Engee documentation

Memristor

Ideal Memristor.

memristor

Description

This block allows you to model an ideal memristor. The behaviour of a memristor is similar to that of a resistor, except that its resistance is a function of the current through the device (integral of current over time). The resistance of a memristor at a given time is determined by the two states of the memristor, A and B, depending on which part of the device is in one of these states. The mathematical model of the memristor is described by the following equations:

ξξ

ξξ

Where:

  • - voltage across the memristor;

  • - current resistance;

  • - current;

  • and - resistances of the memristor in states A and B, respectively;

  • ξ - is the fraction of the memristor in the A state. A positive current flowing from the + terminal to the - terminal increases ξ . Similarly, a positive current flowing from the - terminal to the + terminal decreases ξ . The value of ξ is limited to 0 and 1;

  • - time;

  • - the total charge required to transition the memristor completely from one state to completely another;

  • ξ - a window function that keeps ξ in the window between 1 and 0.

Window function:

ξξ

Where:

  • р - is a positive integer. This function is modified when ξ is close to 0 or 1 to improve computational stability.

Ports

+ is positive
electricity.

Electrical port, represents the positive terminal of the memristor.

- is the negative
electricity

Electrical port, represents the negative terminal of the memristor.

Parameters

Resistance of state A - resistance in state A
1 Ohm (by default) | positive | scalar

The resistance of the memristor when the entire device is in the A state, that is, if ξ . The value must be greater than zero.

Resistance of state B - the whole memristor is in state B.
100 ohms (by default) | positive | scalar

Resistance of the memristor when the entire device is in B state, that is, if ξ . The value must be greater than zero.

Total charge required for full state transition - charge required for full state transition
10 mKl (by default) | positive | scalar

The total charge required for a memristor to transition from fully one state to fully another.

State A fraction at t=0 - the fraction of the memristor in state A at the beginning of the simulation
0 (by default) | min/max: (0,1)

Initial value for ξ at the start of the simulation. The value must be greater than or equal to 0 and less than or equal to 1.

Exponent of the window function - window function exponent
2 (by default) | positive | calculus | scalar.

Indicator of window function that holds the value of ξ between 0 and 1.

Initial value of current i - initial value of current i
`0 (By default)

Initial value of current .

Initial value of voltage v - initial value of voltage v
0 (By default)

Initial value of voltage .