Introduction to MVCNLS Software

The MVCNLS (Multi Variate Complex Nonlinear Least Squares) software makes the model-supported analysis of impedance spectra possible.

Impedance spectra are usually analyzed with an equivalent circuit, whose parameters are connected to the properties of the sample. For this task of the parameter extraction (one speaks of a fit) several programs are commonly used: Equivalent Circuit of B. A. Boukamp, LEVM of J. R. Macdonald as well as ZView/ZPlot. A disadvantage is common to these programs: they regard only a measurement at a time. If one varies a site condition (time, temperature, gas environment, etc..) at the same specimen and measures the impedance spectra for each condition, then one would usually like to describe the parameters of the equivalent circuit as function of the varied condition.
With the standard programs one has to fit each impedance spectrum separately and extract from the (usually noisy) results the parameters of the higher model. This often results in misinterpretation or doubtful results. At this point the MVCNLS software sets:
With MVCNLS several impedance spectra, which obey the same equivalent circuit, are fitted at once. The dependence of each equivalent circuit parameter on the varied condition can be described by a broad selection of functions. The MVCNLS software determines now from all measurements the parameters of these functions. The faulty two-step procedure is avoided by this method and substantially more exact and reliable results can be obtained.

For the actual CNLS fit the NAG function e04unc (nonlinear squares leases according to SQP algorithm) is used. The MVCNLS software was developed during my work at the Universität Karlsruhe (TH). The development was predominantly made in my spare time. Since I would like to distribute the MVCNLS software free of charge and can not assume that all interested colleagues possess C-compilers as well as a NAG license, I'm currently working on the use of a free math library.