Some Features of the Analysis of Broadband Impedance Data Using Distribution of Relaxation Times

The article discusses the preparation of the data of electrochemical impedance spectroscopy (EIS) for representation in the form of distribution of relaxation times (DRT). In the case of broadband EIS, the measurement errors are not normally distributed and, herewith, cannot be modeled by white Gaussian noise. This circumstance is essential because the DRT method is hugely susceptible to measurement errors. It is shown, that considering the variation of the measurement errors across the frequency range improves the quality of the DRT function. Thus due to a comprehensively optimized problem, the DRT may provide a better resolution of distinct charge relaxation processes than the conventional equivalent circuits. The Python application was written for the calculation of nonparametric DRT function, and the actually measured impedance data of solid electrolytes and RC circuits were used to illustrate the methodology of the calculation. The application uses least-square solver for non-negative solutions along with Tikhonov regularization. All the experience gained by using the prior version of the app, written in Matlab, is built into the new product. Some aspects of the selection of regularization parameter by using, so-called, L-curve is also discussed.