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

We investigate the Fourier transform (FT) of the current through a memristor with an alternating-current voltage whose frequency is smaller than the characteristic memristor frequency. When the resultant hysteresis curve in the current-voltage plane is “smooth,” the current transform has weights at odd and even harmonics that decay rapidly and monotonically with the order of the harmonic. We find that, when the hysteresis curve is “sharp,” the FT is significantly broad, with increasing weights at high harmonics. We present a simple model that 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, or the nonlinear dopant drift. Our model predicts that maximal-weight higher harmonics occur most easily in a memristor with a sine voltage and positive polarity.