Exploring a Novel Methodology for DC Analysis in Memristive Circuits with Multiple Operating Points

The memristor and the memristive systems have represented a challenge to be incorporated into a simulation procedure in order to carry out novel applications. The discovery of the physical memristor by the HP Labs has caused widespread interest for modeling the memristive behavior in order to combine this new fundamental circuit element with traditional devices. DC domain analysis represents a fundamental stage in the circuit simulators because the DC operating points are used as starting points in other analysis domains. In this work, the DC response of mathematical memristive systems is explored in order to recognize different scenarios according to the nature of the memristive variable. The piecewise linear formulation has been used in order to establish the memristive phenomenon in the device. As a result of this exploration, a novel DC modeling methodology for memristive systems is introduced. This methodology is capable of generating current-voltage branch relationships that represent the memristive behavior of the device. The memristive model proposed is characterized in order to determinate the impact of the variables on the memristive behavior. Moreover, the existence of multiple DC operation points (MOPs) is treated and the conditions for the occurrence of MOPs are established by two cases of study. Finally, the new contributions of this work compared to previous work are presented and discussed.