  # Fundamentals of Spectral Impedance

The internal resistance of a battery is strongly frequency dependent: it decreases with increasing frequency and exhibits reactive components. Therefore it is called spectral impedance which is depicted either per magnitude and phase (and graphically as Bode plot) or per real part and imaginary part (and graphically as Nyquist plot). A purely ohmic behaviour only exists at one frequency which typically lies in the range of 1kHz, depending on technology and capacity. This so-called AC resistance is typically specified in the data sheets, for the sake of convenience at a fixed frequency of 1kHz. It is measured by imposing a small AC current onto the battery and measuring the resulting AC voltage. The measurement takes around 1 sec.

During operation such fast changes of currents are quite unusual; therefore in order to evaluate the operational behavior, the DC resistance is more appropriate. This is done by measuring the impedance at a lower frequency, typically <1Hz (or in the time domain as step response). Both measurements (AC and DC resistance) take only a few seconds.

The most comprehensive insight into the battery behavior is gained by spectral impedance measurements (also called electrical impedance spectroscopy EIS). Here the (complex) impedance is measured at multiple frequencies (e.g. between 0.1Hz and 1kHz), with a measurement duration of several minutes or longer. The frequency response or the Nyquist plot shows the electrochemical behavior. For instance, if the curve deviates considerably from a typical behavior, damages can be concluded.

The table below shows an overview of common measurement parameters:

 Measurement Parameter Battery Behavior R & D Production Maintenance Service Voltage State of charge (SoC) (Li-Ion, lead) ✓ ✓ ✓ AC resistance Ageing (SoH) ✓ ✓ ✓ ✓ DC resistance Operational behavior ✓ ✓ ✓ Nyquist plot (Impedance Spectrum) Operational behavior, Damages, Model parameters ✓ (✓) (✓) Application Qualification Selection, grading Examination and exchange Diagnosis Reference values are to be determined Existing cells Adjacent cells Data sheet or initial data