Circuit elements

The following elements are available. Since prefixes are possible, each element is referred to as by a special name. The elements’ parameters are called as in the original function. This is the concept of LMFIT.

Names for building the model

Name

Corresponding function

R

impedancefitter.elements.Z_R()

C

impedancefitter.elements.Z_C()

L

impedancefitter.elements.Z_L()

W

impedancefitter.elements.Z_w()

Wo

impedancefitter.elements.Z_wo()

Ws

impedancefitter.elements.Z_ws()

Cstray

impedancefitter.elements.Z_stray()

API reference

impedancefitter.elements.Z_C(omega, C)[source]

Capacitor impedance

Parameters

  • omega (numpy.ndarray) – List of frequencies.

  • C (double) – capacitance of capacitor

Returns

Impedance array

Return type

numpy.ndarray, complex

impedancefitter.elements.Z_CPE(omega, k, alpha)[source]

CPE impedance

\[Z_\mathrm{CPE} = k (j \omega)^{-\alpha}\]
Parameters

  • omega (numpy.ndarray) – List of frequencies.

  • k (double) – CPE factor

  • alpha (double) – CPE phase

Returns

Impedance array

Return type

numpy.ndarray, complex

impedancefitter.elements.Z_L(omega, L)[source]

Impedance of an inductor.

Parameters

  • omega (numpy.ndarray) – List of frequencies.

  • L (double) – inductance

Returns

Impedance array

Return type

numpy.ndarray, complex

impedancefitter.elements.Z_R(omega, R)[source]

Create array for a resistor.

Parameters

  • omega (numpy.ndarray) – List of frequencies.

  • R (double) – Resistance.

Returns

Impedance array

Return type

numpy.ndarray, complex

impedancefitter.elements.Z_stray(omega, Cs)[source]

Stray capacitance in pF

Parameters

  • omega (numpy.ndarray) – List of frequencies.

  • Cs (double) – Stray capacitance, for numerical reasons in pF.

Returns

Impedance array

Return type

numpy.ndarray, complex

impedancefitter.elements.Z_w(omega, Aw)[source]

Warburg element

\[Z_\mathrm{W} = A_\mathrm{W} \frac{1-j}{\sqrt{\omega}}\]
Parameters

  • omega (numpy.ndarray) – List of frequencies.

  • Aw (double) – Warburg coefficient

Returns

Impedance array

Return type

numpy.ndarray, complex

impedancefitter.elements.Z_wo(omega, Aw, B)[source]

Warburg open element

Parameters

  • omega (numpy.ndarray) – List of frequencies.

  • Aw (double) – Warburg coefficient

  • B (double) – Second coefficient

Returns

Impedance array

Return type

numpy.ndarray, complex

Notes

This element is also referred to as finite-length Warburg element with reflective boundary [Barsoukov2018]. Here, the formulation

\[Z_\mathrm{W} = \frac{A_\mathrm{W}}{\tanh\left(B \sqrt{j \omega}\right)\sqrt{j \omega}}\]

is implemented.

impedancefitter.elements.Z_ws(omega, Aw, B)[source]

Warburg short element

Parameters

  • omega (numpy.ndarray) – List of frequencies.

  • Aw (double) – Warburg coefficient

  • B (double) – Second coefficient

Returns

Impedance array

Return type

numpy.ndarray, complex

Notes

This element is also referred to as finite-length Warburg element with transmissive boundary [Barsoukov2018]. Here, the formulation

\[Z_\mathrm{W} = A_\mathrm{W} \frac{\tanh\left(B \sqrt{j \omega}\right)}{\sqrt{j \omega}}\]

is implemented.

impedancefitter.elements.eps(Z1, make_eps)[source]

Return complex permittivity for LMFIT

Parameters

  • Z1 (numpy.ndarray, complex) – Impedance 1 (model fit)

  • make_eps (numpy.ndarray, complex) – Output of function impedancefitter.utils.make_eps()

impedancefitter.elements.log(Z1, dummy)[source]

Return logarithm of impedance for LMFIT

Parameters

  • Z1 (numpy.ndarray, complex) – Impedance 1 (model fit)

  • dummy (numpy.ndarray, complex) – Array full of ones, such that np.log10(dummy) is zero.

impedancefitter.elements.parallel(Z1, Z2)[source]

Return values of parallel circuit.

Parameters
Returns

Impedance array

Return type

numpy.ndarray, complex