Fourier Response of a Memristor: Generation of High Harmonics with Increasing Weights

TL;DR

This paper analyzes how the Fourier spectrum of memristor current varies with hysteresis shape, revealing that sharp hysteresis produces broader harmonic content driven by memristance saturation.

Contribution

It introduces a simple model linking hysteresis shape to Fourier spectrum changes, emphasizing memristance saturation as the key factor.

Findings

Smooth hysteresis leads to rapidly decaying harmonic weights

Sharp hysteresis results in broader, non-monotonic harmonic spectrum

Memristance saturation solely drives the qualitative change in Fourier response

Abstract

We investigate the Fourier transform of the current through a memristor when the applied-voltage frequency is smaller than the characteristic memristor frequency, and the memristor shows hysteresis in the current-voltage plane. We find that when the hysteresis curve is "smooth", the current Fourier transform has weights at odd and even harmonics that decay rapidly and monotonically with the order of the harmonic; when the hysteresis curve is "sharp", the Fourier transform of the current is significantly broader, with non-monotonic weights at high harmonics. We present a simple model which shows that this qualitative change in the Fourier spectrum is solely driven by the saturation of memristance during a voltage cycle, and not independently by various system parameters such as applied or memristor frequencies, and the non-linear dopant drift.