A new DDCC based memristor emulator circuit and its applications

Abstract

Memristor is a new passive circuit element. The interaction of the memristor with other circuit elements is important for designers. In this paper, new memristor emulator circuit is designed using DDCC (differential difference current conveyor) based on CMOS. It is realized that the proposed emulator causes less complexity compared to other designed emulator circuits. Compatibility of memristor with CMOSs and its operation ability at high frequencies are very important for circuit design based on memristor. The emulator based on CMOS can manage to provide these two fundamental properties successfully. In order to test the proposed emulator, it is connected to memristor with both ways, serial and parallel, than MC circuit is analyzed and results are shown at the end of the paper.

Introduction

Prediction [1], [2] and experimental realization of the memristor [3] increased interest in passive circuit element memristor. In 1971, Leon Chua noted mathematical relations between four fundamental circuit components i, v, q and ϕ as shown in Fig. 1.

Resistance (R) is the rate of voltage with current (R=dv/di), capacitance (C) is the rate of charge with voltage (C=dq/dv) and inductance (L) is the rate of change of magnetic flux with current (L=dϕ/di). From symmetry, Chua noticed the absent of the fourth fundamental element which for him should be, called memristor (M), relation between charge and magnetic flux, M =dϕ/dq. Memristor had been just a theory before Williams and co-workers fabricated memristor as a structure of Pt/TiO₂/Pt [3] and they showed realistic mathematical definition/formula of a memristive device that can be used to compute and predict important electrical and dynamical properties of the device [4]. The memristor invented at HP Labs is made of titanium dioxide sandwiched between two platinum contacts as shown in Fig. 2. The structure has two regions with a high dopant concentration (low resistance=R_ON) and a low dopant concentration (higher resistance=R_OFF). Doped and undoped regions provide conductive and insulator layer for device, respectively. The comprehensive study about switching mechanism of memristor is analyzed by Waser and Aono [5].

R_ON state is conductive state of memristor, for another state (R_OFF) memristor behaves like an insulator. Current–Voltage equation of memristor can be seen below. Here,

$$V(t)=\left[R_{ON}\frac{w(t)}{D}+R_{OFF}\left(1-\frac{w(t)}{D}\right)\right]i(t)$$

I(t): Memristor Current, $R_{ON}$: ON state resistance of Memristor

V(t): Memristor Voltage, $R_{OFF}$: OFF state resistance of Memristor

Designers expect wide application area for memristive systems such as; neuromorphic networks, nonvolatile memories, chaotic circuits, logic circuits and so on [6]. In addition automatic gain control circuit [7], programmable analog circuits [8], oscillators [9], [10], basic arithmetic operators [11] are the applications which memristors have already been used in.

Memristor has numerous advantages but it is not available easily. For this reason, a lot of memristor SPICE macro models [12], [13], [14], [15], [16], [17] and emulators [18], [19], [20], [21], [22], [23], [24], [25], [26], [27] are proposed. HP memristor model is one of the earliest models. Various physical memristors and models proposed these years [19] and many mathematical models are highly consistent with the corresponding physical memristors-characteristics of physical memristors show differences from material to material-, such as the threshold adaptive memristor model proposed in [20] and the compact memristor model proposed in [21]. Abdalla and Pickett suggested SPICE model of real TiO₂ memristive device [22]. In addition a physics-based memristor model suggested Williams and co-workers [23]. Another emulator proposed by Kolka et al. [24] consists of Analog Digital Converter Block, Microcontroller Unit and Digital Analog Converter Block. This emulator is programmable and it can be used commercially but its structure is complex. Mutlu and Karakulak [25] suggested emulator based on Op-Amp, which can be used practically. However, this configuration has two OP-AMPS, seven resistors, single capacitor, single diode and a multiplier. In a study by Kim et al. [26] reported that the memristor emulator is employing five OP-AMPs, eight resistors, discrete ten transistors and an adder. Yener and Kuntman [27] proposed memristor emulator based on CMOS consists of four blocks that are employed five Differential Difference Current Conveyors (DDCC), four resistors and single capacitor.

In this paper we will present a very simple memristor emulator using DDCC based on CMOS. In proposed emulator we have a single DDCC, two resistors, one capacitor and one multiplier circuit. Compatibility of memristor with CMOS is very important feature and this emulator achieved successfully. Integrating VLSI designs, working different frequency modes and having a simple structure are one of the prior properties of this emulator. In order to test the proposed emulator, applications (single, serial, parallel and MC circuit) are shown at the end of the paper.