# Changes

,  01:56, 22 September 2015
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=== Creating a model for a memristor device ===

To demonstrate how to write a model evaluator file (SBN file), we
will discuss the simplest memristor model shown in this paper by [[User:KaKiLa| KaKiLa]] et al. (KaKiLa, can you please add a reference to the paper?)

The device model is presented in the original paper as

$\left\{ \begin{array}{l} \dot{x} = \mu I(t)\\ H(x) = \left\{ \begin{array}{l} R \; x \le 0\\ R - (R - r) x \; 0 < x < 1\\ r \; x > 1 \end{array} \right.\\ V(t) = H(x) I(t) \end{array} \right.$

The first thing to do is to change the model from impedance to admittance form
and write the definition of the internal variable in an "implicit form"

$\left\{ \begin{array}{l} Q(V(t), x(t)) = \dfrac{1}{\mu} \dot{x} - I(t) = 0\\ H(x) = \left\{ \begin{array}{l} R \; x \le 0\\ R - (R - r) x \; 0 < x < 1\\ r \; x > 1 \end{array} \right.\\ I(t) = \dfrac{V(t)}{H(x)} \end{array} \right.$

It is then useful to compute the derivatives
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