Technically, a memristor is a passive circuit element that relates flux to charge in the same way resistors relate voltage to current, capacitors relate voltage to charge and inductors relate flux to current. The fact that this fourth combination has been ignored in electronic-circuit theory was discovered by EE professor Leon Chua at the University of California, Berkeley, who wrote a seminal paper about the memristor in 1971.
"Memristors represent a fundamental change in electronic-circuit theory," said Sung-Mo Kang, chancellor of the Engineering School and an EE professor at the University of California at Merced. The most important items in electronics are the voltage, the current, the electrical charge and the flux linkage, he said. "If you consider those four variables as constitutive relations, then you get the equations that describe the resistor, inductor and capacitor."
But there is a fourth combination that everybody had overlooked, said Kang. "Chua's genius was realizing that combination defined a new passive-device type -- the memristor," he said. "Chua's argument was mathematical, but what he was saying is that the memristor had just as much a fundamental right as resistors, inductors and capacitors."
Chua called his discovery a memristor because of its behavior: The device acts as a variable resistance that "remembers" how much current has flowed through it by changing the voltage across its terminals. Thus, it can serve as a memory element that can be flipped "on," with a current in one direction, and "off," with a current in the reverse direction.
"A resistor relates voltage to current and the memristor relates flux to charge," said Notre Dame's Porod. "However, if you sum up flux over time, it becomes a voltage, and if you sum up charge over time it becomes a current. So a device that relates flux to charge, like the memristor, will over time relate voltage to current like a variable resistor that changes its value depending on how much, and in which direction, current has flowed through it."
For 35 years, only Chua and a handful of his former students taught fledgling engineers about the concept of a memristor. In lab classes, using resistors, inductors, capacitors and transistors, Chua had circuit boards built that emulated a memristor. He also wrote many papers providing detailed characterizations for EEs -- effectively telling them how to recognize a memristor when they saw one.