A Flux-Controlled Logarithmic Memristor Model and Emulator

The HP TiO\(_2\) model, as it is well known, is the most widely used physical model of memristor. However, deriving a mathematical model that fully characterizes the HP TiO\(_2\) memristor is a challenging task. As a result, simplified models such as the nonlinear quadratic model and the cubic memristor model are utilized in theoretic quantitative analysis of memristor circuits. These models result in unsatisfactory performance for many applications. To mitigate this problem, this paper proposes a new nonlinear logarithmic model to characterize memristor. Additionally, a memristor emulator circuit is developed. Finally, the relationships among the HP TiO\(_2\) memristor, the logarithmic model, and the emulator are thoroughly discussed.