Complexity

Volume 2019, Article ID 1084312, 8 pages

https://doi.org/10.1155/2019/1084312

## A Novel Generalized Memristor Based on Three-Phase Diode Bridge Rectifier

^{1}School of Electronics and Information, Xi’an Polytechnic University, Xi’an 710048, China^{2}Institute of Water Resources and Hydroelectric Engineering, Xi’an University of Technology, Xi’an 710048, China^{3}School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Correspondence should be addressed to Ningning Yang; nc.ude.utjx.uts@gnay.gningnin

Received 18 April 2019; Accepted 24 June 2019; Published 8 July 2019

Academic Editor: Marcio Eisencraft

Copyright © 2019 Chaojun Wu 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

Memristive characteristics in three-phase diode bridge rectifier circuit are proposed in this paper. The conduction of the diodes is discussed and the characteristics of the pinched hysteresis loop are analyzed by both numerical simulations and circuit simulations. The hysteresis loops of each phase not only are pinched at the origin but also have the other two intersection points in the first quadrant and the third quadrant when three-phase bridge rectifier circuit is running under normal operation. Other conditions are also discussed when a variety of faults conditions occur. The simulation results verify that the three-phase bridge rectifier circuit can be described as a generalized memristor element during several operation states.

#### 1. Introduction

It has been proved that memristive characteristics exist in many systems [1, 2]. Since the discovery of the memristor, it has been widely used in neuromorphic circuits [3], nonvolatile information storage [4], chaotic systems and oscillators [5, 6], and other applications. In recent years, the research of generalized memristor has aroused wide interest of the scholars. A class of diode bridge circuits has been analyzed because of the memristive characteristics [7–14]. A simple electronic circuit which only consists of four diodes and a second-order RLC filter was proved to have memory properties [7]. By replacing the second-order RLC filter with a first-order parallel RC filter, another equivalent realization circuit of a generalized memristor was implemented, which decreases a fundamental circuit element-inductor [8, 9]. Meanwhile, a diode bridge circuit with a series first order RL filter also satisfies the definition of an ideal memristor; as a result, it can be described as a generalized memristor as well [10]. After that, a modified diode bridge circuit cascaded with a second-order filter containing an inductor and a capacitor was proposed and was proved to constitute a generalized memristor [11]. Recently, an improved memristive diode bridge circuit was put forward comprising four diodes and an inductor, which has a much simpler circuit realization [12, 13]. On the basis of the fractional calculus theory, a fractional-order capacitor-based diode bridge circuit was proposed, in which the fractional order capacitor is circuit implemented utilizing Oustaloup approximation technique [14].

Since a single-phase diode bridge rectifier circuit can express the memristive features, does a three-phase diode bridge rectifier circuit have the same characteristics? In this paper, a diode bridge circuit which contains six diodes and a parallel first order RC filter is proposed, and the input voltage of such circuit is three-phase voltage which has the same amplitude and frequency; phase difference of each phase is 120 degrees. In order to study whether a three-phase diode bridge rectifier circuit can be regarded as a generalized memristor under several operating conditions, in Section 2, we theoretically analyze the conduction conditions of six diodes in three-phase diode bridge rectifier circuit under different operating conditions. And the relation curves between input voltages and input currents are given by numerical simulations and circuit simulations. Conclusions are given in Section 3.

#### 2. Three-Phase Bridge Rectifier Circuit Running under Several Conditions

Equipment can be described as a voltage-controlled ideal memristor when a periodic voltage is applied to two terminals of the equipment, and the current response is periodic and has the same frequency [15]. Besides, the locus in the* v-i *plane invariably passes through the origin; the current flowing through the device is always zero when the input voltage is zero, as shown in Figure 1(a). The other two essential characteristics of a memristor are the facts that the areas of the hysteresis loops decrease monotonically as the frequency increases when frequency is greater than a critical value and the pinched hysteresis loop will shrink to a nonlinear single-valued function when the frequency tends to infinite [16].