The Fourth Element

This tutorial clarifies the axiomatic definition of (#FF0000v^#000000 (#FF0000#000000) #000000, #FF0000i^ #000000 (#FF0000#000000) #000000) circuit elements via a lookup table dubbed an A-pad, of admissible (#FF0000v#000000, #FF0000i#000000) signals measured via Gedanken probing circuits. The (#FF0000v^ #000000 (#FF00FF#000000) #000000, #FF0000i^#000000 (#FF00FF#000000) #000000) elements are ordered via a complexity metric. Under this metric, the memristor emerges naturally as the fourth element, characterized by a state-dependent Ohm's law. A logical generalization to memristive devices reveals a common fingerprint consisting of a dense continuum of pinched hysteresis loops whose area decreases with the frequency and tends to a straight line as, for all bipolar periodic signals and for all initial conditions. This common fingerprint suggests that the term memristor be used henceforth as a moniker for memristive devices.