A flexible procedure for analyzing impedance spectroscopy results: Description and illustrations

Abstract

General considerations in nonlinear least squares fitting of small-signal ac frequency response data (conductive or dielectric systems) are first discussed. A very general and flexible complex nonlinear least squares fitting (CNLS) program (LOMFP) is described which runs on microcomputers of the PC and AT type. Advantages and disadvantages of LOMFP are discussed and compared to those of a recent CNLS program developed by Boukamp. LOMFP incorporates many thousands of equivalent circuits fitting possibilities and ten different distributed circuit elements which can be used in these circuits. Its fitting is both speedy and accurate, and it provides considerable insurance against confusing local minima fits with true least squares fits. It is optimized for fitting real, imaginary, or complex data of either partly conducting or purely dielectric character, and it incorporates great flexibility in handling and fitting data in different forms (different immittance levels and rectangular or polar representation). Seven different data weighting choices are provided. Exact synthetic data were generated from a typical Impedance Spectroscopy equivalent circuit, and the effects on CNLS fitting were investigated of rounding the exact data to 4, 3, and 2 decimal places. We present the results of an extensive study of the effects of transforming exact data to different immittance levels and representations and then rounding to two places or of transforming rounded 2-place data directly. We conclude that real data should not be transformed from its original measured form before carrying out CNLS fitting. Finally, the effects were investigated of various kinds of weightings on CNLS fitting of 2-place data, leading to the conclusion that in spite of its advocacy and use by Zoltowski and Boukamp, modulus weighting generally yields misleading and appreciably worse CNLS fitting results than does proportional weighting. The LOMFP program (source and executable files) is available from the first author.