Fourth Fundamental Circuit Element: SPICE Modeling and Simulation
This chapter deals with two possible stages of exploring the memristor as the fourth fundamental circuit element: (1) generation of the model and (2) simulation of the element behavior with the aid of the model. The initial stage, i.e. modeling of the two
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Fourth Fundamental Circuit Element: SPICE Modeling and Simulation Dalibor Biolek and Zdenek Biolek
4.1 Introduction The memristor was originally defined as an electric element which provided the last vacant connection between voltage, current, and their time-domain integrals, i.e. between flux and charge [1]. It is rightly described as the fourth fundamental circuit element next to the resistor, capacitor, and inductor. It turns out that scientists met with the signs of memristive behavior long before the discovery of the memristor itself. These signs were described and modeled using means among which the memristor was missing. Immediately after the introduction of the concept of memristor in 1971 this hypothetical element was used for modeling certain processes that exhibited the attributes of memory behavior. The memristor was used for the modeling of devices based on varied and mutually unrelated physical principles. An example is the work of Oster [2], which shows that the tapered dashpot or an electrochemical system can be modeled as a memristor. Since the 1970s the memristor has gained a firm position as a standard modeling tool in branches which utilize the methods of network thermodynamics [3]. So it soon turned out that the concept of memristor is also useful for fields of study other than electrical engineering. The researchers involved in the modeling of systems that are composed of subsystems of different physical nature, as is common, for example, in electromechanics, now use the so-called generalized memristor [4]. It establishes a link between two physical quantities, which are in the given physical field of study analogous to the flux and the charge; for example in the D. Biolek () Department of Electrical Engineering/Microelectronics, University of Defence/Brno University of Technology, Brno, Czech Republic e-mail: [email protected] Z. Biolek Department of Microelectronics, Brno University of Technology, Brno, Czech Republic e-mail: [email protected] R. Tetzlaff (ed.), Memristors and Memristive Systems, DOI 10.1007/978-1-4614-9068-5__4, © Springer Science+Business Media New York 2014
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case of mechanics, they are the effort and the position. Using the memristor we can therefore model processes in a variety of systems differing in their physical nature, be it mechanical [5], hydraulic [6], neuromorphic [7], or other systems. With this general conception, the memristor can be seen as an element that guarantees a clear correlation between the accumulated effort (momentum, the integral of effort) and the state achieved (displacement, integral of flow). After a report was published on the successful implementation of memristor in TiO2 [8] in 2008, the interest in this element skyrocketed. However, the memristor comes to be considered specifically as an element of electrical nature. Moreover, according to the original definition of the memristor, the state from which the instantaneous value of memristance is derived is the charge (or the flux). In the cours
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