Pinched hysteresis loops in non‐linear resonators

Abstract

This study shows that pinched hysteresis can be observed in simple non‐linear resonance circuits containing a single diode that behaves as a voltage‐controlled switch. Mathematical models are derived and numerically validated for both series and parallel resonator circuits. The lobe area of the pinched loop is found to increase with increased frequency and multiple pinch points are possible with an odd‐symmetrical non‐linearity such as a cubic non‐linearity. Experiments have been performed to prove the existence of pinched hysteresis with a single diode and with two anti‐parallel diodes. The formation of a pinched loop in these circuits confirms the following: (1) pinched hysteresis is not a fingerprint of memristors, and (2) the existence of a non‐linearity is essential for generating this behaviour. Finally, an application in a digital logic circuit is validated.

Revisiting the memristor concept within basic circuit theory

“…1. Adhikari et al 16 report that the v-i relationship shows a pinched hysteresis loop for a periodic input signal or equivalently, as stated by Chua,6 all memristive systems are characterized by the property that a zero output corresponds to a zero input; i.e., that for i ¼ 0, we always have v ¼ 0(this is a property shared also by other one-port devices 17,18 ; furthermore, the existence of a hysteresis loop vs. a single-valued characteristic implies the presence of a nonlinearity 19 ).…”

Pinched Hysteresis Loop with Nonlinear Electronic Components: From Memristor to Hysteristor Concepts

“…Te main advantage of systems with pinched hysteresis loop lies in ofering the capability for memory and timevarying processing information through nonlinear transformations in a unique passive system. Te pinched hysteresis loop characteristic has started to receive formal treatment as research into its progress [6][7][8][9] and nowadays is defned as pinched hysteresis attractor. With the rising need for better understanding of pinched hysteresis attractor, researchers implement emulators through diodes and other passive elements.…”

Analytical model of inverse memelement with fractional order kinetic

“…19,20 By applying the fractional calculus concept, the modeling and analysis attempts of memelement with fractional order kinetic have been proposed in many previous works. [21][22][23][24] Since a novel circuit element with memory, namely, the inverse memristor, has been recently proposed [25][26][27] and often cited [28][29][30][31] where its behavior can be found/emulated in practice, [32][33][34][35] similarly to the memristor, it is worthy to introduce the fractional order kinetic to this new element and performing the modeling/analysis. By this motivation, the analytical model of inverse memelement which is a super set of inverse memristor, with fractional order kinetic, has been derived in this work.…”