The Elusive Memristor
We investigate the properties of the recently discovered memristor (memory resistor). The existence of a memristor as the fourth passive electrical circuit element was predicted in 1971 based on symmetry arguments, but was experimentally discovered just this year. A memristor relates the charge and the magnetic flux in a circuit, and joins the other three well-known passive elements — a resistor, a capacitor, and an inductor — as a basic ingredient of electrical circuits. After an analytical derivation of the properties of a single memristor, we focus on memristor-capacitor (MC), memristor-inductor (ML), and memristor-capacitor-inductor (MCL) circuits. We find that the MC circuit shows non-exponential charge decay with two time-scales, and that the ratio of those time scales is determined by the memristor properties. We show that reversing the polarity of a capacitor in the circuit can change an underdamped MCL circuit into an overdamped one. We show that these unusual properties are closely related to the dynamics of dopant drift inside a memristor, and predict that they can be used to distinguish between different models of the dopant drift. We suggest that, in principle, a mechanical analog of an MCL circuit may permit experimental verification of our results. [arXiv.org, 25 Jul 2008] Read more