A PWL Model of Memristor and Its Application Example, Study Guides, Projects, Research of Advanced Computer Architecture

Download A PWL Model of Memristor and Its Application Example and more Study Guides, Projects, Research Advanced Computer Architecture in PDF only on Docsity! A PWL Model of Memristor and Its Application Example 12' 3 4 I" Dongping Wang " ,Zhiheng Hu ,Xun Yu .Juebang Yu ' 1. University of Electronic Science and Technology of China (UESTC), 2. Sichuan University, China, 3. Chengdu University of Infromation Technology, Chengdu China , 4. Hanmo GIS Tech Company, Chengdu China * e-mail address: d_p_w @163.com, ** e-mail address: j b yu @ u e stc .ed u .cn Abstract-A PWL (PieceWise Linear) model of the new found memristor is proposed in this article. A simple second order circuit containing an inductor, a capacitor, a resistor and a memristor serves as an example to illustrate the application of this model . The circuit equation is established then Matiab simulation is performed. It is believed from this example that the model could provide satisfactory result for analyzing circuits containing memristor(s). 1. INTRODUCTION Though recognized in 1971 by Prof. Leon 0 Chua of UC Berkeley as the 4th passive circuit element [1], memristor almost does not appear in the textbook or literature until May 1, 2008, when the Journal <Nature> published the milestone discovery by Stanley Williams and his Team at HP Information and Quantum Systems Laboratory [2]. The HP Team claimed at the end of April 2008 that the memristor device had been fabricated by them when using nano technology. Soon Prof. Leon Chua gave a Keynote speech "Memristor: The 4th Circuit Element" at the plenary meeting of the 6th International Conference on Communications, Circuits And Systems (ICCCAS) on May 23, 2008 in Xiamen City , China . Soon after , a Memristor and Memristive System [3] (MMS) Symposium (cosponsored by NSF, UC Berkeley and UC Merced, and chaired by UC Merced Chancellor Steve Kang) held on Nov 21 at UC Berkeley [4]. At this Symposium, experts worldwide like Prof. Leon Chua of UC Berkeley, Dr. Stanley Williams, Phil Keukes and Greg Snider of HP. Prof. Rainer Waser of RWTH Aachen University, Germany, Prof. Massimiliano Di Ventra of UC San Diego, Dr. Blaise Mouttet of Geoge Mason University, Dr. Pushkar Apte of SIA, Dr. Jeff Welser of SRC described the theoretical significance and industrial application potentials of the MMS successively. This Symposium attracts attention of a great amount of mass media organizations like Youtube, AOL, broadcast the video of this event for quite a long time [5]. Academic and Industry circles predict that a new round of IT revolution will soon be triggered such as the no-booth time computer will appeared if the memristor based memory is used to substituting the current DRAMs ; Cell phones could be used for months without recharged by using the energy saving memristor memory, brain-like computer could be created by using memristor-based neural network techniques, etc. The appearance of memristor would also request to rewrite the physics textbook since the 4th passive element should be added wherein such that the students could familiar with this kind of device began from their middle school education. Since the memristor is essentially a time-varying and nonlinear device [6], it is difficult for a middle school student and the university freshmen (even sophomore) to understand operating mechanisms of the new device - memristor, we proposed here a PWL model of the memristor, through which we could conduct the quasi-linear analysis of circuits containing memristor(s) . As a result, people having only the background of basic ODE (Ordinary Differential Equation) theory could understand what could be happened in such circuits. On the other hand, this kind of quasi-linear analysis could also be a good approximation to a variety of weak-nonlinear MMS . II. THE INTRODUCTION MEMRISTOR V-I CURVE AND ITS PWLMoDEL According to the recent technology, a real memristor device fabricated by nano technology could be described by a frequency (time) dependant v-i curve depicted in Fig.l [1], As can be seen from this figure, the curve looks like an inclined digit 8. voltage c, Figure 1. A memristor v-i curve. By approximating the curve by a right- inclined X shape PWL curve, we could write the PWL model of the memristor Shown in Fig. 2. 978-1-4244-4888-3/09/$25.00 ©2009 IEEE 932 1.5~----.--------,--- ~-----, -1 Figure 2. An approximation ofthc memristor v-i curve. V/? (I) = Ri/?(I) (3) . dv.. (4)lc (I ) = C - dl iM(t) =g(vM(t)) (5) KCL: i(l) = ic (I) + iL(I) + iM(I) (6) i(l) = iL(t)-i/?(I) (7) KVL: Vc(I) =vI.(I) +v/? (I) (8) vM(I)=vc(l) (9) With the component constituent relations (2) to (5) and the KCL, KVL equations (6) to (9), we get { dv.. 1 (. ().)--- =- -1 - g V +1 dl C I. c dil. =J..(v -R*i +R*i) dt L c I. Let {x = ~cY =11. Then we get (10) (11) Figure 3. An independent current source driven RLCM circuit. dVM 0--> dt dVM 0--< dt (1) Equation (1) can be regarded as an approximation of the constituent relation of the circuit element of the memristance M . { dx =J..(_y_ g(x) + Fsin WI) dt C (12) dy =J..(x-Ry+RFsinwI) dt L Now we are able to perform linear analysis for each section of the memristor v-i curve since equation (1) has been in linear form, and the rest curve sections depicted by equation (12) are already in its affine version. Suppose III. FORCED OSCILLATION IN A SECOND ORDER CIRCUIT CONTAINING A MEMRISTOR Fig. 3 shows an RLCM circuit which is modified from the well-known Chua 's oscillator by substituting the left capacitance of the original circuit by a independent sinusoidal current source i(t) , and the nonlinear element -- Chua's diode by a memristor. In terms of this circuit, we can understand the phenomena occurred when initial conditions of the circuit are given . The element's constituent relations are respectively written as: (14) (13) div (I) =L_L I. dt (2) i(l) =F sin ox R =1, L =1, C = 0.01, F =1, W =100, x(O)=0, yeO) =0 and note also i(O)=O, we then can use the circuit diagram given in Fig . 3 to perform the circuit simulation by using Matlab software package. IV. CIRCUIT SIMULATION RESULTS The Matlab simulation results of the given circuit are performed. The typical waveforms: voltage across the memristor vc(t) , the current passing through the memristor h(t) and phase portrait between vc(t) and h(t) are given in Fig. 4, Fig. 5 and Fig. 6, respectively. Note Fig. 7 shows the FFT result of the vc(t) from which 933