Electro-magnetic interpretation of four-element torus

Abstract

The concept of the memristor was proposed by Leon Chua in 1971, along with some electro-magnetic interpretations according to quasi-static expansion of Maxwell’s equations. In 2003, Chua included the memristor into a four-element torus that has infinite circuit elements. This paper uses the quasi-static method to interpret every circuit element in the torus. Two examples are also provided to show how topologic structure of an element affects its electrical properties by affecting the dominant electro-magnetic field components. Additionally, it is proved that the circuit elements in the torus, except the resistive, capacitive and inductive elements, cannot exist independently. Moreover, the incorrectness in Chua’s interpretation of the memristor, that the memristor cannot be interpreted with the transient quasi-static method due to its memory property, is pointed out. Finally, the limitations of the electro-magnetic interpretation method are discussed.