Theoretically, Memristors, a concatenation of “memory resistors”, are a type of passive circuit elements that maintain a relationship between the time integrals of current and voltage across a two
Theoretically, Memristors, a concatenation of “memory resistors”, are a type of passive circuit elements that maintain a relationship between the time integrals of current and voltage across a two terminal element.
Theoretically, Memristors, a concatenation of “memory resistors”, are a
type of passive circuit elements that maintain a relationship between
the time integrals of current and voltage across a two terminal
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• It is the consolidation of two words namely, MEMORY and RESISTOR.
• As the name suggests its resistance (dV/dI) depends on the charge
that HAD flowed through the circuit.
• When current flows in one direction the resistance increases, in
contrast when the current flows in opposite direction the resistance
• However resistance cannot go below zero.
• When the current is stopped the resistance remains in the value that
it had earlier.
• It means MEMRISTOR “REMEMBERS” the current that had last flowed
• Theory was developed in 1971 by Professor Leon
Chua at University of California, Berkeley.
• In 2008, a team at HP Labs under R.Stanley Williams
claimed to have found Chua's missing memristor
based on an analysis of a thin film of titanium
• In March 2012, a team of researchers from HRL
Laboratories and the University of Michigan
announced the first functioning memristor array
built on a CMOS chip.
Professor Leon Chua
R. Stanley Williams
Memristors behaves like a pipe whose diameter varies according to
the amount and direction of the current passing through it
If the current is turned OFF, the pipes diameter stays same until it is switched ON again
It Remembers what current has flowed through it
• Leon Chua extrapolated a
conceptual symmetry between
the nonlinear resistor (voltage
vs. current), nonlinear capacitor
(voltage vs. charge) and
nonlinear inductor (magnetic
flux linkage vs. current).
• He then inferred the possibility
of a memristor as another
fundamental nonlinear circuit
element linking magnetic flux
linkage and charge.
• The memristor was originally defined in terms of a non-linear
functional relationship between magnetic flux linkage Φm(t) and the
amount of electric charge that has flowed, q(t)
f(Φm (t),q(t)) = 0
• The variable Φm ("magnetic flux linkage") is generalized from the
circuit characteristic of an inductor.
• It does not represent a magnetic field here.
• The symbol Φm may be regarded as the integral of voltage over time.
• In the relationship between Φm and q, the derivative of one with
respect to the other depends on the value of one or the other
• So each memristor is characterized by its memristance function
describing the charge-dependent rate of change of flux with charge.
Substituting the flux as the time integral of the voltage, and charge as
the time integral of current
Device Characteristic property (units) Differential equation
Resistor Resistance (V per A, or Ohm, Ω) R = dV / dI
Capacitor Capacitance (C per V, or Farads) C = dq / dV
Inductor Inductance (Wb per A, or Henrys) L = dΦm / dI
Memristor Memristance (Wb per C, or Ohm) M = dΦm / dq
• The above table covers all meaningful ratios of differentials of I, Q,
Φm, and V.
• No device can relate dI to dq, or dΦm to dV, because I is the
derivative of Q and Φm is the integral of V.
Current-voltage characteristics for the resistor, capacitor, inductor and memristor.
• It can be inferred from this that memristance is charge-dependent
• 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)) can vary with time.
• Solving for voltage as a function of time produces
V(t)= M(q(t)) I(t)
This equation reveals that memristance defines a linear relationship
between current and voltage, as long as M does not vary with charge.
• The memristor is static if no current is applied.
V(t)= M(q(t)) I(t)
• 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, I2
P(t) = V(t) I(t) = I2
• As long as M(q(t)) varies little, such as under alternating current, the
memristor will appear as a constant resistor.
• If M(q(t)) increases rapidly, however, current and power consumption
will quickly stop.
• TiO2-x region doped with oxygen vacancies
• In the TiO2-x region, the ratio between titanium atoms and oxygen atoms has been
altered such that there is less oxygen than in a regular TiO2 sample
• The resistance of the device when w = D will be designated RON and when w = 0 the
resistance will be designated as ROFF .
Contribution of HP Labs
Effective Electrical Structure of the HP MemristorResistance Naming Convention
The effective IV behaviour of the structure can be represented as equation
Contribution of HP Labs
Further Calculations leads to:
• For RON<< ROFF the memristance function was determined to be
M(q(t)) = ROFF . (1-
• where ROFF represents the high resistance state
• RON represents the low resistance state
• μv represents the mobility of dopants in the thin film
• D represents the film thickness.
An array of 17 purpose-built
dioxide memristors built at HP
Labs, imaged by an atomic
The wires are about 50 nm, or
150 atoms, wide.
Applications of a Memristor
Non-volatile memory applications
• Memristors can retain memory states, and
data, in power-off modes.
• Non-volatile random access memory, or
NVRAM is the first application that comes
to mind when we hear about memristors.
• There are already 3nm Memristors in
Low-power and remote sensing
• Coupled with memcapacitors and
meminductors, the complementary
circuits to the memristor which allow
for the storage of charge.
• Memristors can possibly allow for
nano-scale low power memory and
distributed state storage, as a further
extension of NVRAM capabilities.
• These are currently all hypothetical
in terms of time to market.
• While the Memristor can be used at its
extreme resistance values in order to
provide digital memory, it can also be
made to behave in an analog manner.
• One potential application of this
behaviour is that of a dynamically
adjustable electric load .
• Thus, existing electronic circuit topologies
with characteristics that depend on a
resistance can be made with Memristors
that behave as variable, programmable
Memristor patents include applications in
• Programmable Logic
• Signal Processing
• Neural Networks
• Control Systems
• Reconfigurable Computing
• Brain-computer Interfaces
Advantages of Memristors
• Has properties which can not be duplicated by the other circuit
elements (resistors, capacitors, and inductors
• Capable of replacing both DRAM and hard drives
• Smaller than transistors while generating less heat
• Works better as it gets smaller which is the opposite of transistors
• Devices storing 100 gigabytes in a square centimeter have been
created using memristors
• Quicker boot-ups
• Requires less voltage (and thus less overall power required)
Disadvantages of Memristors
• Not currently commercially available
• Current versions only at 1/10th the speed of DRAM
• Has the ability to learn but can also learn the wrong patterns in the
• Since all data on the computer becomes non-volatile, rebooting will not
solve any issues as it often times can with DRAM.
• Suspected by some that the performance and speed will never match
DRAM and transistors.