True internal resistance is identified from the earliest measurable voltage step, while polarization resistance is identified from the additional voltage drop that develops during the rest of the pulse. In a current-pulse test, the total apparent resistance is modeled as:
[ R_t(t)=R_i+R_p(t) ]
The initial voltage change gives an estimate of the ohmic or “true” internal resistance, (R_i); the time-dependent increase in voltage loss is attributed to polarization, (R_p).
The key distinction is time. Measure the voltage response immediately after the current changes to estimate (R_i), then track the continuing voltage relaxation or drop to determine the polarization contribution.
How the Two Resistances Appear During a Pulse
The immediate voltage step represents (R_i)
When a current pulse is applied, the cell voltage changes almost instantaneously because current encounters resistance in the current collectors, conductive pathways, separator, electrolyte, contacts, and other ohmic elements.
For a current step (\Delta I), the initial resistance estimate is:
[ R_i \approx \frac{\Delta V_{\text{instantaneous}}}{\Delta I} ]
The measurement must be taken quickly enough that slower electrochemical processes have contributed minimally.
Polarization develops after the initial step
Following the immediate voltage change, the voltage typically continues to move during the pulse. This additional change results from electrochemical polarization, including charge-transfer limitations, concentration gradients, ion transport through interfacial films such as the SEI, and solid-state diffusion.
At a selected later time (t):
[ R_p(t) \approx \frac{\Delta V(t)-\Delta V_{\text{instantaneous}}}{\Delta I} ]
Thus, the corresponding total resistance is:
[ R_t(t)=\frac{\Delta V(t)}{\Delta I} ]
Because polarization accumulates with time, the apparent resistance measured at 100 milliseconds or 1 second is generally higher than the value measured within the first few milliseconds.
How High-Current Pulse Testing Separates Them
Apply a precisely controlled current step
The test system applies a known change in current, such as a transition from a low-current baseline to a high-current discharge pulse. The current change must be measured accurately because both resistance calculations depend directly on (\Delta I).
A four-wire measurement setup and low-inductance connections help prevent contact and lead losses from being incorrectly assigned to the cell.
Capture the voltage response at high time resolution
The voltage waveform is recorded from before the pulse through the pulse and into the recovery period. The earliest valid voltage difference after the current transition is used to estimate (R_i).
A practical calculation is:
[ R_i \approx \frac{V_{\text{before}}-V_{\text{after, early}}}{I_{\text{pulse}}-I_{\text{before}}} ]
The sign convention changes between charging and discharging, but the physical interpretation remains the same.
Use later time points to quantify polarization
Voltage values are then evaluated at defined later times. For example, measurements near 100 milliseconds and 1 second include progressively more electrochemical response than the earliest measurement.
The difference between the later resistance and the initial resistance provides a time-dependent polarization estimate:
[ R_p(t)\approx R_t(t)-R_i ]
This is usually reported at a specified time rather than as one universal value, because polarization is not instantaneous or constant.
Analyze the recovery response as well
When the pulse ends, the voltage recovers in stages. The immediate recovery is associated mainly with the ohmic component, while slower recovery reflects relaxation of polarization processes.
Analyzing both the pulse onset and pulse termination can improve separation of the fast and slow contributions, particularly when the voltage response is fitted with an equivalent-circuit or time-domain model.
What the Voltage Transient Represents Physically
Ohmic losses occur throughout the cell
The (R_i) component is associated with comparatively fast electrical and ionic conduction losses. It includes contributions from current collectors, electrode conductive networks, separator and electrolyte conduction, tabs, welds, contacts, and measurement connections.
It is often called “true” internal resistance, but the measured value still depends on test bandwidth and setup quality.
Charge-transfer polarization is an early dynamic process
After the ohmic step, electrode reaction kinetics begin to affect the voltage. Charge-transfer resistance reflects the difficulty of moving charge across the electrode-electrolyte interface.
This contribution can appear very early in a pulse, so a millisecond measurement should not automatically be treated as perfectly pure (R_i).
Transport and diffusion polarization develop more slowly
As the pulse continues, lithium concentration gradients form in the electrolyte and active particles. These transport limitations produce additional voltage loss that can dominate the later portion of the pulse.
On a time-resolved analysis, the transient may therefore contain successive contributions from uncompensated ohmic loss, interfacial-film transport, charge transfer, and solid-state diffusion.
Why Test Timing and Instrumentation Matter
“Immediate” is defined by the test system
The first voltage sample is not necessarily the true physical instant after the current step. The result is limited by the current-source rise time, voltage-sampling rate, filtering, synchronization, wiring inductance, and sensor bandwidth.
The reported (R_i) should therefore be tied to a measurement time or fitting method, such as “resistance at 1 millisecond,” rather than presented without test conditions.
Very short pulses reduce polarization contamination
Pulses lasting only a few tens of milliseconds are commonly used to emphasize the fast voltage response and limit the buildup of polarization. Shorter effective measurement windows generally provide a closer estimate of the ohmic component.
However, excessively short or poorly synchronized measurements can capture switching artifacts, inductive effects, or current overshoot instead of the cell’s resistance.
A single pulse does not produce one universal resistance
Both (R_i) and (R_p) vary with state of charge, temperature, current direction, pulse duration, aging, and prior cell history. A resistance value is meaningful only when these conditions are reported.
For example, low state of charge and high state of charge can produce larger dynamic resistance or polarization than the middle state-of-charge range.
Understanding the Trade-offs
A short pulse improves separation but reduces dynamic information
A short pulse is useful for estimating (R_i), but it may not reveal slower polarization mechanisms that determine sustained high-power performance.
A longer pulse exposes charge-transfer and diffusion limitations, but its voltage drop cannot be interpreted as ohmic resistance alone.
The measured initial drop can include non-cell resistance
Poor welds, connectors, busbars, fixture contacts, and measurement leads can appear as part of the initial resistance. High-frequency AC testing or fixture compensation can help identify these contributions, but neither method automatically removes every cell-internal dynamic effect.
The test should distinguish cell resistance from fixture and interconnection resistance through calibration and a four-terminal measurement arrangement.
DC pulse resistance and AC impedance are not interchangeable
A high-frequency AC measurement emphasizes the real, fast impedance component and is useful for quality control and connection defects. A DC pulse measurement captures a time-dependent voltage response that can include ohmic loss and electrochemical overpotential.
Comparing values from the two methods requires matching frequency, time scale, temperature, state of charge, and measurement configuration.
Charging and discharging can produce different results
The voltage response may differ with current direction because reaction kinetics, concentration gradients, and side reactions are not identical during charge and discharge. In some chemistries, charging can also introduce additional effects such as gas-related overvoltage.
Resistance comparisons should therefore specify whether the pulse was applied during charging or discharging.
Making the Right Choice for Your Goal
Use the pulse waveform and test conditions together when selecting the appropriate resistance metric.
- If your primary focus is instantaneous power capability: Use the earliest validated voltage response after the current step to estimate (R_i), while documenting the instrument time resolution and current rise time.
- If your primary focus is sustained pulse performance: Evaluate (R_t) at a defined later time and calculate (R_p(t)=R_t(t)-R_i) to quantify the accumulated polarization.
- If your primary focus is identifying cell defects or poor connections: Combine calibrated four-wire DC pulse measurements with high-frequency AC impedance measurements.
- If your primary focus is electrochemical failure analysis: Fit the full transient and recovery response across multiple time scales to separate film transport, charge transfer, and diffusion contributions.
The reliable distinction is to treat (R_i) as the fast voltage-step component and (R_p) as the additional, time-dependent voltage loss revealed as the pulse continues.
Summary Table:
| Aspect | True Internal Resistance (R_i) | Polarization Resistance (R_p) |
|---|---|---|
| Measurement Time | Immediately after current step (early ms) | At later times during pulse (e.g., 100 ms, 1 s) |
| Physical Origin | Ohmic losses in current collectors, electrolyte, separator, contacts | Charge-transfer, concentration gradients, diffusion, SEI film |
| Voltage Response | Instantaneous voltage step | Additional voltage drop over time |
| Calculation | R_i = ΔV_instantaneous / ΔI | R_p(t) = (ΔV(t) - ΔV_instantaneous) / ΔI |
| Dependence on Time | Minimal (but still time-dependent due to measurement) | Strongly time-dependent |
| Influence of Test Setup | High (requires fast sampling, low inductance) | Less sensitive to setup (but requires accurate timing) |
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