Memristive diode bridge with LCR filter

Abstract

The class of nonlinear dynamical systems known as memristive systems was defined by Chua and Kang back in 1976. Since then, many studies have addressed the search for physically-realisable memristive systems. In this reported work, it is proved that the class of memristive systems encloses an elementary electronic circuit comprising a full-wave rectifier with a second-order RLC filter.Introduction: The existence of a resistor endowed with memory was conjectured by Chua back in 1971 [1]. Just a few years later, Chua and Kang realised that the memory-resistor (memristor) is just one element from a class of nonlinear dynamical systems, the memristive systems, characterised, in general, by a state-dependent algebraic relation between input and output and by a system of ordinary differential equations governing the time evolution of the state [2]. Since then, scientists have devoted much effort in the search for physical realisations of memristive systems. In this field of research the most well-known breakthrough was undoubtedly achieved in 2008 at Hewlett-Packard (HP) Laboratories (Labs), where Williams recognised the first memristor nano-device [3]. Subsequently, a thorough experimental investigation of the switching dynamics of a set of metal-dioxide-metal memristive nano-devices [4] led to a better understanding of the key physical mechanisms underlying the nonlinear behaviour under observation. In 2011 we proposed a versatile boundary-condition-based model (BCM) for memristive switching nano-structures [5]. The BCM state equation includes a boundary-condition-controlled switching window function. The tunability of the window's switching mechanism allows the BCM to capture the nonlinear behaviour of a large class of memristive nano-films, including all dynamics attributed to the HP memristor and reported in [3]. Taking inspiration from the BCM switching function, we recently investigated the possibility to realise a memristive electronic system through switching networks, frequently used in power electronics applications. This investigation led us to prove that the Graëtz bridge with the RLC series filter is a memristive system. In particular, the proposed circuit manifests the fingerprint of memristive systems [6], i.e. a pinched hysteretic current-voltage loop for any state initial condition and for any nonzero amplitude and any nonzero and non-infinite frequency of any periodic sign-varying driving source. The peculiarity of our circuit is that it acts as a nonlinear resistor at direct current (DC) and at infinite frequency of any periodic sign-varying driving source with nonzero amplitude. It is a common belief that the only memristor realisations employing already-existing components are the complex topologies based upon the mutator-based active circuits presented in [1]. This circuit represents the first-ever realisation of a memristive electronic system using only passive components (four diodes, an inductor, a capacitor and a resistor).

Everything You Wish to Know About Memristors But Are Afraid to Ask

“…Not only do pinched hysteresis loops provide the characteristic fingerprints of all memristors, they all behave in a similar fashion as a function of the frequency of the periodic excitations [21]. In particular, it can be proved that beyond some critical frequency f * , the area of each lobe of the pinched hysteresis loop of all memristors is a strictly monotone-decreasing function of the frequency f. Moreover, at sufficiently high frequencies, the pinched hysteresis loops must tend to straight lines (whose slope depends on the amplitude of the exciting periodic waveform) for all Generic Memristors, or to a single-valued function (whose precise curve varies with the amplitude of the periodic input signals) in the v vs. i plane for all Extended Memristors [21], [5], [36].…”

An Improved Memristive Diode Bridge‐Based Band Pass Filter Chaotic Circuit

“…Different from the diode bridge-based memristor emulators reported in [16,18,39], an improved memristive diode bridge emulator with much simpler circuit realization is designed as shown in Figure 1(a), where V and represent the voltage and current at the input port 11 , respectively, and V and stand for the voltage and current across the inductor . Consider that the diode bridge is implemented by four unified diodes, where V and represent the voltage across and the current through the diode ( = 1, 2, 3, 4), respectively.…”

“…Thus, various kinds of physically implementable equivalent circuits which can manifest the three fingerprints of memristors [17] have attracted much attention [2,[6][7][8][9][10][11][12][13][14][15][16][17][18]. Popularly, the circuits implemented by operational amplifiers and analog multipliers [7][8][9][10][11][12] as well as the circuits consisting of diode bridge cascaded with RC [13][14][15], LC [16], and RLC [18] filters have been used for experimental measurements in memristor based circuits. The most significant feature of the memristive diode bridge emulators is ungrounded limitation, which makes it as a serial expandable and flexible element in designing memristor based circuit [19].…”

A Memristive Diode Bridge-Based Canonical Chua’s Circuit

“…With reference to Equation (15), the memristive Chua's circuit is non-dissipative in the neighborhood of S0. Considering that S0 is a repulsive point, the orbit will be excluded from this region, and ultimately settles onto an attractor around the two unstable saddle-foci in dissipative region.…”

“…Memristor-based chaotic circuits can be OPEN ACCESS involving each pair of parallel diodes [15]. Its mathematical model is described by the following equation: …”