Modeling memristive behavior using Drude Model

The gaping hole left by the absence of a fourth fundamental circuit element to bridge the gap between charge and magnetic flux was finally filled in 1971 when Leon Chua theorized the existence of memristors. Though his paper was nothing shy of complexity and ingenuity, it was left largely unappreciated until in 2008 when Stanley Williams and his team at Hewlett-Packard´s (HP) Labs realized the memristor in device form. Despite the fact that the relationships governing the behavior of HP´s titanium dioxide (TiO₂) memristor have already been stated, this paper takes a radical and simpler spin on deriving equivalent relations. The equations illustrating the relationship between charge-magnetic flux and current-voltage for memristor are derived using the Drude Model of electrical conduction. Several assumptions are taken into account while using this approach, and the end equations obtained are utilized to simulate the characteristic curves of memristor using MATLAB.