Multivariate analysis of multiple impedance spectra

A one-step method for evaluation of multiple impedance measurements in a multivariate analysis is presented. Usually two steps are necessary to extract model parameters like activation energy from impedance measurements at two or more temperatures. First, each measurement is analyzed with CNLS (complex nonlinear least squares) software using the same equivalent circuit. Second, activation energy is obtained in a NLS fit of conductivity data. This two-step procedure could lead to doubtful results as fit errors because of noise in the first step could prevent reliable results in the second step. Error estimates of model parameters are only based on the second step, ignoring the quality of the first step. Using a one-step method, model parameters are directly obtained from multiple impedance measurements, often resulting in more reliable results and meaningful error estimates than for the two-step procedure. Similar approaches to the one proposed have been reported in literature. Although some approaches are reported to be implemented in a software package, none of these are available to the community. The aim of this paper is to clearly point out the mathematics used and the benefits of a simultaneous analysis of impedance spectra.