Impedance

impedance.py

What this library is for

impedance.py is a Python package for electrochemical impedance spectroscopy (EIS) analysis. It covers the common analysis path from instrument file import through validity checks, equivalent-circuit fitting, parameter inspection, model prediction, and Nyquist/Bode visualization.

When to use this vs. alternatives

• Use impedance.py for EIS spectra, impedance-specific preprocessing, Lin-KK validation, equivalent circuit model fitting, and publication-style Nyquist or Bode plots.
• Use SciPy directly only for custom optimization outside the impedance.py circuit abstraction, or after checking whether CustomCircuit, custom circuit elements, bounds, constants, or global_opt=True cover the case.
• Use pandas/openpyxl to convert Excel exports to a clean frequency/Zreal/Zimag table, then pass arrays or CSV-like data into impedance.py; impedance.py does not currently expose a dedicated Excel reader.
• Do not treat EIS as generic nonlinear regression without checking EIS assumptions. The data should be causal, linear, and stable; use Lin-KK or a measurement-model residual check before trusting fitted parameters.

Canonical workflow

Start from the maintained fitting and validation examples, then adapt the circuit and initial guesses to the physical system.

import numpy as np
import matplotlib.pyplot as plt

from impedance import preprocessing
from impedance.models.circuits import CustomCircuit
from impedance.validation import linKK
from impedance.visualization import plot_nyquist, plot_residuals

frequencies, Z = preprocessing.readCSV("eis.csv")
frequencies, Z = preprocessing.ignoreBelowX(frequencies, Z)

M, mu, Z_kk, res_real, res_imag = linKK(
    frequencies, Z, c=0.85, max_M=50, fit_type="complex"
)

circuit = CustomCircuit(
    circuit="R_0-p(R_1,CPE_1)-Wo_1",
    initial_guess=[0.02, 0.01, 1e-3, 0.9, 0.05, 100],
)
circuit.fit(frequencies, Z, weight_by_modulus=True)
Z_fit = circuit.predict(frequencies)

names, units = circuit.get_param_names()
fit = dict(zip(names, circuit.parameters_))
conf = dict(zip(names, circuit.conf_))

fig, (ax_nyq, ax_res) = plt.subplots(2, 1, figsize=(5, 8))
plot_nyquist(Z, fmt="o", ax=ax_nyq)
plot_nyquist(Z_fit, fmt="-", ax=ax_nyq)
plot_residuals(ax_res, frequencies, (Z - Z_fit).real / np.abs(Z),
               (Z - Z_fit).imag / np.abs(Z))
fig.tight_layout()

For deeper examples, read:

• Fitting impedance spectra: https://impedancepy.readthedocs.io/en/latest/examples/fitting_example.html
• Validation of EIS data: https://impedancepy.readthedocs.io/en/latest/examples/validation_example.html
• Looping through multiple spectra: https://impedancepy.readthedocs.io/en/latest/examples/looping_files_example.html

Key conventions and gotchas

• frequencies are in Hz and Z should be a complex NumPy array. CSV import expects frequency, real impedance, imaginary impedance columns.
• Circuit strings use - for series and p(X,Y) for parallel elements. Multiple elements of the same type need numeric identifiers, commonly R_0 or R0; keep the initial_guess order aligned with get_param_names().
• Bounds default to non-negative values, with CPE alpha bounded above by 1. Supplying bounds changes SciPy's optimizer from unconstrained Levenberg-Marquardt to trust-region reflective.
• weight_by_modulus=True uses |Z| weighting and is the standard fallback when experimental variance estimates are unavailable.
• Fitted values are available as circuit.parameters_; confidence estimates are available as circuit.conf_. Users often miss these because examples also show print(circuit).
• linKK has an open issue in some Python 3.12/Colab environments where fit_type="complex" can raise NameError: name 'np' is not defined. If this appears, record the package/Python versions and either try a patched impedance.py checkout or use the measurement-model residual workflow.
• Treat vendor file readers as convenience importers, not authoritative calibration tools. For VersaStudio .par data, an open issue reports that raw .par EIS values can differ from calibrated data exported from within VersaStudio.

Anti-patterns

• Do not fit only the real part or only the imaginary part with a generic curve_fit call unless the user explicitly asks for that model. impedance.py fits real and imaginary components together by default.
• Do not optimize unconstrained arbitrary RC networks and report parameters as physical truth. Compare plausible circuits, inspect confidence estimates, residuals, and Nyquist/Bode overlays, and use domain knowledge to choose the model.
• Do not skip initial guesses. Equivalent-circuit fits are sensitive to starting conditions; use physically plausible guesses, constants, bounds, or global_opt=True for hard cases.
• Do not blindly call ignoreBelowX() without inspecting the sign convention and raw data. It trims points below the x-axis in the package convention, and the examples use it as a preprocessing step, not as a universal validity rule.
• Do not rely on a saved model as a black box across experiments. When loading a model for a new spectrum, verify that constants, fitted-as-initial behavior, and circuit parameter order match the intended experiment.

Diagnostic checks

Before trusting outputs, the agent should:

• Plot the raw data and fit together as Nyquist and, when frequency matters, Bode plots.
• Run Lin-KK or a measurement-model residual check and inspect residual structure, not just scalar error.
• Check circuit.parameters_, circuit.conf_, and get_param_names() together so parameter values are labeled correctly.
• Compare fitted parameter magnitudes with physically plausible ranges and confirm CPE alpha values remain within bounds.
• Refit from at least one alternate plausible initial guess for high-dimensional circuits or ambiguous spectra.
• Save the circuit JSON and analysis script/notebook when results are meant to be reproducible.

Pointers to deeper material

• Documentation: https://impedancepy.readthedocs.io/en/latest/
• Tutorial examples: https://impedancepy.readthedocs.io/en/latest/examples/fitting_example.html
• Validation example: https://impedancepy.readthedocs.io/en/latest/examples/validation_example.html
• Source repository: https://github.com/ECSHackWeek/impedance.py
• Paper: Murbach et al. (2020), "impedance.py: A Python package for electrochemical impedance analysis", Journal of Open Source Software 5(52),
  2349. https://doi.org/10.21105/joss.02349
• Lin-KK method: Schönleber et al. (2014), "A Method for Improving the Robustness of linear Kramers-Kronig Validity Tests", Electrochimica Acta 131, 20-27. https://doi.org/10.1016/j.electacta.2014.01.034