Ideal memristor with nonlinear dopant drift approach

**Library:**Simscape / Foundation Library / Electrical / Electrical Elements

This block allows you to model an ideal memristor with a nonlinear dopant drift approach. The behavior of memristor is similar to a resistor, except that its resistance (also called memristance) is a function of the current that has passed through the device. The memristance is defined by two states, A and B, with some fraction of the device in one of those states at a given time.

The nonlinear dopant drift model, [1], is described with the following equations:

*V* =
*M*·*I*

*M* =
*ξ**·R*_{A}+(1 –
*ξ*)*·R*_{B}

$$\frac{d\xi}{dt}=\frac{I}{{Q}_{0}}{F}_{p}\left(\xi \right)$$

where

*V*is the voltage across the memristor.*M*is the memristance.*I*is the current entering the + terminal.*R*_{A}and*R*_{B}are the resistances of the A and B states, respectively.*ξ*is the fraction of the memristor in state A. A positive current from the + terminal to the - terminal increases*ξ*. Similarly, a positive current from the - terminal to the + terminal decreases*ξ*. The value of*ξ*is bounded by 0 and 1.*t*is time.*Q*_{0}is the total charge required to make the memristor transition from being fully in one state to being fully in the other state.*F*is a "window" function, which keeps_{p}(ξ)*ξ*in the window between 1 and 0, and therefore gives zero drift at the boundaries of the device.

The window function is

*F*_{p}(*ξ*) = 1 –
(2*ξ* –
1)^{2p}

where *p* is a positive integer. This function is modified when
*ξ* is close to either 0 or 1, to improve numerical
stability.

Use the **Variables** tab in the block dialog
box (or the **Variables** section in the block Property
Inspector) to set the priority and initial target values for the block
variables prior to simulation. For more information, see Set Priority and Initial Target for Block Variables.

[1] Joglekar, Y. N., and S. J. Wolf. "The elusive memristor:
properties of basic electrical circuits."* European Journal of
Physics*. 30, 2009, pp. 661–675.

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