Development of Behavioral Models for Memristors

Abstract

The memristors are electronic devices that have been introduced as passive elements, where the magnetic flux between their two terminals is a function of the total electrical charge that passes through the element. These elements can be used in various applications such as logic circuits or non-volatile memories. In this work we intend to develop behavioral models memristors that, after being tested and validated, allow the implementation of oscillator circuits. A first implementation of macromodels in LTspice was considered in order to verify the non-linear behaviors presented by this device. Due to this type of behavior, particularly at the borders of this element, the introduction of window functions is presented by modeling the best way its operation. The presented models were developed in Matlab environment, using the Euler method to solve differential equations. The implementation of this method presents numerical approximation errors, causing the hysteresis loop for several periods to not coincide. The introduction of Runge-Kutta method of order 4.5 is presented, where by using a variable step it is possible to present better results at the computation level. The validated models were introduced in VerilogA environment in order to demonstrate a small example of an oscillator based on memristors without using reactive elements.