Memristor - Background

Background

In his 1971 paper, Chua extrapolated the conceptual symmetry between the nonlinear resistor (voltage vs. current), nonlinear capacitor (voltage vs. charge), and nonlinear inductor (magnetic flux linkage vs. current), and inferred the memristor as a similarly fundamental nonlinear circuit element linking magnetic flux linkage and charge. In contrast to a linear (or nonlinear) resistor the memristor has a dynamic relationship between current and voltage including a memory of past voltages or currents. Other scientists had already proposed dynamic memory resistors such as the memistor of Bernard Widrow but Chua attempted to introduce mathematical generality.

The resistance of a memristor depends on the integral of the input applied to the terminals (rather than on the instantaneous value of the input as in a varistor). Since the element "remembers" the amount of current that has passed through it in the past, it was tagged by Chua with the name "memristor". Another way of describing a memristor is that it is any passive two-terminal circuit element that maintains a functional relationship between the time integral of current (called charge) and the time integral of voltage (often called flux, as it is related to magnetic flux). The slope of this function is called the memristance M and is similar to variable resistance.

The definition of the memristor is based solely on the fundamental circuit variables of current and voltage and their time-integrals, just like the resistor, capacitor, and inductor. Unlike those three elements however, which are allowed in linear time-invariant or LTI system theory, memristors of interest have a dynamic function with memory and may be described by any of a variety of functions of net charge. There is no such thing as a standard memristor. Instead, each device implements a particular function, wherein the integral of voltage determines the integral of current, and vice versa. A linear time-invariant memristor, with a constant value for M, is simply a conventional resistor. Like other two-terminal components (e.g., resistor, capacitor, inductor), real-world devices are never purely memristors ("ideal memristor"), but will also exhibit some amount of capacitance, resistance, and inductance.