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Added a modified open Warburg element to the circuit elements #270

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Added a modified open Warburg element to the circuit elements #270

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24 changes: 24 additions & 0 deletions impedance/models/circuits/elements.py
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Original file line number Diff line number Diff line change
Expand Up @@ -190,6 +190,30 @@ def Ws(p, f):
Z = Z0 * np.tanh(np.sqrt(1j * omega * tau)) / np.sqrt(1j * omega * tau)
return Z

@element(num_params=3, units=["Ohm", "sec",""])
def Ws(p, f):
"""defines a modified open (finite-space) Warburg element, for use in the
non-ideal cases where the open Warburg element is not suitable as presented in [1]

Notes
---------
.. math::
Z = \\frac{Z_0}{{ j \\omega \\tau }^{\\frac{\\alpha}{2}}}
\\tanh{{j \\omega \\tau }^{\\frac{\\alpha}{2}}

where :math:`Z_0` = p[0] (Ohms) and
:math:`\\tau` = p[1] (sec) = :math:`\\frac{L^2}{D}` and
:math:`\\alpha` = p[2]

[1] `EC-Lab Application Note 51, BioLogic Instruments (2014)
<https://biologic.net/wp-content/uploads/2019/08/dc-characterizations_supercapacitor-an51.pdf>`_.

"""
omega = 2 * np.pi * np.array(f)
Z0, tau, alpha = p[0], p[1], p[2]
Z = Z0 * np.coth((1j * omega * tau)**(alpha/2)) / (1j * omega * tau)**(alpha/2)
return Z


@element(num_params=2, units=["Ohm^-1 sec^a", ""])
def CPE(p, f):
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