Abstract
Impedance spectra obtained by fast Fourier transformation of the response to a multi-sine potential perturbation are shown to be consistent with the Kramers–Kronig relations, even for systems that are nonlinear and nonstationary. These results, observed for measurements on a Li/SOCl2 battery, were confirmed by numerical simulations. Consistency with the Kramers–Kronig relations was confirmed by use of the measurement model developed by Agrawal et al. and by a linear measurement model approach developed by Boukamp and implemented by Gamry. The present work demonstrates that application of the Kramers–Kronig relations to the results of multi-sine measurements cannot be used to determine whether the experimental system satisfies the conditions of linearity, causality and stability.
Highlights
Since the resolving power of the technique comes from the ability to interrogate events occurring at different timescales, the accessible range of frequencies is an important parameter to discuss
Unlike the conventional step-sine Electrochemical Impedance Spectroscopy (EIS) in which excitation signals are applied at each frequency separately, MS-EIS excites the sample by one composite signal containing numerous frequencies intended for investigation
The obtained impedance results were tested for the compliance with Kramers–Kronig relations with measurement model methods
Summary
Since the resolving power of the technique comes from the ability to interrogate events occurring at different timescales, the accessible range of frequencies is an important parameter to discuss. Smith et al, who applied pseudorandom white noise excitation signals to measure the self-exchange rate constants for Cr(CN)64−/Cr(CN)63− system.[18] The technique was named Fourier Transform Admittance due to the reliance on FFT to obtain the admittance values. They described the data processing involved for FFT impedance and highlighted the advantages of using the technique.[19]
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