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UA MATH 485 - Memristor

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Authors Troy Comi Aaron Gibson and Joseph Padilla Mentor Jefferson Taft April 8 8 2010 Tucson AZ University of Arizona April 8 2010 Cl i l Ci i Classical Circuits Four Fundamental Circuit Variables 1 Charge q Ch 2 Voltage v 3 Current I 4 Magnetic g Flux Three Classical Fundamental Circuit Elements 1 Capacitor dq C dv 2 Resistor dv R di 2 3 Inductor d L di Two Additional Relationships 1 dq i dt 2 d v dt Modeling of RLC Circuit with Applied Voltage L Q R Q Q C V t April 8 2010 Existence of the Memory Resistor v i q Strukov et al Nature Vol 453 2008 80 83 An element that is Passive Dissipative 2 terminal Effectively a resistor with resistance that depends on charge that has passed through memory April 8 2010 Existence of the Memory Resistor v i q Strukov et al Nature Vol 453 2008 80 83 Applications Higher density circuits Unique modeling possibilities Generation of special waveforms Signal processing April 8 2010 Memristor The Fourth Element Proposed Chua P d by b Leon L Ch in i 1971 using i an argument based b d on symmetry Described by the sixth relationship between the four fundamental circuit variables d M dq Faraday s y Law of Induction states the induced EMF or voltage g in a closed circuit is equal to the time rate of change in magnetic flux Therefore the memristor equation can be expressed as the following v M M q i i Similar equation to resistors described by Ohm s Law v R i Memristance can reduce to resistance if certain conditions are met Memristor combination of memory and resistor Symbol for memristor Chua LO IEEE Transactions on Circuit Theory Vol CT 18 No 5 1971 April 8 2010 Properties of Memristors p between current and voltage g Non linear relationship Reduces to resistor for large frequencies as evident in the i v characteristic curve May also reduce to a resistor based on d fi d state defined t t variables i bl Memory capacities based on different resistances produced by the memristor Non volatile memory possible if the magnetic flux and charge through the memristor have a positive relationship M 0 Does not store energy Similar to classical circuit elements a system of memristors can also be described as a single memristor memristor Chua LO IEEE Transactions on Circuit Theory Vol CT 18 No 5 1971 April 8 2010 i v Characteristic Curve Pinched hysteresis unique to memristors No N combination bi i off other h fundamental circuit elements makes Lissajous figure Proof by Chua and Kang published in 1976 Strukov et al Nature Vol 453 2008 80 83 Chua LO Kang SM Proceedings of the IEEE 64 Issue 2 1976 April 8 2010 Generalization of Memristance Recall the derived equation for memristance v M q i This can be generalized further by considering a set of state variables x x1 x2 xn These state variables are dependant on the specific implementation p of the memristor We can use the state variables to make a substitution in our memristance equation v M x i dx dt f x i The state variables must be related to the current This generalization leads to a unique set of equations for different memristors and memristive systems Chua LO Kang SM Proceedings of the IEEE 64 Issue 2 1976 April 8 2010 Example of a Memristive System Consider a light bulb bulb In general general a light bulb can be thought of as a resistor However as the filament heats up the resistance of the bulb increases This behavior creates a non linear resistance which can be described with the following temperature dependant equations V R0T I M T i dT dt aTi2 b t4 tt04 f T i where R0 T0 a and b are constants These equations satisfy our conditions for a memristive system Cunningham W J Journal of Applied Physics Vol 23 No 6 1952 April 8 2010 Difficulties in Finding Memristors Why has it taken almost four decades to find a memristor Memristors are not new Memristive properties have been observed by researchers for more than three decades Pinched hysteresis curve is a unique property of a memristor However researchers did not made the connection with their observations observations Often described as anomalous inductance resistance and disregarded in certain practical applications e g J Josephson h Junction J i Direct link between charge and magnetic flux not y necessary Chua LO IEEE Transactions on Circuit Theory Vol CT 18 No 5 1971 April 8 2010 Formation and Applications Physical model Electroforming Light emmiting memristor Memristors in logic gates Modeling simple learning April 8 2010 Memristor Found Pt TiO2 x Pt RTotal RON w t w t ROFF 1 D D w t w t v t RON ROFF 1 i t D D dw t RON V i t dt D w t V RON q t D v Ron M q Roff 1 q t D2 Strukov et al Nature Vol 453 2008 80 83 April 8 2010 F i off TiO2 Memristor M i Formation TiO 2 TiO 2 x 2 x O 2 V Yang et al Nanotechnology 20 2009 21501 April 8 2010 F i off TiO2 Memristor M i Formation TiO 2 TiO 2 x 2 x O 2 V Yang et al Nanotechnology 20 2009 21501 April 8 2010 Light Emitting Memristor 2 Zakhidov et al Organic Electronics 11 2010 150 153 April 8 2010 Memristive Logic Gates Borghetti et al PNAS Vol 106 No 6 2009 1699 1703 April 8 2010 Simple Learning Circuit Pershin et al Physical Review E 80 2009 021926 April 8 2010 Simple Learning Circuit Pershin et al Physical Review E 80 2009 021926 April 8 2010 Simple Learning Circuit Pershin et al Physical Review E 80 2009 021926 April 8 2010 HP Simulations HP Nature Paper Strukov et al Nature Vol 453 2008 80 83 Our Simulation April 8 2010 HP Simulations Cont HP Nature Paper Strukov et al Nature Vol 453 2008 80 83 Our Simulation April 8 2010 HP Simulations Cont HP Nature Paper Strukov et al Nature Vol 453 2008 80 83 Our Simulation April 8 2010 Future Directions More precise modeling Learning circuits in parallel signal processing Additional voltage waveforms April 8 2010 References Borghetti et al PNAS Vol 106 No 6 2009 1699 1703 Chua LO IEEE Transactions on Circuit Theory Vol CT 18 No 5 1971 Chua LO Kang SM Proceedings of the IEEE 64 Issue 2 1976 Cunningham g W J J JJournal of Applied pp Physics y Vol 23 3 No 6 1952 Kumar IETE Technical Review Vol 26 Issue 1 2009 Pershin et al Physical Review E 80 2009 021926 Strukov et al Nature Vol 453 2008 80 83 Yang et al Nanotechnology 20 2009 21501 Zakhidov et Zakhidov et al al Organic Electronics 11 2010 150 153 150 153


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