Internal resistance stands as a pivotal parameter dictating the performance, power capability, and health state of a lithium ion battery. It fundamentally comprises ohmic resistance and polarization resistance. The ohmic component arises from ionic conduction in the electrolyte and electronic conduction through electrodes, separators, and current collectors. Polarization resistance, a dynamic entity, stems from kinetic limitations of electrochemical reactions (charge transfer) and mass transport limitations (diffusion). Accurately characterizing this internal resistance is therefore essential for battery modeling, state-of-health estimation, and system design. Two principal experimental techniques are employed: Electrochemical Impedance Spectroscopy (EIS) and Direct Current Resistance (DCR) measurement. While EIS provides a frequency-domain decomposition of various resistance contributions, DCR offers a time-domain snapshot of the total internal resistance under a specific load pulse. Understanding the correlation between these two methods is crucial for cross-validating data and for practical applications where one method may be preferred over the other. This work systematically investigates the relationship between DCR and EIS measurements across a range of State-of-Charge (SOC) conditions for both full-cell and half-cell configurations of a lithium ion battery.
EIS operates by applying a small-amplitude sinusoidal voltage or current perturbation across a wide frequency range (e.g., from millihertz to megahertz) to a lithium ion battery. The system’s response is analyzed to obtain a complex impedance spectrum. A typical Nyquist plot for a Li-ion cell features a high-frequency intercept on the real axis (representing the ohmic resistance, $R_s$), followed by one or more depressed semicircles (representing interfacial resistances like the Solid Electrolyte Interphase (SEI) film resistance $R_f$ and the charge transfer resistance $R_{ct}$), and a low-frequency tail (associated with Li-ion diffusion, $W$). An equivalent circuit model, such as $R_s(QR_f)(QR_{ct})W$, is often used to fit the spectrum and extract these individual parameters. The characteristic time constant, $\tau$, associated with the electrochemical polarization (e.g., the sum $R_s + R_f + R_{ct}$) can be derived from the frequency at the apex of the corresponding semicircle or the intersection point between the semicircle and the diffusion tail: $\tau = 1 / (2 \pi f_{peak})$. This time constant represents the characteristic response time of the dominant Faradaic processes.
In contrast, the DCR method applies a direct current pulse of specified magnitude ($I_{pulse}$) and duration ($t_{pulse}$) to the lithium ion battery. The instantaneous voltage change ($\Delta V$) immediately before and after the pulse application is measured. The DCR is then calculated using Ohm’s law:
$$ DCR(t_{pulse}) = \frac{| \Delta V |}{I_{pulse}} $$
The magnitude of the measured DCR depends heavily on $t_{pulse}$. A very short pulse (e.g., 10 ms) primarily captures the ohmic drop ($R_s$), as the slower polarization processes have not fully developed. As the pulse lengthens, the voltage drop incorporates increasing contributions from the charge transfer and eventually diffusion polarizations. Therefore, DCR is not a single value but a function of the measurement timescale: $DCR = R_s + R_{pol}(t)$.
The central hypothesis linking these methods is that for a given lithium ion battery at a specific state, the impedance measured by a DC pulse of duration $t$ should be comparable to the real-axis impedance extracted from an EIS spectrum at an angular frequency $\omega$ where $\omega \approx 1/t$. More specifically, the total resistance from EIS up to a frequency corresponding to the reciprocal of the pulse time should equate to the DCR value at that pulse time. This study aims to verify this by using the time constant $\tau_{R_s+R_f+R_{ct}}$ derived from EIS as the guiding parameter for selecting the DCR pulse duration and then comparing the resulting impedance values.
Experimental Methodology
The investigation was conducted using both full-cells and half-cells. The positive electrode was LiNi$_{0.6}$Co$_{0.2}$Mn$_{0.2}$O$_{2}$ (NCM622) and the negative electrode was graphite. Single-layer pouch cells were fabricated. For the full-cell, NCM622 was paired with graphite. For the positive half-cell, NCM622 was paired with a lithium metal foil. The electrolyte was 1 M LiPF$_6$ in a mixture of ethylene carbonate (EC), diethyl carbonate (DEC), and ethyl methyl carbonate (EMC) (1:1:1 by volume).
Cell Conditioning and Preparation: All assembled cells underwent a formation cycle at 0.05C followed by three capacity calibration cycles at 0.1C. Cells were then charged to the desired SOC (from 10% to 90% in 10% increments) using a constant current-constant voltage (CC-CV) protocol at 0.1C and held at that SOC for subsequent impedance measurements. All tests were performed at a constant temperature of 25°C.
Electrochemical Impedance Spectroscopy (EIS): EIS measurements were conducted using a potentiostat with a frequency range from 100 kHz to 0.01 Hz. A sinusoidal voltage perturbation amplitude of 5 mV was applied, confirmed to be within the linear response region of the cell. The obtained spectra were fitted with appropriate equivalent circuits to extract $R_s$, $R_f$, and $R_{ct}$. The time constant $\tau_{R_s+R_f+R_{ct}}$ was determined from the characteristic frequency of the middle-frequency semicircle.
Direct Current Resistance (DCR): DCR tests were performed using a battery cycler. For each SOC, the cell was subjected to a series of charge and discharge current pulses with varying magnitudes (up to 1C rate) but with a fixed, common pulse duration. The pulse duration for the DCR test was explicitly chosen to match the $\tau_{R_s+R_f+R_{ct}}$ value obtained from the EIS measurement at that specific SOC. The voltage difference $\Delta V$ was calculated between the voltage immediately before the pulse and the voltage at the end of the pulse. A linear regression of $\Delta V$ versus $I_{pulse}$ was performed, and the slope of the fitted line provided the DCR value for that pulse time. The process was repeated for both charge and discharge pulses.
Data Correlation: The DCR value (average of charge and discharge, unless specified) at pulse time $t_{pulse} = \tau_{EIS}$ was directly compared to the sum $R_s + R_f + R_{ct}$ from the EIS fit. The relative deviation was calculated as:
$$ \alpha = \frac{|R_{DCR} – R_{EIS}|}{R_{EIS}} \times 100\% $$
where $R_{EIS} = R_s + R_f + R_{ct}$. A relative deviation of less than 15% was considered indicative of a good correlation between the two measurement techniques.
| Test Parameter | Condition / Value |
|---|---|
| Cell Types | NCM622/Graphite Full-cell; NCM622/Li Half-cell |
| Electrolyte | 1M LiPF$_6$ in EC:DEC:EMC (1:1:1 vol.) |
| Test Temperature | 25 °C |
| SOC Range | 10%, 20%, …, 90% |
| EIS Frequency Range | 100 kHz to 0.01 Hz |
| EIS Perturbation | 5 mV (sinusoidal voltage) |
| DCR Pulse Current Range | Up to 1C |
| DCR Pulse Time Basis | $\tau_{R_s+R_f+R_{ct}}$ from EIS at each SOC |
| Key Comparison Metric | $R_{DCR}(t=\tau_{EIS})$ vs. $R_s+R_f+R_{ct}$ |
Results and Discussion
1. Fundamentals of DCR and EIS Responses
Initial experiments on a full lithium ion battery at 50% SOC established the foundational behavior of both techniques. For DCR, pulses of different currents (1-9 mA) were applied for fixed durations ranging from 0.01 s to 10 s. For each fixed pulse time, the voltage change $\Delta V$ was perfectly linear with the applied current $I_{pulse}$, yielding a single DCR value (the slope) for that timeframe. This confirms that within a reasonable current range (where the system response remains linear), the DCR is a function solely of pulse duration, not pulse magnitude. The values are summarized below:
| Pulse Time, $t_{pulse}$ (s) | Measured DCR ($\Omega$) | Linear Fit $R^2$ |
|---|---|---|
| 0.01 | 0.750 | 0.996 |
| 0.10 | 0.860 | 0.999 |
| 1.00 | 0.966 | 0.999 |
| 2.00 | 1.029 | 0.999 |
| 10.00 | 1.334 | 0.999 |
The monotonic increase in DCR with $t_{pulse}$ is classical: shorter pulses capture primarily $R_s$, while longer pulses incorporate progressively more polarization resistance from charge transfer and diffusion.
For EIS on the same lithium ion battery, the influence of the perturbation amplitude was checked. Voltage amplitudes from 1 mV to 100 mV were applied. The resulting Nyquist plots were virtually identical, and the fitted parameters $R_s$, $R_f$, and $R_{ct}$ showed minimal variation (typically < 3%). This verifies that a 5 mV perturbation is well within the linear, non-perturbative regime suitable for EIS analysis on a lithium ion battery.
2. Correlation in Full-Cell Configuration
The core experiment involved measuring both EIS and DCR across the SOC range for the NCM622/Graphite full-cell. At each SOC, the EIS-derived time constant $\tau_{R_s+R_f+R_{ct}}$ was calculated. This specific $\tau$ value was then used as the pulse duration for the DCR test at that SOC. The results are comprehensively presented in the table below.
| SOC (%) | EIS: $R_s+R_f+R_{ct}$ ($\Omega$) | EIS: $\tau$ (s) | DCR$_{chg}$ ($\Omega$) | DCR$_{dis}$ ($\Omega$) | Avg. DCR ($\Omega$) | Rel. Dev. $\alpha$ (%) |
|---|---|---|---|---|---|---|
| 90 | 0.636 | 0.398 | 0.704 | 0.703 | 0.704 | 10.7 |
| 80 | 0.619 | 0.398 | 0.700 | 0.698 | 0.699 | 12.9 |
| 70 | 0.642 | 0.464 | 0.709 | 0.706 | 0.708 | 10.3 |
| 60 | 0.640 | 0.398 | 0.704 | 0.703 | 0.704 | 10.0 |
| 50 | 0.640 | 0.464 | 0.711 | 0.707 | 0.709 | 10.8 |
| 40 | 0.652 | 0.631 | 0.728 | 0.730 | 0.729 | 11.8 |
| 30 | 0.678 | 0.736 | 0.760 | 0.759 | 0.760 | 12.1 |
| 20 | 0.737 | 1.000 | 0.829 | 0.830 | 0.830 | 12.6 |
| 10 | 0.892 | 1.585 | 0.995 | 1.018 | 1.007 | 12.9 |
The data reveals several key findings for the full lithium ion battery. Firstly, the DCR values from charge and discharge pulses are nearly identical ($R^2 > 0.999$ for all linear fits), indicating symmetrical kinetic behavior around the equilibrium point at each SOC. Secondly, both the EIS-derived resistance ($R_s+R_f+R_{ct}$) and the DCR show a consistent trend: they decrease as SOC increases from 10% to ~80%, and then plateau or slightly increase at the highest SOC. This is typical for layered oxide cathodes, where impedance is often lowest in the mid-SOC range. Most importantly, the absolute values show excellent agreement. The relative deviation $\alpha$ between the average DCR (at $t_{pulse} = \tau_{EIS}$) and $R_s+R_f+R_{ct}$ from EIS is less than 14.2% across the entire 10-90% SOC range. This strong correlation validates the hypothesis that the DCR measured with a pulse time equal to the electrochemical time constant $\tau$ effectively captures the same resistive phenomena (ohmic + charge transfer + SEI) that are resolved in the mid-to-high frequency arc of the EIS spectrum. The small systematic overestimation by DCR (~10-13%) could be attributed to the inclusion of a very initial portion of the diffusion-related voltage drop within the pulse, which is not part of the $R_s+R_f+R_{ct}$ sum from EIS.
3. Correlation in Half-Cell Configuration
To probe the generality of this correlation, the study was extended to a positive half-cell (NCM622 vs. Li). The same protocol was followed. The results, however, unveiled a more nuanced picture, as shown in the following table for the charging pulse DCR.
| SOC (%) | EIS: $R_s+R_f+R_{ct}$ ($\Omega$) | EIS: $\tau$ (s) | DCR$_{chg}$ ($\Omega$) | Rel. Dev. $\alpha$ (%) | Correlation |
|---|---|---|---|---|---|
| 90 | 0.536 | 0.398 | 0.585 | 9.1 | Good |
| 80 | 0.542 | 0.293 | 0.580 | 7.0 | Good |
| 70 | 0.649 | 0.398 | 0.580 | 10.6 | Good |
| 60 | 0.561 | 0.341 | 0.591 | 5.3 | Good |
| 50 | 0.586 | 0.293 | 0.617 | 5.3 | Good |
| 40 | 0.627 | 0.215 | 0.660 | 5.3 | Good |
| 30 | 0.531 | 0.224 | 0.738 | 39.0 | Poor |
| 20 | 0.730 | 0.215 | 1.038 | 42.2 | Poor |
| 10 | 8.076 | 0.158 | 10.633 | 31.7 | Poor |
For the half-cell lithium ion battery, a clear dichotomy is observed. In the mid-to-high SOC range (40% to 90%), the correlation remains excellent, with relative deviations $\alpha$ less than 10.7%. The trend of impedance with SOC is also consistent between the two methods in this range. However, at low SOC (10%, 20%, 30%), the correlation breaks down dramatically, with deviations soaring to 30-42%.
This divergence can be rationalized by considering the fundamental differences between full-cell and half-cell operation, especially at voltage extremes. In a full-cell, the working SOC corresponds to a specific, relatively stable voltage plateau for both electrodes within their respective stability windows. In a half-cell (e.g., NCM622 vs. Li), the electrode potential versus Li/Li$^+$ swings widely during (dis)charge. At low SOC, the NCM622 cathode is in a deeply discharged state, often corresponding to a region of its voltage profile with high differential capacitance or near a phase transition boundary. In such a state, even the small 5 mV EIS perturbation or the short current pulse for DCR can cause a non-negligible shift in the local thermodynamic state of the electrode. This means the “linearity” assumption, crucial for both EIS and the linear $\Delta V$ vs. $I$ analysis in DCR, is more likely to be violated. The electrode’s impedance may be highly sensitive to the exact potential, leading to inconsistent values between the two techniques which probe the system slightly differently. Furthermore, the stability of the half-cell interface at low potentials might be poorer, causing the system state to drift slightly between the sequential EIS and DCR measurements, exacerbating the discrepancy. This finding is critical as it highlights that the robust correlation between DCR and EIS in a commercial lithium ion battery (full-cell) may not automatically translate to half-cell studies, particularly at extreme states-of-charge where electrode behavior is less linear and more complex.
Conclusion
This investigation establishes a clear and practical correlation between Direct Current Resistance (DCR) and Electrochemical Impedance Spectroscopy (EIS) measurement techniques for lithium ion battery characterization. The key to linking these methods lies in the time domain. By using the characteristic electrochemical time constant $\tau_{R_s+R_f+R_{ct}}$ extracted from an EIS Nyquist plot as the pulse duration for a DCR test, the two methods yield quantitatively comparable impedance values for the ohmic and charge-transfer controlled processes.
For a commercial-type NCM622/Graphite full lithium ion battery, this correlation holds strongly across a wide State-of-Charge range (10-90% SOC), with relative deviations consistently below 15%. This implies that for many practical engineering applications focused on full cells, a carefully timed DC pulse test can provide information essentially equivalent to the sum of the high-to-medium frequency resistances obtained from a more complex EIS measurement. This is significant for embedded battery management systems where performing full EIS is impractical, but controlled pulse tests are feasible.
The study also reveals an important limitation: the correlation is SOC-dependent and system-dependent. In a NCM622 vs. Lithium half-cell configuration, the strong correlation only persists in the mid-to-high SOC range (40-90%). At low SOC, significant discrepancies arise, likely due to increased non-linearity and potential dependence of the electrode impedance, violating the fundamental assumptions of both small-signal EIS and the linear DCR analysis.
In summary, this work provides a validated framework for connecting time-domain and frequency-domain impedance analyses of lithium ion battery systems. It underscores that DCR is not an arbitrary metric but one intrinsically linked to the kinetic time constants of the battery. By consciously aligning the DCR measurement timescale with the relevant electrochemical time constant, engineers and researchers can ensure data consistency, cross-validate results from different equipment, and leverage simpler pulse tests to gain insights traditionally reserved for more sophisticated EIS techniques, at least for stable full-cell systems. Future work could explore this correlation for different cell chemistries, under aging conditions, and across a wider temperature range to further generalize its applicability.