The Fourth Element

  • Leon ChuaEmail author


This tutorial clarifies the axiomatic definition of \((v^{(\alpha )},i^{(\beta )})\) circuit elements via a look-up-table dubbed an A-pad, of admissible (vi) signals measured via Gedanken Probing Circuits. The \((v^{(\alpha )},i^{(\beta )})\) elements are ordered via a complexity metric. Under this metric, the memristor emerges naturally as the fourth element Tour (Nature 453:42–43, 2008 [1]), 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 \(\omega \) and tends to a straight line as \(\omega \rightarrow \infty \), 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.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeleyUSA

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