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How do I create and read my DRT plots in Pulsenics Analytics?

Generate Distribution of Relaxation Times plots from EIS spectra and tune DRT options (series elements, constraints, regularization, and frequency selection) for meaningful results.

Goal

Use DRT to re-express your EIS spectra as contributions across relaxation time, helping you separate overlapping processes that may appear as one broad feature in Nyquist or Bode plots.

What DRT is (high level)

DRT uses the same impedance data you already measured and reorganizes it as a distribution over relaxation times.

  • x-axis: relaxation time (fast to slow responses)

  • y-axis: contribution to impedance

  • peaks: dominant relaxation regions that may correspond to different processes

DRT does not create new data. It changes how the same data is represented.

Tip
If you need deeper background, the Pulsenics Help Center white paper “Introduction to Distribution of Relaxation Times” is the recommended reference.

Before you start

  • You validated measurement quality (recommended: current/voltage magnitude checks and KK test).

  • You already created frequency response plots using markers.

  • Choose markers where the system was stable and spectra look trustworthy.

1) Open DRT in the Frequency Response tab

  1. In Analytics, go to the Frequency Response tab.

  2. Under Select analysis, choose Distribution of Relaxation Times (DRT).

  3. Ensure Group by markers is enabled so each trace corresponds to your marker selections.

2) Select what you are analyzing

You are answering two questions:

Which hardware am I comparing?

  • Select the CMU and channel(s) (or equivalent voltage sensing setup) that contain the impedance data you want to analyze.

Which spectra am I including?

  • Select marker type (absolute or relative).

  • Select the specific markers (for example, 20 A, 15 A, 10 A steps).

  1. Click Apply to generate the first DRT plot.

What you should see: DRT traces for each selected marker/spectrum.

3) Use common DRT options (most-used first)

A) Add elements in series (often an inductor)

Why:

  • Wiring inductance is common and can distort DRT results.

  • Inductance often appears as a negative feature in DRT.

How:

  1. Open DRT options.

  2. Add an Inductor in series (you can also add a capacitor or Warburg element if needed).

  3. Click Apply.

What you should see

  • A cleaner DRT shape after compensating for inductive effects.

  • A table of fitted series elements and fit quality (including RMSE).

B) Non-negative constraint

Why:

  • Some DRT solutions can show negative peaks due to regularization or noisy data.

  • In many practical workflows, non-negative DRT is easier to interpret.

How:

  1. Enable Non-negative constraint.

  2. Click Apply.

Note
Negative peaks can sometimes reflect real behavior, but they are often artifacts. If you see negatives, compare back to Nyquist/Bode and verify with the DRT impedance fit (below).

C) Regularization (advanced control)

Regularization controls the tradeoff between smoothness and detail.

Most of the time:

  • the dashboard’s automatic settings give stable, usable results.

If you need custom control, enable custom regularization:

Alpha (smoothing strength)

  • Higher alpha: smoother, less noise, but can flatten small real features

  • Lower alpha: more detail, but can become spiky if data is noisy

L1 ratio (solution style)

  • Higher L1 ratio: more “sparse” solution with fewer distinct peaks

  • Lower L1 ratio: smoother and more spread out

If you leave these blank, the dashboard selects settings automatically per trace.

D) Frequency inclusion and exclusion

Why:

  • Noisy or unreliable frequencies can distort DRT.

How:

  1. Specify frequency ranges to include (example: 50 to 5,000 Hz).

  2. Use an exclamation mark to exclude specific frequencies or ranges (example: exclude 120 Hz).

  3. Apply to a single trace or copy settings across traces, then click Apply.

Important
Excluding even one frequency can change the result significantly, so use this only when you have a clear reason.

4) Check DRT fit quality (reality check)

A) Review the DRT results table

After applying DRT options, review:

  • RMSE of the DRT fit

  • fitted series elements (for example R∞ and L0 if an inductor is used)

B) Plot DRT impedance fit

This is the key validation step for DRT interpretation.

  1. Enable Plot DRT impedance fit.

  2. Compare the DRT-derived fit to your measured impedance data (for example on Nyquist axes).

How to interpret

  • If the DRT impedance fit tracks the measured spectrum well, your DRT peaks are more trustworthy.

  • If the fit does not match the measured data, do not interpret the peaks as physical processes yet. Adjust options or revisit data quality.

Recommended workflow checklist

  1. Pick markers from stable regions

  2. Create initial DRT plot (default settings)

  3. Add series inductor if inductive behavior is present

  4. Apply non-negative constraint (common default)

  5. Only then adjust regularization if needed

  6. Exclude frequencies only when clearly unreliable

  7. Confirm with DRT impedance fit overlay

Verify success

  • DRT plot shows consistent peaks that shift logically across conditions.

  • RMSE is reasonable for your use case.

  • DRT impedance fit overlays well with the measured spectrum.

Common issues

  • Negative peaks: try series inductor and/or non-negative constraint, then confirm with impedance fit.

  • Spiky DRT: increase alpha (more smoothing) or reduce noisy frequencies.

  • Over-smoothed DRT: decrease alpha (less smoothing) but watch for noise artifacts.

  • DRT fit does not match Nyquist/Bode: do not interpret peaks; revisit frequency selection, regularization, or data validity.

Related workflows

  • Create frequency response plots (Bode and Nyquist)

  • Validate spectra using KK test

  • Equivalent circuit modeling (ECM) (next video)