Toward the complete relational graph of fundamental circuit elements

A complete and harmonized fundamental circuit relational graph with four linear and four memory elements is con- structed based on some newly defined elements, which provides a guide to developing novel circuit functionalities in the future. In addition to resistors, capacitors, and inductors, which are defined in terms of a linear relationship between charge q, current i, voltage v, and magnetic flux φ, Chua proposed in 1971 a fourth linear circuit element to directly relate φ and q. A nonlinear resistive device defined in memory i-v relation and dubbed memristor, was later attributed to such an element and has been realized in various material structures. Here we clarify that the memristor is not the true fourth fundamen- tal circuit element but the memory extension to the concept of resistor, in analogy to the extension of memcapacitor to capacitor and meminductor to inductor. Instead, a two-terminal device employing the linear ME effects, termed transtor, directly relates φ and q and should be recognized as the fourth linear element. Moreover, its memory extension, termed memtranstor, is proposed and analyzed here.