1. MEMRISTOR
The fourth fundamental circuit element
Presented by,
Mahesh K C 1BM10EC058
Reviewers
Mrs. K. P. Lakshmi Mr. K N Madhusudhan
Associate professor Assistant professor
A seminar on

2. Contents
• Introduction
• A brief look at the basic elements
• The invention
• Features
• Physics of the Memristor
• An analogous system
• Comparison between Resistor and Memristor
• Applications

3. Introduction
• The MEMRISTOR stands for MEMory ResISTOR.
• It is the fourth passive fundamental circuit element.
• It is basically a semi-conductor whose resistance depends on the device history.
• The resistance is a function of its state variable.
• Circuit symbol

4. A brief look at the basic elements
• The three basic elements are RESISTOR, INDUCTOR and CAPACITOR
• Resistor was invented by Georg Ohm in 1827.
• Inductor was invented by Joseph Henry in 1831.
• Capacitor was invented by Ewald Georg von Kleist in 1745.
Resistor Inductor Capacitor

5. The invention
• The four fundamental variables of circuit theory are
Charge (Q) Voltage (V) Current (I) Flux (𝜑)
• The relation between the variables are defined as follows
𝒗 =
𝒅𝝋
𝒅𝒕
(1) 𝒊 =
𝒅𝒒
𝒅𝒕
….(2)
𝒅𝒗 = 𝑹𝒅𝒊….(3) 𝒅𝒒 = 𝑪𝒅𝒗…..(4) 𝒅𝝋 = 𝑳𝒅𝒊….(5)
• There was no relation to relate the flux with the charge.

6. • Leon Chua postulated the memristor on grounds of symmetry in 1971.
• The Memristor relates the flux with the charge.
• Thus it completed the interrelation between the pair of variables.
• R Stanley Williams devised the first ever memristor at the HP labs in 2008.
Tetrahedron of symmetry

7. Dr. Leon Chua R Stanley Williams
Key contributors

8. Features of the Memristor
• It is a fundamental two terminal element.
• It retains its resistance level even after power had been shut down.
• But it does not store energy.
• It is characterized by a quantity called as Memristance.
𝑴 𝒒,𝝋 = 𝒅𝝋/𝒅𝒒
• The memory is characterized by one or more state variable.

9. Contd..
• Memristor is characterized by a constitutive relation ⱷ ⱷ, 𝑞 = 0
• The memristor is charge-controlled if this relation can be expressed as a single-valued
function ⱷ = ⱷ 𝑞
• The memristance of a charge controlled Memristor is given by 𝑴 𝒒 =
𝒅𝝋 𝒒
𝒅𝒒
• It is flux-controlled if this relation can be expressed as a single-valued function 𝑞 =
𝑞 ⱷ
• The memductance of a flux controlled Memristor is given by 𝑾 𝝋 = 𝒅𝒒(𝝋)/𝒅𝝋

10. Physics of the memristor
• R. Stanley Williams found an ideal memristor in titanium dioxide (TiO2) which is a wide band gap
semiconductor.
• Ti belongs to the group 4 elements. It is a transition metal with an atomic number of 22
• TiO2in its pure state is highly resistive but its conductivity can be increased by doping.
• In TiO2, the dopants do not stay stationary in a high electric field; they tend to drift in the direction
of the current.
TiO2

11. A B
Figure
𝑣 = 𝑅 𝑜𝑛
𝑤
𝐷
+ 𝑅 𝑜𝑓𝑓 1 −
𝑤
𝐷
𝑖Electronic current
𝑑𝑤 𝑡
𝑑𝑡
= 𝜇 𝑣
𝑅 𝑜𝑛
𝐷
𝑖(𝑡)Ionic drift

12. Working
• When an oxygen atom, which is negatively charged, is removed from its substantial site
in TiO2, a positively charged oxygen vacancy is created (V0
+) is created, which act as a
carrier.
• When a negative potential is applied to electrode, the positively charged oxygen
vacancies (V0
+) are attracted towards electrode A, the length of undoped region
increases thus resistance increases.
• When a positive potential is applied at electrode A the positively charged oxygen
vacancies are repelled and moved into the undoped TiO2. This ionic movement towards
electrode B reduces the length of undoped region decreasing the resistance.

13. Appearance
The first realized memristor, produced
at the HP lab.
Memristor used in cross bar switch

14. An analogous system
Water pipe analogy

15. • Water pressure is analogous to voltage and the water flowing is analogous to the charge.
• When water flows in forward direction, the diameter of the pipe increases thus decreasing
the resistance.
• When water flows in reverse direction, the diameter of the pipe decreases thus increasing
the resistance.
• When the water is shut off, the pipe retains its most recent diameter.
• It starts from the same diameter when the water flows through for the next time.

16. Comparison between Resistor and Memristor
• They are passive two terminal elements.
• The SI unit is ohms.
• The resistor has a fixed value of resistance, whereas the memristance depends on the device history.
• The I-V curve for a resistance is linear and it is non-linear for a memristor. (Also called the pinched
hysteresis loop)

17. Applications
• Nano scale nature
• Replacement for flash memory
• Replacement for DRAM
• Neural networks

18. References
[1] Chua, Leon O (September 1971), "Memristor-The Missing Circuit Element", IEEE Transactions on Circuit
Theory CT-18
(5): 507–519, doi:10.1109/TCT.1971.1083337
[2] An introduction to the memristor – a valuable circuit element in bioelectricity and bioimpedance Gorm K.
Johnsen 1,2
1. Institute of Energy Technology, 2007 Kjeller, Norway
2. Department of Physics, University of Oslo, 0316 Oslo, Norway
[3] Robust Hybrid Memristor-CMOS Memory: Modeling and Design Baker Mohammad, Member, IEEE, Dirar
Homouz,
and Hazem Elgabra
[4] Memristor-based IMPLY Logic Design Procedure, Shahar Kvatinsky, Avinoam Kolodny and Uri C. Weiser
Department of
Electrical Engineering Technion – Israel Institute of Technology Haifa 32000 ISRAEL

19. THANK YOU