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Page 1: The Missing Fundamental Element

THE MISSING FUNDAMENTAL ELEMENT

Memristor

PRESENTED BY –

SAURAV ROY

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3 FUNDAMENTAL PASSIVE CIRCUIT ELEMENTS

Inductor, L (H)

Capacitor, C (F) Resistor, R (Ω)

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SYMMETRY OF RELATIONSHIPS

Voltage (V)

Current(i)

Charge (q)

Flux (Φ)

dΦ = Ldi Inductors

??

v=dΦ/dt i=dq/dt

Resistors dv=Rdi

dq=CdvCapacitors

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FOUNDER OF MISSING ELEMENT

Leon Chua proposed the existence of memristor in 1971.

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o For all passive memristors the generalized forms are defined as follows

Where x= (x1,x2,x3….xn)denotes n state variables x1,x2,x3…..xn which do not depend on any external voltage or current.

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SYMMETRY OF RELATIONSHIPS

MemristorsdΦ=Mdq

Voltage (V)

Current(i)

Charge (q) Flux (Φ)

dΦ = LdiInductorsv=dΦ/dt

i=dq/dt

Resistors dv=Rdi

dq=CdvCapacitors

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Any two terminal devices which exhibits a pinched hysteresis loop in the V-I plane when driven by any bipolar periodic voltage or current waveform, for any initial conditions, is a memristor.

It depends on the frequency.

The area enclosed within the part of the pinched hysteresis loop in the first quadrant, and the third quadrant, of the vi plane shrinks continuously as the frequency ꙍ increases, and the hysteresis loop tends to a straight line through the origin as ꙍ tends to ∞.

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A memristor is a semiconductor whose resistance varies as a function of flux and charge. This allows it to “remember” what has passed through the circuit.

Definition

Memristor is a hypothetical non-linear passive two terminal electrical component relating electric charge  and magnetic flux linkage.

MEMRISTOR

MEMORY RESISTOR+

Memristor

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In 2008 a team lead by Stanley Williams created the first memristor.

As its effect depends on atomic-scale movements, it only poped up on the nanoscale of William’s devices.

For RON<<ROFF the memristance was to be determined as follows

This is the curve that observed by HP which is similar to the prescribed curve of Leon. O Chua.

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WORKING PRINCIPLE

o Applied voltage makes the oxygen vacancies (+ve) to shift towards the –ve voltage.

• 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 .

PT PTTiO(2-x)TiO2

3 nm

2 nm

OxidizedReduced

(-)ve (+)ve

D

W

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o In the year 1952, Hodgkin & Huxley had erroneously named two circuit elements associated with the Potassium ion and the Sodium ion as time-varying conductance in there model.

o Leon Chua et al. 2012 solved many hitherto unsolved paradox associated with the Hodgkin-Huxley time varying potassium conductance is in fact a first order memristor and the Hodgkin-Huxley time varying Sodium conductance is in fact a second order memristor. Memristive synapses are obviously becoming reality, but their real competitive advantage against mainstream technologies (such as CMOS-based floating-gate memories) has yet to be evaluated .

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• Memristors Acts as a Synapse

A memristor has a memory and at the same time is also able to change data encoded by its resistance state. In this sense, a memristor is similar to a synapse,

The Human Brain possesses nearly 10 billion neurons,each of which has direct synaptic connections to nearly 10,000 neurons.A connection between two neurons in the brain with a high level of plasticity that is able to modify the efficiency of signal transmission between neurons under the influence of the transmission itself. A memristor enables scientists to build a true neural network,and the physical properties of memristors mean that a minimum, they can be made as small as conventional chips.

Synapse

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• AS A NON VOLATILE MEMORY

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CONCLUSIONoThe other applications of memristors are as follows:• As Image Processor• As pattern Recognizer• Can perform logic operations• In artificial neural networks• Can work as both memory and logic functions• Higher data density due to nano-scale size• Compatible with CMOS process and provide

innovating nanotechnology due to the fact that it performs better the smaller it becomes.

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[1]Chua L., Memristor-The missing circuit element. IEEE Transactions on Circuit Theory, vol.18, n.5, pp. 507- 519, 1971. [2]By Sally Adee, The Mysterious Memristors , 1 May 2008 .[3] L. Chua, V. Sbitnev, and H. Kim, Hodgkin–Huxley axon is made of memristors, Int. J. Bifurcat. Chaos, vol. 22, no. 3, 2012. [4] L. O. Chua and S. M. Kang, Memristive devices and systems, Proc. IEEE, vol. 64, no. 2, pp. 209-223, Feb. 1976.[5]D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, The missing memristor found, Nature, vol. 453, pp. 80-83, 2008.[6]M. G. Bray and D. H. Werner, Passive switching of electromagnetic devices with memristors, Appl. Phys. Lett., vol. 96, pp. 0735041-735043, 2010. [7]J. Borghetti, G. S. Snider, P. J. Kukes, J. J. Yang, D. R. Stewart, and R. S. Williams, Memristive’ switches enable ‘stateful’ logic operations via material implication, Nature, vol. 464,pp. 873–876, 2010.[8]K. Kim, S. Shin, and S.-M. Kang, Field programmable stateful logic array, IEEE Trans. Comput.-Aided Design pp. 1800-1813, Dec. 2011. [9]G. S. Snider, BSpike-timing dependent learning in memristive nano-devices, in Proc. IEEE/ACM Int. Symp. Nanoscale Architecture, 2008, pp. 85-92.[10]T. Chang, S. H. Jo, and W. Lu, Short-term memory to long-term memory transition in a nano scale memristor, Amer. Chem. Soc. (ACS) Nano, vol. 5, pp. 7669-7676, 2011.[11]Hyongsuk Kim, P.Sah ,Changju Yang, Tamas Roska, and L.Chua, Memristor bridge synapses ,vol.100,No.6,June 2012, pp. 2061.[12]B. Linares-Barranco and T. Serrano-Gotarredona, Memristance can explain spike-time-dependent-plasticity in neural synapses, Nature Preceding, Mar. 31, 2009.[13]Y. V. Pershin and M. Di Ventra,Neuromorphic, Digital and Quantum Computation With Memory Circuit Elements,arXiv:1009.6025v3 [cond-mat.mes-hall].[14]A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to the conduction and excitation in nerve, J. Physiol., vol. 117, pp. 500–544, 1952. [15]L. Chua, V. Sbitnev, and H. Kim, Hodgkin–Huxley axon is made of memristors, Int. J. Bifurcat. Chaos, vol. 22, no. 3, 2012. [16]M. Laiho, E. Lehtonen, A. Russell and P. Dudek ,Memristive synapses are becoming reality, TheNeuromorphicEngineer.

References

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