Elliptical fitting as an alternative approach to complex nonlinear least squares regression for modeling electrochemical impedance spectroscopy

Electrochemical impedance spectroscopy is an important procedure with the ability to describe a wide range of physical and chemical properties of electrochemical systems. The spectral behavior of impedimetric sensors is mostly described by the Randles circuit, whose parameters are determined by regression techniques on the basis of measured spectra. The charge transfer resistance as one of these parameters is often used as sensor response. In the laboratory environment, the regression is usually performed by commercial software, but for integrated, application-oriented solutions, separate approaches must be pursued. This work presents an approach for elliptical fitting of the curve in the Nyquist plot, which is compared to the complex nonlinear least squares (CNLS) regression technique. For this purpose, artificial spectra were generated, which were considered both with and without noise superposition. Although the average error in calculating the charge transfer resist ance from noisy signals using the elliptical fitting of â2.7% was worse than the CNLS with 2.4 · 10â2%, the former required only about 1/225 of the computing time compared to the latter. Following application-oriented evaluations of the achievable accuracies, the elliptical approach may turn out to be a resource saving alternative.