Pinched Hysteresis Loops In Nonlinear Resonators

TL;DR

This paper demonstrates that pinched hysteresis loops can occur in simple nonlinear resonator circuits with diodes, challenging the idea that such loops are exclusive to memristors and highlighting the role of nonlinearity.

Contribution

It provides mathematical models, experimental validation, and an application example showing that pinched hysteresis is not unique to memristors but can arise in diode-based nonlinear resonators.

Findings

Pinched hysteresis observed in diode-based resonators.

Loop area increases with frequency.

Multiple pinch-points can occur with certain nonlinearities.

Abstract

This paper shows that pinched hysteresis can be observed in simple nonlinear 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 nonlinearity such as a cubic nonlinearity. 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 that: 1) pinched hysteresis is not a finger-print of memristors and that 2) the existence of a nonlinearity is essential for generating this behavior. Finally, an application in a digital logic circuit is validated.