A compact, low‐frequency, memristor‐based oscillator

Abstract

Summary A relaxation oscillator using a memristor is hereby presented. The memristor is used to substitute the function of a capacitor in an equivalent RC oscillator. The voltage across the memristor changes according to the quantity and polarity of the current passing through, thus substituting the changing voltage across a capacitor in the equivalent RC oscillator. The memristor has the advantage of occupying much less area than the equivalent capacitor, which may be important when trying to build on‐chip oscillators for portable or medical applications. Copyright © 2014 John Wiley & Sons, Ltd.

Generalized boundary condition memristor model

“…Let the post-synaptic and pre-synaptic action potentials at nodes 1 and 2 of the circuit in Figure 3, that is, v 1 (t) = v pos (t) and v 2 (t) = v pre (t), have attenuation factors α pos and α pre , respectively. The memristor voltage is thus expressed as v(t) = v pos (t) À v pre (t) = α pos spk(t À t pos ) À α pre spk(t À t pre ), where spk(Á) is defined in Equation (12).…”

“…Since the discovery of memristance is in nature, announced by Hewlett Packard (HP) labs senior fellow Williams in 2008, the interest in memristors has considerably grown both in academia and industry for diverse circuit applications including memory (, ) and oscillators (). As more and more memristor realizations are presented, the development of mathematical models for the nonlinear dynamics of these devices and the establishment of solid theoretical foundations on their circuit properties () turn to be a fundamental issue for the progress of memristor‐based integrated circuit design.…”

A class of versatile circuits, made up of standard electrical components, are memristors

“…Applying Kirchhoff's Voltage Law (KVL) to the input and output port gives 5 The local passivity conditionthat is, assumption (3)in conjunction with the zero-crossing propertythat is, assumption (4)implies that v k i k ≥ 0 at all times, that is, the passivity of nonlinear resistor R k , k ∈ {a, b, c, d}. 6 Throughout this manuscript, the explicit dependence of all signals upon time is omitted for simplicity. Figure 1.…”

Current‐input current‐output analog half center oscillator and central pattern generator circuits with memristors

“…Moreover, there are existing CPG designs using cellular neural networks (CNNs) which use “approximated chemical synapses,” reminiscent of memristors, to enable switching between different patterns of locomotion without having to reorganize CNN structures . Furthermore, the HP memristor has been used to design a low frequency oscillator, reminiscent of the behavior of the HCOs in this work . These facts and the compatibility of weak inversion circuits and memristors, motivated the idea of adding memristors to the design of Nakada et al in which the couplings between oscillators are implemented by transistors emulating synaptic weights.…”