Technology · Impedance spectroscopy
An impedance spectrum separates a cell's internal processes by their speed.
Electrochemical impedance spectroscopy (EIS) applies a small alternating current to a cell and measures the voltage response across a wide frequency range. The resulting spectrum shows conduction resistance, the reaction at the electrode surface and the movement of lithium through the electrode material separately. The cell information that capacity, power and maintenance decisions need comes from that separation.
Principle
A small excitation, two measurements: amplitude and phase.
A small sinusoidal current is applied to the cell, and the cell answers with a voltage wave at the same frequency. The excitation is kept small because the method holds only where the cell behaves linearly, and the measurement must not move the cell's operating point. The same measurement is repeated from high frequency to low.
Z(f) = V(f) / I(f) = Z′ + jZ″
- Current amplitude
- Voltage amplitude
- Phase shift φ
- 01
Amplitude ratio
The ratio of voltage amplitude to current amplitude is the magnitude of the impedance: how strongly the cell opposes current at that frequency.
- 02
Phase angle
How far the voltage wave lags the current wave. Zero phase means pure resistance; a growing lag means capacitive behavior.
- 03
Frequency sweep
Each internal process responds on its own time scale: ion conduction at once, the surface reaction more slowly, diffusion slowest of all. Sweeping the frequency pulls these processes apart.
Reading the spectrum
On a Nyquist plot, each region is a physical process.
A Nyquist plot draws the impedance at each frequency as a single point: the real part on the horizontal axis, the negative imaginary part on the vertical. Frequency falls from left to right; high frequencies show fast processes, low frequencies slow ones.
- Ohmic resistance · high frequency
- SEI and charge-transfer arcs · mid frequency
- Diffusion tail, Warburg · low frequency
- Frequency falls from left to right
At very high frequency the curve dips below the axis. That part comes from the inductance of the cables and the cell's construction.
- 1
Ohmic resistance
Where the curve meets the horizontal axis at high frequency. R0 is the series resistance of the electrolyte, separator, current collectors and connections. It sets the immediate voltage drop under load and part of the heat the cell produces.
- 2
Arcs: SEI and charge transfer
The arcs at mid frequencies. Ion transport through the solid electrolyte interphase (SEI) on the anode and the charge-transfer reaction at the electrode surface appear here. An arc's width shows how much resistance that process meets; the two often appear as two overlapping arcs.
- 3
Diffusion tail (Warburg)
At low frequency, a line that rises at about 45 degrees in the ideal case. It shows lithium moving by diffusion inside the electrode particles and through the electrolyte. It is the slowest process and takes the longest to measure.
Equivalent circuit
An equivalent circuit turns the spectrum into parameters that can be tracked.
The spectrum is fitted to a model that represents each process with a circuit element. The most common starting point is the Randles circuit: a series resistance R0, then a branch in parallel with the double-layer capacitance Cdl. That branch holds the charge-transfer resistance Rct in series with a Warburg element W for diffusion. Real cells usually need a constant-phase element (CPE) in place of the ideal capacitor and an extra RC branch for the SEI.
The fitted parameters are numbers that can be tracked over time. A cell's condition is read from how they trend, more than from any single measurement.
- R0 · series (ohmic) resistance
- Cdl · double-layer capacitance
- Rct · charge-transfer resistance
- W · Warburg diffusion element
Aging and faults
Each aging mechanism leaves its mark in a different region of the spectrum.
Comparing two spectra of the same cell taken at different times shows where a change comes from. The reading rests on general electrochemistry; a cell's actual condition is judged together with its temperature, state of charge and history.
- Series resistance grows; the curve shifts right
- The arcs grow: SEI and charge-transfer resistance rise
Shape only; the axes carry no values.
- 01
Growing ohmic resistance
The curve shifts right. Electrolyte decomposition and the degradation of contacts and current collectors cause this shift.
- 02
SEI growth
The SEI arc widens. As the layer on the anode thickens, ions pass through it less easily, and the reaction that builds it consumes active lithium.
- 03
Loss of active material
The charge-transfer arc grows. Particle cracking or loss of contact with the electrode reduces the reaction area, so the same current has to pass through a smaller surface.
- 04
Lithium plating
At low temperature or during fast charging, lithium can deposit as metal on the anode surface. It leaves changes in the charge-transfer region that are most visible right after charging; the change over time says more than any single spectrum.
- 05
Temperature
When the temperature falls, charge transfer and diffusion slow down and the arcs grow. That is not aging, which is why every spectrum is read together with the temperature at which it was taken.
Measuring in the field
We are taking EIS out of the lab and into the running system, cell by cell.
In the lab, a cell is rested, held at a constant temperature and connected to an instrument. Battery decisions are made in the field, on a system under load. Moving the measurement into the field means solving four engineering problems together.
- 01
Excitation during operation
The cell is already carrying a load current. We design the excitation to ride on top of that current and the response to be separated from it, with the excitation kept small enough not to affect the system's operation.
- 02
Noise
Switching noise from power converters and sudden load changes can bury the cell's small voltage response. We design the measurement electronics and the signal processing together for that environment.
- 03
Temperature
The spectrum changes with temperature. Every measurement is designed to carry the cell's temperature, and we are developing models that separate the effect of temperature from the effect of aging.
- 04
Time and scale
A storage system holds a large number of cells, and each measurement must be comparable with the others. We design every measurement to carry the same clock, so spectra from different cells and events in the system can be read on one time axis.
Our approach
Measurement electronics and models, together.
Sense is being developed as the measurement board that sits on the battery module. It is designed to measure voltage, temperature and impedance, and to turn the spectrum into indicators of the cell's internal resistance and chemical state with models that run on the board.
Designed data flow
Sense
Cell
Excitation, response and spectrum; interpretation on the board.
Core
Pack and container
Cell indicators feed balancing, protection and usable-capacity decisions.
Site
Facility
Health information from the cells feeds the facility's capacity and fault decisions.
Let's talk about cell measurement.
Write to us about our measurement approach, Sense and working together.