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=== Creating a model for a memristor device ===
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To demonstrate how to write a model evaluator file (SBN file), we
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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?)
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The device model is presented in the original paper as
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$+ \left\{ + \begin{array}{l} + \dot{x} = \mu I(t)\\ + H(x) = \left\{ + \begin{array}{l} + R \; x \le 0\\ + R - (R - r) x \; 0 < x < 1\\ + r \; x > 1 + \end{array} + \right.\\ + V(t) = H(x) I(t) + \end{array} + \right. +$
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The first thing to do is to change the model from impedance to admittance form
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and write the definition of the internal variable in an "implicit form"
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$+ \left\{ + \begin{array}{l} + Q(V(t), x(t)) = \dfrac{1}{\mu} \dot{x} - I(t) = 0\\ + H(x) = \left\{ + \begin{array}{l} + R \; x \le 0\\ + R - (R - r) x \; 0 < x < 1\\ + r \; x > 1 + \end{array} + \right.\\ + I(t) = \dfrac{V(t)}{H(x)} + \end{array} + \right. +$
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It is then useful to compute the derivatives
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