Ocs package: Difference between revisions

1,112 bytes added ,  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
<math>
\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.
</math>
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"
<math>
\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.
</math>
It is then useful to compute the derivatives
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