The physical and circuit-theoretic significance of the Memristor : Full version

TL;DR

This paper explores the physical and circuit-theoretic significance of the memristor, emphasizing its relation to resistors, inductors, and capacitors, and discusses its implications for circuit theory and nonlinearity.

Contribution

It provides a comprehensive analysis of the memristor's physical basis and advocates for expanding circuit theory to incorporate this new element.

Findings

Memristor exhibits features of resistors, inductors, and capacitors.

The presence of voltage and current variables implies magnetic and electrostatic energies.

Circuit theory should be expanded to include memristors as a fundamental element.

Abstract

It is observed that the inductive and capacitive features of the memristor reflect (and are a quintessence of) such features of any resistor. The very presence of the voltage and current state variables, associated by their electrodynamics sense with electrical and magnetic fields, in the resistive characteristic v = f(i), forces any resister to accumulate some magnetic and electrostatic fields and energies around itself, i.e. L and C elements are always present. From the circuit-theoretic point of view, the role of the memristor is seen, first of all, in the elimination of the use of a unique v(i). This makes circuits with hysteresis characteristics relevant, and also suggests that the concept of memristor should influence the basic problem of definition of nonlinearity. Since the memristor mainly originates from the resistor, it was found necessary to overview some unusual cases of resistive circuits. The present opinion is that the framework of basic circuit theory and its connection with applications should be logically expanded in order to naturally include the new element.