Active and Passive Electronic Components

Volume 2017 (2017), Article ID 1609787, 12 pages

https://doi.org/10.1155/2017/1609787

## A Novel Floating Memristor Emulator with Minimal Components

^{1}College of Information Engineering, Xiangtan University, Xiangtan, Hunan 411105, China^{2}Department of Optoelectronic Engineering, Xiangtan University, Xiangtan, Hunan 411105, China

Correspondence should be addressed to Zhijun Li

Received 4 July 2017; Revised 23 August 2017; Accepted 6 September 2017; Published 19 October 2017

Academic Editor: Jiun-Wei Horng

Copyright © 2017 Zhijun Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A new floating emulator for the flux-controlled memristor is introduced in this paper. The proposed emulator circuit is very simple and consists of only two current feedback operational amplifiers (CFOAs), two analog multipliers, three resistors, and two capacitors. The emulator can be configured as an incremental or decremental type memristor by using an additional switch. The mathematical model of the emulator is derived to characterize its behavior. The hysteresis behavior of the emulator is discussed in detail, showing that the pinched hysteresis loops in - plane depend not only on the amplitude-to-frequency ratio of the exciting signal but also on the time constant of the emulator circuit itself. Experimental tests are provided to validate the emulator’s workability.

#### 1. Introduction

The memristor, next to the resistor, the capacitor, and the inductor, was postulated as the fourth passive circuit element by Chua in 1971 [1]. It is defined as a two-terminal element that provides the missing constitutive relationship between charge and flux. Ignited by the successful fabrication of a real nanoscale memristor by HP Labs in 2008 [2], tremendous research has been devoted to explore memristor-based potential applications in such areas as resistive random access memory (RRAM) [3, 4], analog circuits [5, 6], digital circuits [7, 8], chaotic circuits [9, 10], and neural networks [11, 12]. Although memristor has many potential applications, it is not available as a universal electronic device for ordinary researchers. For this reason, a lot of SPICE models [13–15] were implemented to serve as a possible alternative to simulate memristor. But they cannot be used to build real-world applications. Recently, Bio Inspired Technologies has launched the world’s first commercially available memristor [16]. However, it has a high price and can only be applied under special conditions in order to avoid irreparable damage [17]. Therefore, a replacement that behaves like a real memristor is still urgently needed to allow ordinary researchers to study memristor-based practical applications. Indeed, many memristor emulator circuits have been developed in recent years [17–32]. For example, using a JFET to implement the required nonlinearity, a memristor emulator constructed with five operational amplifiers, a floating capacitor, a large number of resistors, and an analog multiplier is presented in [19]. In addition to its complexity, the emulator reported in [19] is grounded and therefore is unsuitable for use as a two-terminal device in more complicated circuits. A unified approach for transforming nonlinear resistors into memristors is developed in [20], but the resultant emulators based on this methodology are limited by grounded operation. Emulator presented in [21, 22] can well imitate the features of TiO_{2} memristor. However, the circuits are very complex and are built with an analog multiplier and a number of operational amplifiers (OAs), resistors, and MOS transistors. In order to make circuits in [21, 22] have a capacity of floating operation, further modification was made in [23] by adding a current conveyor. In [24], Sanchez-Lopez et al. proposed a floating memristor emulator which can operate at a high operating frequency (up to 14 kHz). But the circuit uses a large number of active and passive elements, namely, five CFOAs, one analog multiplier, and a number of passive elements. Two simplified emulators with higher operating frequency were presented in [17, 26]. However, the grounded restriction places a substantial obstacle on their connectivity with other circuit elements. The emulator circuit in [27] uses a light-dependent resistor (LDR) to provide the required nonlinearity. Although the emulator circuit is very simple, it can only work at low frequency and has a narrow variation range of memristance. Pershin and Ventra built a memristor emulator using digital and analog mixed circuits [28]. The resolution of its memristance, however, is limited by the limited performance of the A/D converters. Using diode-resistive networks to implement the required nonlinearity, a binary-level emulator was developed in [29] and a continuous-level emulator implemented by using the nonlinear transfer characteristics of OTA was presented in [30] by Abuelma’atti and Khalifa. However, the grounded restriction is still the main obstacle to its connectivity with other circuit elements. A floating emulator, which is built with four CFOAs and avoids the use of analog multipliers, was developed by the same authors [31]. In order to make it successfully emulate a floating memristor, the emulator circuit must satisfy strict parameter matching conditions. An electronically tunable memristor emulator circuit is presented in [32] and its memristance value can be controlled by changing transconductance parameters of the used OTAs.

In this paper, we propose a floating memristor emulator, which is built with two CFOAs, two analog multipliers, and five passive elements. In fact, multipliers are often used to realize the product of voltage and flux (current and charge) for the design of the flux-controlled (charge-controlled) memristor emulators [21–27]. Different from the above design methods, however, herein the multipliers are employed to construct a floating voltage-controlled resistor (VCR). The emulator is implemented by using the flux across it as the controlled voltage of the VCR. The proposed emulator not only has a simple topology but also can be configured as an incremental or decremental type memristor. The mathematical model of the emulator is derived in detail. Its hysteresis behavior is further discussed, showing that the pinched hysteresis loops in - plane depend not only on the amplitude-to-frequency ratio of the exciting signal but also on the time constant of the emulator circuit itself. Furthermore, PSpice simulations and experimental tests are included to demonstrate the properties of the emulator. The organization of the paper is as follows: in Section 2, we introduce our emulator circuit and derive its mathematical model, hysteresis behavior analysis is performed in Section 3, and PSpice simulations and experimental results are given in Sections 4 and 5, respectively. We conclude the paper in the last section.

#### 2. Proposed Floating Emulator Circuit

The memristor completes the missing link between charge and flux . When its constitutive relation is expressed as a single-valued function , the memristor is flux-controlled and can be characterized by its memductance , which describes the ratio of change of the charge with respect to the flux across the device:The corresponding - relationship of the memristor in this case is expressed as

The proposed floating flux-controlled memristor emulator circuit is shown in Figure 1. It is composed of two AD844 type CFOAs, two AD633 type analog multipliers, three resistors, and two capacitors. Here, and are parasitic resistors at -terminal of and ; and and and are the parasitic resistors and capacitors associated with -terminal. Each CFOA is characterized by the following terminal relations [20]:where , , and are the port transfer ratios. From Figure 1, the current through the resistor can be expressed asThe current will be transferred to -terminal of and it will be integrated by the capacitors and to produce a output voltage at -terminal of given byThe influence of the parasitic resistor on the emulator circuit is negligible due to its high resistance value which is approximately 3 M. Substituting (4) into (5), one can obtain the output voltage given byConsidering the fact that , (6) can be rewritten aswhere corresponds to the flux across the emulator and it is defined as . Here, we consider that the initial condition of the integrator is zero. Similarly, one can obtain the output voltage :Analog multipliers and and the resistors and construct a floating voltage-controlled resistor (VCR) and is the controlled voltage. Referring to the input-to-output characteristic of AD633, the output voltages and can be given asThus, the currents and can be expressed asIt is can be inferred from (10) that holds if is satisfied. Thus, the equivalent conductance of the VCR can be described aswhere . From Figure 1, when the switch is switched to node , that is, , the emulator realizes an incremental type memristor and the corresponding memductance can be expressed asWhen the switch is switched to node , that is, , the emulator is equivalent to a decremental type memristor whose memductance is decided byThus the emulator has the same advantage as the emulators in [17, 23]; that is, the incremental or decremental type memristor can be interchanged by using an additional switch . Due to , , , and and assuming that , (12) and (13) can be described as the following unified expression:It can be seen from (14) that the two different type memductances are linearly dependent on the flux ; thus the emulator is flux-controlled, and it can be controlled by a voltage imposed on the input terminals.