Institutionen för systemteknik Department of Electrical Engineering Examensarbete A Study of the Memristor Models and Applications Examensarbete utfört i Elektroteknik vid Tekniska högskolan i Linköping av Vahid Keshmiri LiTH-ISY-EX—11/4455--SE Linköping 2014 Department of Electrical Engineering Linköping tekniska högskola Linköping universitet Linköping universitet SE-581 83 Linköping, Sweden 581 83 Linköping No Title Page LITH-EX-11/4455 A Study of the Memristor Models and Applications 2 of 115 Table of Contents 1. Introduction ..............................................................................................................................13 1.1 Motivation ...............................................................................................................................................14 1.2 Working environment ............................................................................................................................15 1.3 Work specification .................................................................................................................................15 1.4 Outline of thesis .....................................................................................................................................15 2. A Brief History of circuit elements ............................................................................................17 2.1 Introduction ............................................................................................................................................17 2.2 Research reviews ..................................................................................................................................17 2.3 The Resistor, The Capacitor, The Inductor .........................................................................................25 2.3.1 The Resistor ................................................................................................................................................................. 25 2.3.1.1Ohm's law................................................................................................................................................................26 2.3.1.2Resistors in series...................................................................................................................................................27 2.3.1.3Resistors in parallel.................................................................................................................................................27 2.3.1.4Power dissipation....................................................................................................................................................27 2.3.2 The Capacitor ............................................................................................................................................................... 28 2.3.2.1Current-voltage relation...........................................................................................................................................30 2.3.2.2Capacitors in parallel...............................................................................................................................................30 2.3.2.3Capacitors in series.................................................................................................................................................31 2.3.2.4Energy Storage........................................................................................................................................................31 2.3.2.5Non-ideal behavior..................................................................................................................................................31 2.3.3 The Inductor ................................................................................................................................................................. 32 2.3.3.1Current-voltage relation...........................................................................................................................................32 2.3.3.2Inductors in parallel configurations:.........................................................................................................................33 2.3.3.3Inductors in series configurations:...........................................................................................................................34 2.3.3.4Stored energy.......................................................................................................................................................... 34 2.3.3.5Ideal and real inductors...........................................................................................................................................35 2.3.3.6Applications............................................................................................................................................................. 35 2.4 Origin of the memristor .........................................................................................................................35 2.4.1 The Missing Link ........................................................................................................................................................... 37 2.5 Chua's memristor ..................................................................................................................................38 2.6 HP Labs ...................................................................................................................................................42 3. The Memristor ..........................................................................................................................45 3.1 Introduction ............................................................................................................................................45 3.2 Memristor definition ..............................................................................................................................45 3.3 Memristance ...........................................................................................................................................46 3.4 Memristor analogy .................................................................................................................................46 3.5 Memristor properties .............................................................................................................................47 3.5.1 Flux-charge relation ......................................................................................................................................................47 3.5.2 Current-voltage relation ................................................................................................................................................48 3.5.3 Switching mechanism ...................................................................................................................................................48 3.5.3.1Thermal switching....................................................................................................................................................50 3.5.3.2Electronic switching.................................................................................................................................................51 3.5.3.3Ionic switching......................................................................................................................................................... 51 3.6 Switching speed ....................................................................................................................................52 3.7 Memristive systems ...............................................................................................................................52 4. Memristor Models ....................................................................................................................53 4.1 Introduction ............................................................................................................................................53 4.2 Models ....................................................................................................................................................53 4.2.1 Linear Ion Drift model ...................................................................................................................................................53 4.3 Window functions ..................................................................................................................................56 This document is released by Electronics Systems (ES), Dep't of E.E., Linköping University. Repository refers to ES No Title Page LITH-EX-11/4455 A Study of the Memristor Models and Applications 3 of 115 4.3.1 Strukov et al. .................................................................................................................................................................57 4.3.2 Benderli ........................................................................................................................................................................ 57 4.3.3 Joglekar ........................................................................................................................................................................ 58 4.3.4 Biolek ...........................................................................................................................................................................