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The Memristor

The first new passive circuit element since the 1830s might transform computer hardware

Brian Hayes

Hysteresis and Memory

2011-03CompSciHayesFC.jpgClick to Enlarge ImageThe resistor, the capacitor, the inductor and the memristor are all described as “passive” circuit elements, to distinguish them from “active” devices such as transistors, which can amplify signals and inject power into circuits. But the memristor differs from the other passive components in a crucial way: It is necessarily a nonlinear device. In an ideal resistor, as mentioned above, the relation between current and voltage is one of simple proportionality, and so the graph of this relation is a straight line of slope R. The equivalent graph for an ideal memristor is not a line but a curve, where the slope varies from place to place.

In the TiO2 memristor it’s easy to see where the nonlinearity comes from. Suppose the device is connected to a source of constant voltage. As current passes through the memristor in the “forward” direction—enlarging the conductive, doped, layer—the memristance decreases; this allows more current to pass, which further reduces the memristance, and so on. Reversing the polarity of the voltage source leads to the opposite kind of feedback loop, where increasing memristance causes still further increases.

2011-03CompSciHayesFD.jpgClick to Enlarge Image

The nature of the nonlinearity can be seen clearly by tracing the response of the device to a sinusoidal signal—a smoothly alternating voltage. The plot starts at zero volts and zero amperes. As the voltage steadily increases, so does the current, at an accelerating rate reflecting the nonlinear memristance. Then, after the voltage reaches its maximum and starts to fall again, the current continues to rise briefly because the resistance of the TiO2 film is still diminishing. When the current finally does retreat, the descending branch of the curve does not retrace the path of the ascending branch. Instead it forms a loop, called a hysteresis loop (a term borrowed from the study of magnetic systems). Specifically, the memristor’s curve is a “pinched” hysteresis loop, because the two branches cross at the origin. It’s a characteristic of the memristor that whenever the voltage is zero, so is the current, and vice versa. This fact implies that the memristor stores no energy, not even briefly. (The same is true of resistors, but not of capacitors or inductors.)

Hysteresis creates a fundamental distinction between resistors and memristors. In a resistor, current is a simple, single-valued function of voltage; the same voltage always elicits the same current. The hysteresis curve of a memristor driven by a sinusoidal input signal implies that the same voltage can yield two different currents. More generally, when we consider inputs other than simple sine waves, a given voltage can correspond to many different values of current. What value is observed depends on the internal state of the memristor, which in turn depends on its history. This is just another way of saying that the memristor retains a memory of its own past.

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