The fourth element: characteristics, modelling and electromagnetic theory of the memristor

Abstract

In 2008, researchers at the Hewlett-Packard (HP) laboratories published a paper in Nature reporting the development of a new basic circuit element that completes the missing link between charge and flux linkage, which was postulated by Chua in 1971(Chua 1971 IEEE Trans. Circuit Theory 18, 507-519 (doi:10.1109/TCT.1971). The HP memristor is based on a nanometre scale TiO 2 thin film, containing a doped region and an undoped region. Further to proposed applications of memristors in artificial biological systems and non-volatile RAM, they also enable reconfigurable nanoelectronics. Moreover, memristors provide new paradigms in application-specific integrated circuits and field programmable gate arrays. A significant reduction in area with an unprecedented memory capacity and device density are the potential advantages of memristors for integrated circuits. This work reviews the memristor and provides mathematical and SPICE models for memristors. Insight into the memristor device is given via recalling the quasi-static expansion of Maxwell's equations. We also review Chua's arguments based on electromagnetic theory.

An introduction to the memristor – a valuable circuit element in bioelectricity and bioimpedance

“…dv/di=R and di/dv=1/R) contain the same physics. A more rigorous review on how the four circuit variables can be deduced from Maxwell's equations can be found in Kavehei et al [35].…”

PSPICE modeling of meminductor

“…3(b) for the control parameter p = 2. Details can be found in [3,9]. As a conclusion, the more sophisticated Biolek window models well the device behavior also near its boundary states, but numerical problems in transient analysis due to the discontinuities at boundary points can appear more frequently than in the case of the Joglekar window.…”

“…The discovery of solid-state memristor in Hewlett-Packard (HP) labs, reported in Nature in May 2008 [1], initiated a growing interest in computer modeling and simulation of memristor [2][3][4][5][6][7][8][9], the fourth fundamental passive element, theoretically predicted by Chua in 1971 [10]. The reason consists in the fact that the above device is not currently available as off-the-shelf circuit.…”

Purely Imaginary Eigenvalues (PIE) in Extended Circuits with Mem-Devices

“…Our second goal is to extend the hyperbolicity analysis to circuits with memristors and other mem-devices (memcapacitors and meminductors) [ 35,36,37,38,39,40,41,42,43,44]; these devices, whose origin can be traced back to the 1971 paper [45] by Leon Chua, are taking a very relevant role in electronics, stemming from the report of the design of a nanometer memristor by HP in 2008 [46]. Our approach is based on the use of time-domain branch-oriented circuit models which capture explicitly the circuit topology; the differential-algebraic form of these models drives the spectral study to a matrix pencil setting.…”