Mixed potential for RLC circuits with memristors

In two seminal articles published in 1964, Brayton and Moser introduced the concept of a mixed potential as a fundamental theoretic tool to describe and analyze a class RCL of circuits containing three basic circuit elements, namely, (possibly) nonlinear resistors, capacitors and inductors. In this paper, it is shown for the first time that a mixed potential can be introduced for a class RLCM of circuits containing all four basic circuit elements, namely, linear resistors, inductors, capacitors and (nonlinear) memristors. This is possible provided a memristor circuit is analyzed not in the traditional voltage-current domain but rather in the flux-charge domain. The flux-charge analysis method (FCAM) plays a crucial role in the extension, in particular, a key step is a fundamental duality principle established via FCAM between an RLCM circuit in the flux-charge domain and a nonlinear RLC circuit in the voltage-current domain. Several examples are discussed where the mixed potential is explicitly found. These include basic circuits with memristors, such as Chua’s circuit with a memristor and also large-scale memristor arrays with a neural architecture. This paper is devoted to the introduction of a mixed potential for memristor circuits and the study of its main theoretic properties, as the possibility to write the circuit state equations in the flux-charge domain in an effective and compact form via the mixed potential.