Circuit Elements¶
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impedance.circuit_elements.A(p, f)[source]¶ defines a semi-infinite Warburg element
Notes
\[Z = \frac{A_W}{\sqrt{ 2 \pi f}} (1-j)\]
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impedance.circuit_elements.C(p, f)[source]¶ defines a capacitor
\[Z = \frac{1}{C \times j 2 \pi f}\]
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impedance.circuit_elements.E(p, f)[source]¶ defines a constant phase element
Notes
\[Z = \frac{1}{Q \times (j 2 \pi f)^\alpha}\]where \(Q\) = p[0] and \(\alpha\) = p[1].
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impedance.circuit_elements.G(p, f)[source]¶ defines a Gerischer Element
Notes
\[Z = \frac{1}{Y \times \sqrt{K + j 2 \pi f }}\]
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impedance.circuit_elements.K(p, f)[source]¶ An RC element for use in lin-KK model
Notes
\[Z = \frac{R}{1 + j \omega \tau_k}\]
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impedance.circuit_elements.T(p, f)[source]¶ A macrohomogeneous porous electrode model from Paasch et al. [1]
Notes
\[Z = A\frac{\coth{\beta}}{\beta} + B\frac{1}{\beta\sinh{\beta}}\]where
\[A = d\frac{\rho_1^2 + \rho_2^2}{\rho_1 + \rho_2} \quad B = d\frac{2 \rho_1 \rho_2}{\rho_1 + \rho_2}\]and
\[\beta = (a + j \omega b)^{1/2} \quad a = \frac{k d^2}{K} \quad b = \frac{d^2}{K}\][1] G. Paasch, K. Micka, and P. Gersdorf, Electrochimica Acta, 38, 2653–2662 (1993) doi: 10.1016/0013-4686(93)85083-B.
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impedance.circuit_elements.W(p, f)[source]¶ defines a blocked boundary Finite-length Warburg Element
Notes
\[Z = \frac{R}{\sqrt{ T \times j 2 \pi f}} \coth{\sqrt{T \times j 2 \pi f }}\]where \(R\) = p[0] (Ohms) and \(T\) = p[1] (sec) = \(\frac{L^2}{D}\)
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impedance.circuit_elements.num_params(n)[source]¶ decorator to store number of parameters for an element