors
voltage (in green), current (in yellow), and resistance (in white). A graph of
voltage versus current is also shown.
The graphs
below the circuit show the memristors voltage (in green), current (in yellow),
and resistance (in white). A graph of voltage versus current is also shown.
6.
APPLICATIONS OF MEMERISTOR
Some of
applications of Memristor are given below
A.arithmethic operations
B.logic operations
C.memory unit
Basic arithmetic operations
For
performing any arithmetic operation such as addition, subtraction,
multiplication or division, at first, two operands should be represented by
some ways. In almost all of currently working circuits, signal values are
represented by voltage or current. However, as explained in previous section,
analog values can be represented by the Memristance of the Memristor. When 2
Memristor connected in series there corresponding Memristor are added. By this
concept addition operation is done
Any subtraction, such as M1−M2 , can be written as M1+ (− M2). This means that for doing subtraction,
Memristor should be connected in series with another Memristor which its
Memristance is –M2 .
A simple opamp-based inverting amplifier which
intrinsically is a Memristance divider. The output voltage of this circuit is –M2/M1
In
bellow circuit output is (M1+M2)(M1||M2) =M1.M2 so it performs multiplication
operation
Logic operations
Consider the set of memristors as
shown in Fig.24 shows nand gate. The Memristor Mem1 of inverting configuration
is replaced by set of memristors Mem1-Mem3, which are connected in parallel.
The control terminals of Mem1-Mem3 are connected. The Memristor Mem4 is
unconditionally open by applying a high negative voltage – at the control terminal.
Then a voltage is applied at the common control terminal and is applied
to the control of Mem4. In the scenario where memristors Mem1-Mem3 are
open, the voltage at the terminal X is close to 0. The voltage drop across Mem4
is , which is enough to close Mem4. In the scenario where one Memristor Mem1 is
closed and Mem2 and Mem3 are open, the intermediate node settles close to and
the voltage across Mem4 is not enough to close the Memristor. Similar results
occur when Mem2 or Mem3 are open. Hence, the logical computation can be treated
as Mem4 = (Mem1.Mem2.Mem3)` which is NAND operation. This configuration is
referred to as ‗wired-AND‘ as various inputs are wired together to produce
result.
Memristor Memory
Next, the sense amplifier stage as shown in Fig. 6 fully
converts the sensed memristor state to a full-swing digital output. The
voltage Vx will be compared with the referencevoltage Vref which is half of Vin. If the
memristor stores logic zero, Vx is less than Vref and output Vo
is VL. If memristor stores logic one, Vx is greater than Vref
and output Vo would be VH.
Fig. illustrates a memristor-based
memory array with peripheral circuits. Just like a typical memory array such as
that of DRAM, it still has row decoder, sense amplifier and column selector/decoder.
In addition, there is a pulse generator unit and a selector unit. Pulse
generator generates read/writes pattern signals shown in Fig. 4(b) and Fig.
5(c). In Fig. 7, when Pselect signal is high, NMOSs are short and
PMOSs are open, signal directly goes through. If Pselect signal is
low, NMOSs are open and PMOSs are short so signal gets negative in sign.
Furthermore, the purpose of the selector unit is to switch the memristor
to ground for a write operation and Rx for a read operation. Read
Enable (RE) signal controls the MUX to switch properly depending on
whether it is a read or a write operation.
7. BENEFITS OF USING MEMRISTORS
The
advantages of using Memristor are as given below:
Ø It provides greater resiliency and reliability when
power is interrupted in data centers.
Ø Memory devices built using Memristor have greater data
density.
Ø Faster
and less expensive than present day devices
Ø Uses less energy and produces less heat.
Ø Would allow for a quicker boot up since information is
not lost when the device is turned off.
Ø The information is not lost when the device is turned
off.
Ø A very important advantage of Memristor is that when
used in a device, it can hold any value between 0 and 1. However present day
digital devices can hold only 1 or 0. This makes devices implemented using
Memristor capable of handling more data.
8. Future Research
Recently,
researchers have defined two new memdevices- memcapacitor and meminductor, thus
generalizing the concept of memory devices to capacitors and inductors. These
devices also show ―pinched‖ hysteresis
loops in two constitutive variables— charge—voltage for the memcapacitor and
current—flux for meminductor. Figure 13 shows the symbols for the memcapacitor
and the meminductor.
Conclusion:-
In a system contains
mainly ALU and memory units. But they size can be reduced when they fabricate
with memristors .so it leads a revolution in electronics
REFERENCE
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