Skip to content
English
Contact us
  • There are no suggestions because the search field is empty.

Run a linear Kramers-Kronig fit on a saved Nyquist plot to confirm steady state, linearity, and causality before deeper analysis.

Run a linear Kramers-Kronig fit on a saved Nyquist plot to confirm steady state, linearity, and causality before deeper analysis.

Goal

Confirm your EIS spectra are valid before performing deeper analysis by fitting a linear Kramers-Kronig (KK) test in the Analytics page.

Why KK validation matters

EIS spectra are only meaningful if the measurement is taken under conditions that satisfy the core requirements of EIS:

  • Steady state: voltage and current are not drifting significantly during the measurement window

  • Linearity: voltage and current vary proportionally for the applied perturbation

  • Causality: the observed response is driven by the applied EIS signal (not dominated by noise)

A good KK fit increases confidence that these criteria are being met.

Before you start

  • You already created a frequency response Nyquist plot in Analytics.

  • The Nyquist plot is saved and available to select for validation.

Important
KK fitting in the dashboard requires selecting a frequency response plot (commonly Nyquist) first.

1) Open the Validation tab

  1. In Analytics, open the Analysis panel.

  2. Go to the Validation tab.

What you should see: a menu to choose a frequency response plot and options for the KK test.

2) Select the plot to validate

  1. In the Frequency response plot dropdown, select the Nyquist plot you want to validate.

Tip
Choose a Nyquist plot that was created using the marker selections you care about.

3) Choose KK mode

  1. Ensure you are using Linear KK test mode (as opposed to other modes if available).

4) Configure circuit element selection (M selection)

The KK fit is performed using a Voigt-style circuit model with multiple RC elements. The key control is how many elements are used.

Common options include:

  • Automatic (default): the software chooses the number of elements

  • Overfitting detection: attempts to avoid overfitting the measurement noise

  • Custom: you manually choose the number of RC elements (M)

Recommended starting point:

  • Use the default automatic option first, then adjust only if needed.

5) Optional: enable Robust KK fitting (outlier handling)

If your data has obvious noisy or outlier points, enable Robust KK.

  • This reduces the influence of outlier points so the fit represents the overall trend more reliably.

Use robust mode when:

  • one or a few points clearly deviate from the rest of the spectrum

  • you suspect intermittent noise artifacts

6) Choose which frequencies to include (full range or constrained)

By default, you can fit the entire measured frequency range.

You can also constrain the fit by specifying frequency rules, such as:

  • fitting only within a frequency window (example: 100 to 1,000 Hz)

  • omitting specific frequencies

  • fitting above or below a threshold

Recommended starting point:

  • Fit the full range first. Constrain frequencies only when you have a reason to exclude parts of the spectrum.

7) Run the KK validation and overlay it on the graph

  1. Click Validate.

  2. Enable Show on graph (or equivalent) to overlay the KK fit on top of your Nyquist data.

What you should see

  • The KK fit plotted over your Nyquist spectrum

  • A root mean squared error (RMSE) value for the fit

8) Interpret the results (RMSE and fit quality)

What “good” looks like

  • KK fit closely overlays the measured Nyquist curve.

  • RMSE is low.

Common guidance:

  • RMSE below 5% is typically considered acceptable for valid data.

  • RMSE below 1% is typically excellent.

What the KK fit is telling you

A good fit supports that the data is:

  • reasonably steady-state during the measurement window

  • approximately linear for the applied perturbation

  • causal and not dominated by noise

If the fit is poor (high RMSE):

  • the system may be drifting during the measurement

  • the response may be non-linear (perturbation too large)

  • the response may be noise-limited (perturbation too small or poor SNR)

  • parts of the frequency range may be unreliable

9) Use the detailed KK outputs to refine the fit (if needed)

In the Validation results panel, review:

  • RMSE

  • number of circuit elements used (M)

If you suspect overfitting or poor representation:

  • try enabling overfitting detection

  • try robust KK

  • try constraining the frequency range and re-validating

Example workflow:

  • Fit full range → review RMSE

  • If poor, fit a constrained range (example 100 to 1,000 Hz) and compare RMSE

  • Prefer the configuration that best represents the full spectrum without chasing noise

Verify success

  • The KK fit overlays your Nyquist data closely.

  • RMSE is within an acceptable range for your use case.

  • You can confidently proceed with deeper analysis (ECM fitting, comparisons, reporting).

Common issues

  • I cannot run KK validation: ensure you have a saved Nyquist plot selected in the Validation tab.

  • RMSE is high: check for drift (time-domain), poor SNR (voltage magnitude), or non-linear response; try robust KK or constrain frequencies.

  • Fit looks like it is following noise: try overfitting detection or reduce the number of elements (custom M).

Related workflows

  • Create frequency response plots (Bode and Nyquist) in Analytics

  • Create time-domain plots in Analytics

  • Monitor incoming data and verify signal quality

  • Equivalent circuit modeling (ECM) workflow (future article)