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

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.