The evaluation of electrochemical impedance spectra using a modified logarithmic Hilbert transform

摘要

The well-known transform functions of Kramers-Kronig (KK) and Hilbert are often used to validate the experimental data obtained by impedance spectroscopy. However, the linear form of the transform function (KK) can lead to severe problems if it is applied to practical measurements. Whereas experiments are performed in a limited frequency range, the KK transform assumes a theoretical range of zero to infinite. Furthermore, the KK does not detect all-pass contributions to the transfer function. These components appear as artefacts in an impedance spectrum. The KK transform can only detect violations of stability, causality, linearity and continuity, whereas the logarithmic (Hilbert) transform technique (HIT) detects all-pass components too. Nevertheless, the general form of the HIT procedure also suffers from the 'limited bandwidth problem'. Due to the fact that electrochemical systems can be considered as two-poles, the authors developed an algorithm (Z-HIT) for the validation of experimental EIS data using the HIT technique. The fundamen- tal principles as well as the mathematical derivation of the Z-HIT algorithm are described. It is shown by examples that the Z-HIT technique is a well-suited tool for testing the quality of impedance data.