Application of the Kramers-Kronig Relations to Multi-Sine Electrochemical Impedance Measurements

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. (C) 2020 The Author(s). Published on behalf of The Electrochemical Society by IOP Publishing Limited.