Ideal memristor with nonlinear dopant drift approach
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, , is described with the following equations:
V = M·I
M = ξ·RA+(1 – ξ)·RB
V is the voltage across the memristor.
M is the memristance.
I is the current entering the + terminal.
RA and RB 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.
Q0 is the total charge required to make the memristor transition from being fully in one state to being fully in the other state.
Fp(ξ) is a "window" function, which keeps ξ in the window between 1 and 0, and therefore gives zero drift at the boundaries of the device.
The window function is
Fp(ξ) = 1 – (2ξ – 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.
To set the priority and initial target values for the block variables prior to simulation, use the Variables tab in the block dialog box (or the Variables section in the block Property Inspector). For more information, see Set Priority and Initial Target for Block Variables.
+— Positive terminal
Electrical conserving port associated with the memristor positive terminal.
-— Negative terminal
Electrical conserving port associated with the memristor negative terminal.
Resistance of state A— Entire memristor in state A
1 Ohm(default) | positive scalar
The resistance if the entire memristor is in state A, that is, if ξ = 1. The value should be greater than 0.
Resistance of state B— Entire memristor in state B
100 Ohm(default) | positive scalar
The resistance if the entire memristor is in state B, that is, if ξ = 0. The value should be greater than 0.
Total charge required for full state transition— Charge required for full transition between states
10 mC(default) | positive scalar
The total charge flow that is required to transition the memristor from being fully in one state to being fully in the other state.
State A fraction at t=0— Fraction of memristor in state A at start of simulation
0(default) | min/max: (0,1)
The initial condition for ξ at the start of the simulation. This parameter sets a high priority variable target within the block. The value should be greater than or equal to 0 and less than or equal to 1.
Exponent of the window function— Drift control at the boundaries
2(default) | positive integer scalar
The exponent, p, of the window function, which keeps the value of ξ between 0 and 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.