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Linear vs. non-linear systems in impedance measurements (EIS linearity) – Battery – Application Note 9

Latest updated: August 31, 2021


Impedance measurements on linear systems do not vary with the DC bias or with the amplitude of the modulation. This is not the case of non-linear systems, which correspond to most of the real systems. Using an electrical circuit whose response is non-linear and time-invariant, this note describes several examples of the differences noted on the impedance graphs at different operating potential and different amplitudes of the modulation. Exercises are proposed as well as guidelines to make sure impedance measurements on non-linear systems are correct.



Electrochemical Impedance Spectroscopy (EIS) is an interesting tool devoted to the study of linear systems. However, electro-chemical systems are often non-linear. Before explaining the different ways of dealing with this issue, we will point out the main differences between linear and non-linear systems. These differences of behavior are shown in Table I. The impedance measurement was performed using the potentiostatic mode. The potential is defined by:    (1) where EWE is the stationary potential for the impedance measurement, Va is the potential amplitude of the sine signal, f is the frequency, and t is the time.


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