High-frequency resistance (HFR) in fuel cells and electrolyzers
High-frequency resistance, or HFR, is one of the most useful single numbers from a PEM cell. It is quick to measure, it is needed to correct polarization curves, and tracking it over a test tells you a lot about the membrane. Here is what it is and how to use it.
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Step by step
Record an impedance spectrum
Run EIS at a fixed operating point, sweeping from high to low frequency with a small AC amplitude. Keep conditions steady during the sweep, and record the spectrum for each condition or time point you want to compare.
Plot it as a Nyquist plot
Plot the negative imaginary impedance against the real impedance. Our free tool at /tools/eis-nyquist-plotter draws this for you from a data file.
Read the real-axis intercept at high frequency
At the high-frequency end of the plot, the curve crosses the real axis. That intercept is the HFR. Inductance from cables can pull the curve below the axis at the highest frequencies, so the intercept is often found where the curve crosses zero imaginary impedance, by interpolation or fit.
Or measure it by current interrupt
A current interrupt measures the instant voltage jump when the load current is switched off. The jump divided by the current gives an ohmic resistance. It is faster than a full spectrum, though it needs fast data acquisition and it can differ somewhat from the EIS value.
Use HFR to iR-correct polarization curves
Multiply the current by the HFR and add that product back to the measured cell voltage (for a fuel cell). The corrected curve shows the kinetic and mass transport behaviour without the ohmic loss.
Track HFR over the test
Plot HFR against time, cycles or condition. A steady value suggests a stable membrane and contacts, while a trend can point to changing hydration, membrane thinning or growing contact resistance.
What HFR represents
HFR is the total ohmic resistance of the cell. It includes the proton resistance of the membrane, the electronic resistance of the cell components such as plates and diffusion layers, and the contact resistances between them. In a PEM cell the membrane is often the dominant part, and its resistance depends strongly on how well it is hydrated.
Because several contributions are lumped together, HFR alone does not say which one changed. Compare it with the other test signals and, where you can, repeat the measurement at known conditions, for example with different compression or humidification.
If you normalise by active area you get an area-specific resistance in ohm cm2, which lets you compare cells of different sizes.
Doing it in Vizalyze
The function EIS parameters per file (R_ohm, R_pol, R_total) returns one row per spectrum, with the ohmic resistance as the high-frequency real-axis intercept, the polarisation resistance as the arc width, and the total resistance. Plotting those rows against file order or time gives you the HFR trend across a durability test.
The function is part of the Scientific & Simulation and Lab & Instruments packs. The 14-day trial includes every feature and format, with no credit card. As with any automatic method, check the intercept on a few spectra against the Nyquist plot before relying on the trend.
Frequently asked questions
Is HFR the same as ohmic resistance?
In practice the terms are used interchangeably. HFR is the ohmic resistance read at high frequency, where capacitive and kinetic effects drop out of the response.
Why does my Nyquist curve go below the real axis at high frequency?
That is usually inductance from cables and the test setup. Read the HFR where the curve crosses the real axis, and reduce the effect with short, twisted cabling where possible.
Can I get HFR without EIS?
Yes. A current interrupt measurement gives an ohmic resistance from the instant voltage change, and some test stations report an HFR directly.
Does a rising HFR mean the membrane is failing?
Not necessarily. It can reflect drying, contact changes or membrane thinning. Treat it as an indicator and confirm with other diagnostics.