Journal of Switching Hub Volume 4 Issue 3 Design and Modeling of 4x4-bit RAM using Memristor Garima Kulshreshtha* Assistant Professor, Department of Electronics and Communication Engineering, IILM Academy of Higher Learning, College of Engineering and Technology, Greater Noida, Uttar Pradesh, India Email: *[email protected] DOI: http://doi.org/10.5281/zenodo.3574045 Abstract The memristor is a non-linear resistor which changes its state relative to the net electric flux passing through its two terminals. It saves its state after an electrical bias is removed. Hewlett Packard is credited for the large deal of efforts which has been spent in the research community to derive a suitable model able to capture the nonlinear dynamics of the nano- scale structures, based on titanium dioxide (TiO2) thin film. When more than one memristors are connected together than the behavior of the device is difficult to predict because the polarity-dependent nonlinear variation in the memristance of individual memristor. The relationships among flux, charge and memristance of diverse composite Memristor, using the HP-TiO2 model has been studied, and the characteristics of complex memristor circuits are analyzed. In this work, we are implementing a 4x4-bit RAM using memristor which works as an EPROM. Keywords: D-flip-flop, memristor, RAM, titanium dioxide INTRODUCTION performance of digital circuits without the System performance based on some basic need of further reduction of transistor features like interactivity, interactional, dimensions [2]. The memristors are and reflexionality; which can’t be achieved currently under development and without the involvement of time and improvement by various teams memory-related concepts and constructs. including Hewlett-Packard, SK Hynix, and Therefore, a great chance to develop HRL Laboratories. A team belongs to HP interaction-based computing systems Labs found missing element memristor arrives with the invention of the memristor based on the thin film of titanium dioxide and memristive systems opened up by in 2008. The applications of memristors these new possibilities of nano-electronic are noelectronic memories, computer design. The memristor was originally logic, and neuromorphic computer visualized in 1971 by circuit theorist Prof. architectures. The HP team also Leon Chua as a missing non-linear passive announced the commercial applications of two-terminal electrical component relating memristor technology will be Flash, SSD, electric charge and magnetic flux linkage DRAM, and SRAM in 2011. A i.e. the time integrals of current and researcher’s team from HRL Laboratories voltage [1]. According to the governing and the University of Michigan announced mathematical relations, the memristor's the first functioning memristor array built electrical resistance depends upon its on a CMOS chip in the year 2012. previous state and present electrical biasing conditions, and when combined In this paper, we will discuss that the with transistors in a hybrid chip, memristor is a necessary and useful memristors could radically improve the building block in circuit theory for the 18 Page 18-30 © MAT Journals 2019. All Rights Reserved Journal of Switching Hub Volume 4 Issue 3 future semiconductor industry. We will voltage v to the current i, R = dv/di. As a first introduce the history of memristor and strictly mathematical exercise, he explored then explain the TiO2 structure of the properties of this potentially new memristor and their functioning in sections nonlinear circuit element, and found that it 2 and 3. Then, we will analyze the was essentially a resistor with memory– it characteristics of complex memristor was a device that changed its resistance circuits in section 4 by using MATLAB depending on the amount of charge that Simulation. 4-bit RAM and 4x4 memory flowed through the device, and thus he using non-volatile memristive concepts are called this hypothetical circuit element M explained here. All the discussions on a “MEMRISTOR”. This conclusion was memristor-based memory design are given independent of any physical mechanism in section 5. Finally, Section 6 concludes that might couple the flux and charge and this paper. in fact, he did not postulate any mechanism at all. Moreover, the memristor Memristor definition did not even require causality. According to the general mathematical model, a memristor is any passive In other words, the mathematical electronic circuit element that displays a relationship between flux and charge could pinched hysteresis loop in its i-v be the result of some other cause – any characteristic, independent of what the mechanism that led to the constraint physical mechanism is that causes the embodied by the equation dφ = Mdq hysteresis. The model is useful because it would lead to a device with the properties provides quantitative means to predict the of a memristor. He published these initial properties of such a device in an electronic findings [1] essentially as a curiosity; it circuit. However, no mathematical model was not obvious at that time that such a is perfect- it is only an approximation to circuit element existed. In the beginning it real behavior- this is as true for a resistor may be hard to see the potential of a newly as a memristor. introduced fourth element and difficult to use properly, often mixing it up with the As a result of Prof. Leon Chua’s work on other three; however, if it turns out to be nonlinear circuit elements, he made an more suitable to certain tasks, who knows interesting observation, for traditional how useful it might be in the end? Fig. 1 linear circuits; there are only three shows the electronic symbol representation independent two-terminal passive circuit of a memristor element. From the elements: the resistor R, the capacitor C symmetry diagram in Fig. 2, we see how and the inductor L. However, when he the memristor finds its natural place in the generalized the mathematical relations to circuit theory along with the five other be nonlinear, there was another combinations of pairs of circuit variables. independent differential relationship that in principle coupled the charge q that flowed through a circuit and the flux φ in the circuit, M = dφ/dq, that was mathematically different from the Figure 1: Symbol representing a nonlinear resistance that coupled the memristor in an electric circuit. 19 Page 18-30 © MAT Journals 2019. All Rights Reserved Journal of Switching Hub Volume 4 Issue 3 Figure 2: Symmetry diagram showing the 6 distinct possible realizations based on the four circuit variables symbol. As per Chua, it is not possible to panel shows an applied voltage sine implement an equivalent circuit for a wave (gray) versus time with the memristor using any combination of corresponding current for a resistor only passive nonlinear components like- (blue), a capacitor (red), an inductor resistors, capacitors and inductors. (green) and memristor (purple). The Fig. Thus, the memristor represents an 3 shows the I-V characteristics of all the independent 'basis function' for four devices, with the characteristic constructing passive nonlinear circuits pinched hysteresis loop of the [3], so it has a status similar to the memristor. It is also presented by nonlinear resistor, capacitor, and inspection that the memristor curve inductor. The Fig. 3 below is an cannot be implemented by combining illustration of this argument. The upper the others. Figure 3: Characteristics of passive components. 20 Page 18-30 © MAT Journals 2019. All Rights Reserved Journal of Switching Hub Volume 4 Issue 3 Structure of TiO2 Memristor memristor as a function of time [4]. M(q) In the TiO2 memristor, a thin undoped is physically restricted to be positive for all titanium dioxide (TiO2) layer and a thin values of q. A negative value would mean oxygen-deficient doped titanium dioxide that it would perpetually supply energy (TiO2-x) layer are sandwiched between when operated with alternating current. two platinum electrodes. When a voltage (or current) is applied to the device, the DIGITAL CIRCUIT width of the TiO2 and TiO2-xlayer changes IMPLEMENTATION as a function of the applied voltage (or Memristor Model current). Memristor is the basic and precious part of the more extensive newly developed system model, so it is useful to try to model it in the MATLAB Simulink environment [5]. However, the basic environment offers to model in the input- output form, though this it is not possible to be seen memristor as a two-terminal element but as a black box with one input (voltage) and one output (current). If this limitation does not obstruct the user then Figure 4: Cross-section of the first HP MATLAB Simulink is very suitable for TiO2-memristor [4]. the model construction. Fig. 5 shows a functional memristor model. We need to The total resistance (memristance) of this give more attention on the adjustment of system is the addition of the doped and the separate blocks and simulation parameters. undoped part. This gives the dynamic state The exciting harmonic voltage source we of high and low conductance between the used here with the amplitude of 1V and the boundaries. The state variable (w(t)-in this frequency of 1Hz. Thus, the model could particular case) describes how the be finished but if the vectors of voltage memristance of the element evolves with and course are known it is very handy to time try to calculate the charge and flux vectors, for which they describe the memristor The variable w is proportional to the explicitly. charge q. When the current I is passing through the boundary between the higher The hysteresis loops are formed since the and lower conductive states, the current is current through the memristor does not shifted either to the right or to the left with vary linearly with the applied voltage, respect to time factor. Fig. 4 shows the unlike a resistor that follows Ohm’s law.