Harmonic Analysis Based Method for Perturbation Amplitude Optimization for EIS Measurements

Abstract

The impedance concept is defined by Ohm's generalized law. Ohm's law requires the fulfilment of 3 conditions in order to be valid: causality, linearity and stability. In general, electrochemical systems are highly nonlinear systems; and therefore, in order to achieve linearity low amplitude perturbations have to be used during EIS measurements. However, small amplitude perturbations lead to low signal-to-noise ratios. Consequently, the quality of an EIS measurement is determined by a trade-off: the perturbation amplitude should be big enough in order to obtain a good signal-to-noise ratio; and at the same time, it should be small enough in order to avoid significant nonlinear effects. The optimum perturbation amplitude corresponds with the maximum perturbation amplitude that ensures a pseudo linear response of the system. In this work, a method for experimentally determining the optimum perturbation amplitude for performing EIS measurements of a given system is presented. The presented method is based on the harmonic analysis of the output signals; and in this work, it was applied to a highly nonlinear system: the cathodic electrode of an alkaline water electrolyser. The presented method allows optimising the perturbation amplitude in both, constant amplitude and frequency dependant amplitude strategies.

CuO improved (Sn,Sb)O2 ceramic anodes for electrochemical advanced oxidation processes

“…In this research, a perturbation amplitude of 20 mV was used for all the EIS measurements. This amplitude was selected using the selection methodology presented in previous works …”

Improvement of the Electrochemical Behavior of (Sb, Sn, Cu)O Ceramic Electrodes as Electrochemical Advanced Oxidation Anodes

“…[44] For this reason, validation is a fundamental part of the preliminary analysis of experimental EIS spectra. [52,53] The uncompensated resistance is given by the high frequency intersect of the EIS spectrum with the real axis: [54] in this work, the uncompensated resistance for each overpotential was determined from the high frequency intersect of the experimentally measured impedance spectrum at that overpotential with the real axis. [47,48] In this work, the EIS measurements were performed at 100 frequencies logarithmically spaced between 10 kHz and 10 mHz.…”

“…This amplitude was selected using the selection methodology presented in previous works. [52,53] The uncompensated resistance is given by the high frequency intersect of the EIS spectrum with the real axis: [54] in this work, the uncompensated resistance for each overpotential was determined from the high frequency intersect of the experimentally measured impedance spectrum at that overpotential with the real axis. Both, the CVs and the pseudo-steady-state polarization curve, were IÀ R corrected using the procedure described by Hrbac and co-…”

Optimization of the Perturbation Amplitude for EIS Measurements Using a Total Harmonic Distortion Based Method

“…So, even if theoretically an infinitely small perturbation amplitude (→ 0) is required for the electrochemical system to behave pseudo-linearly [39]; in practice, the amplitude of the AC signal has to be chosen in order to be small enough to guarantee the pseudolinear behavior of the system, but large enough to be able to measure the response of the system [1]. In this context, the concept of optimum perturbation amplitude arises: the optimum amplitude corresponds with the amplitude that maximizes the SNR without violating significantly the linearity condition [40]. At the end of the day, the optimum perturbation amplitude is defined by the trade-off between the maximization of the SNR, and the fulfilment of the linearity behavior condition.…”

“…Since the selection of the perturbation amplitude is critical for the quality of the measured EIS spectra, it is a fundamental part of the experimental design of any experiment that involves EIS [41]. The optimum perturbation amplitude depends strongly on the studied electrochemical system [30], and can even vary from one operation point to another for a given system [40]. However, for potentiostatic EIS, there is a well-stablished criterion according to which the applied perturbation amplitude should be lower than the thermal voltage ( ()*+,-) [32], given by:…”