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Design of a Memristor-Based Digital to Analog Converter (DAC) electronics Article Design of a Memristor-Based Digital to Analog Converter (DAC) Ghazal A. Fahmy * and Mohamed Zorkany Electronics Department, National Telecommunication Institute, Cairo 11768, Egypt; [email protected] * Correspondence: [email protected] Abstract: A memristor element has been highlighted in recent years and has been applied to several applications. In this work, a memristor-based digital to analog converter (DAC) was proposed due to the fact that a memristor has low area, low power, and a low threshold voltage. The proposed memristor DAC depends on the basic DAC cell, consisting of two memristors connected in opposite directions. This basic DAC cell was used to build and simulate both a 4 bit and an 8 bit DAC. Moreover, a sneak path issue was illustrated and its solution was provided. The proposed design reduced the area by 40%. The 8 bit memristor DAC has been designed and used in a successive approximation register analog to digital converter (SAR-ADC) instead of in a capacitor DAC (which would require a large area and consume more switching power). The SAR-ADC with a memristor- based DAC achieves a signal to noise and distortion ratio (SNDR) of 49.3 dB and a spurious free dynamic range (SFDR) of 61 dB with a power supply of 1.2 V and a consumption of 21 µW. The figure of merit (FoM) of the proposed SAR-ADC is 87.9 fj/Conv.-step. The proposed designs were simulated with optimized parameters using a voltage threshold adaptive memristor (VTEAM) model. Keywords: memristor; DAC; ADC; sneak path Citation: Fahmy, G.A.; Zorkany, M. Design of a Memristor-Based Digital 1. Introduction to Analog Converter (DAC). Electronics 2021, 10, 622. https:// Chua has discovered the existence of a passive two-terminal fundamental element, doi.org/10.3390/electronics10050622 which is called a memristor [1]. This element is characterized by the relationship between R t R t charge flux–linkage f(t) and charge q(t), where f(t) = −¥ v(t)dt and q(t) = −¥ i(t)dt Academic Editor: Kris Campbell respectively. This element has been presented as a fourth fundamental element. However, since that time, no physical element with f (f, q) = 0 characteristics had been yet discovered. Received: 29 January 2021 Finally, in 2008, the Hewlett–Packard (HP) team proved the practical existence of the Accepted: 26 February 2021 memristor [2]. Since 2008, the memristor has become an interesting research topic and Published: 7 March 2021 attracted many scientists to conduct research on memristors in terms of several fields (such as modeling, fabrication, and characterization) and employ it towards different Publisher’s Note: MDPI stays neutral applications. with regard to jurisdictional claims in The change of flux–linkage f(t) due to the change of charge q(t) is known as mem- published maps and institutional affil- ristive change (M), expressed as Wb/c or W, where M = df/dq. The memristor has a iations. characteristic behavior proposed by Chua [1] and modeled by at least 15 transistors and some passive components to emulate the behavior of a single memristor. Figure1 shows the relationship between the basic two-terminal elements: resistor, capacitor, inductor, and memristor. Copyright: © 2021 by the authors. Nowadays, memristor technology has entered different and important domains. It can Licensee MDPI, Basel, Switzerland. be used to build neuromorphic biological systems, artificial neural networks (ANN) (based This article is an open access article on its good ability to retain digital memory), and logic circuits. These features also enable it distributed under the terms and to play a role in new digital computer technology. It is very efficient to use in smart remote conditions of the Creative Commons sensing and Internet of Thing (IoT) applications, as it has a very low power consumption. Attribution (CC BY) license (https:// Due to these features of memristors, they have an efficient and effective way to store digital creativecommons.org/licenses/by/ data (as well as analog data) with power-efficient criteria [3]. 4.0/). Electronics 2021, 10, 622. https://doi.org/10.3390/electronics10050622 https://www.mdpi.com/journal/electronics ElectronicsElectronics 20212021, 10, 10, x, 622FOR PEER REVIEW 2 of 17 2 of 16 FigureFigure 1. The1. The relationship relationship between between the basic the two-terminal basic two-terminal elements (resistor, elements capacitor, (resistor, inductor, capacitor, inductor, andand memristor). memristor). TheNowadays, memristor has memristor been used intechnology non-linear analog has entere circuitd designs different (such and as oscillators important domains. It and digital to analog converters), since it has a lower area and is faster than the conventional CMOScan be circuit. used The to memristorbuild neuromor is a naturalphic counterpart biological to the systems, fundamental artificial digital neural to analog networks (ANN) relationship,(based on asits the good memristance ability to value retain changes digital according memory), to the and applied logic voltage. circuits. Along These features also withenable this, it the to memristor’s play a role current in new state digital depends computer on its previous technology. state, so itIt was is very recently efficient to use in usedsmart to design remote a digital sensing to analog and Internet converter of (DAC). Thing Since (IoT) the DACapplications, is the main as component it has a very low power of all data-driven acquisition circuits, it is the link between the analog signals of the real worldconsumption. and the digital Due signal to processingthese features field. So of much memristors, of the applied they research have is an conducted efficient and effective toway overcome to store the designdigital challenges data (as ofwell DAC as circuits, analog such data) as its with low areapower-efficient and low power criteria [4]. [3]. One ofThe the newest memristor ways to has overcome been used these in challenges non-linear is to analog use memristor circuit technology designs (such [5]. as oscillators Therefore,and digital there to are analog a few different converters), research since directions it has for a lower the use area of memristors and is faster in DAC than the conven- designs. For example, L. Danial et al. were able to calibrate a DAC design configuration tional CMOS circuit. The memristor is a natural counterpart to the fundamental digital to using neural networks as an artificial intelligence technique [6]. Another kind of research implementedanalog relationship, hybrid DAC as and the ADC memristance with a hybrid circuitvalue using changes memristors. according As L. Gaoto the et al. applied voltage. demonstrated,Along with DAC this, and the Hopfield-network memristor’s current ADC circuits state are depends able to utilize on post-fabricationits previous state, so it was resistancerecently tuning used featuresto design [7]. a Additionally, digital to analog F. Cai et converter al. designed (DAC). an integrated Since CMOSthe DAC is the main re-programmablecomponent of memristor all data-driven system based acquisition on DAC andcircui ADCts, for it theis the efficient link multiplicationbetween the analog signals of accumulated operations, and they subsequently used that design to implement a multi- layerof the neural real network world [and8]. the digital signal processing field. So much of the applied research is conductedA 2 bit hybrid to memristor overcome and the a CMOS design technology-based challenges of DACDAC were circuits, presented such in as [9], its low area and usinglow apower non-overlapped [4]. One signalof the to newest achieve ways the basic to cellovercome for DAC. these In this challenges model, the DAC is to use memristor areatechnology does not significantly[5]. Therefore, reduce there due to are the usea few of five different transistors, research one resistor, directions and a for the use of buffer circuit, all of which affect the total area of DAC. Moreover, the author did not memristors in DAC designs. For example, L. Danial et al. were able to calibrate a DAC declare how to extend his proposed 2 bit DAC to n bit DAC. In this work, we proposed adesign 2 bit memristor configuration DAC without using an neural included networks resistor element,as an artificial transistors, intelligence or buffer that technique [6]. An- willother reduce kind the of DAC research area significantly. implemented Moreover, hybrid the nDAC bit DAC and has ADC been with addressed a hybrid in circuit using thismemristors. work and has As been L. Gao verified et al. by demonstrated, two case studies. DAC There and are severalHopfield-network designs using aADC circuits are memristorable to utilize to develop post-fabrication an analog to digital resistance converter tuning (ADC) features [10,11]. For [7]. example, Additionally, a hybrid F. Cai et al. de- CMOS–memristor logic gate (known as memristor-ratioed logic (MRL)) has been deployed insigned the digital an integrated blocks of the CMOS pipeline re-programmable ADC to decrease the memristor clock delay further system and based increase on DAC and ADC thefor logic the density efficient [12, 13multiplication]. A memristor-based of accumulated flash ADC was operations, also provided and in [ 14they]. In thissubsequently used work,that adesign successive to implement approximation a multi-layer register analog neural to digital network converter [8]. (SAR-ADC) using the proposedA 2 bit memristor hybrid memristor DAC has been and provided a CMOS to achievetechnology-based low area and lowDAC power, were as presented in [9], will be explained in Section5. usingIn this a non-overlapped work, a basic cell for signal DAC thatto achieve uses a memristor the basic element cell for has DAC. been proposed.In this model, the DAC Thearea proposed does not DAC significantly cell was used reduce to design due a thermometerto the use codeof five to analogtransistors, and study one resistor, and a thebuffer characteristics circuit, all of DAC.
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