Approximability of impedance spectra by RC elements and implications for impedance analysis

• Requirements for impedance spectra to be approximated by RC elements
• An analytical formula for approximating multiple real poles by RC elements
• Theoretical foundation of impedance validity testing by fitting RC elements
• A generalization of the distribution function of relaxation times

A commonly used class of impedance spectra validity tests is based on fitting serially connected parallel coupled pairs of resistor and capacitor (RC elements) to a measured impedance spectrum. If the model approximates the spectrum well, the measurement is considered valid. It is considered invalid if approximation is poor. Despite being widely used, theoretical justification is still missing. It is not clear which electrochemical processes could be approximated by such a model and hence, for which processes a poor approximation of the spectrum truly indicates a false measurement, instead of merely a lack of generality of the model. The scope of this paper is to derive from a system theory point of view, which class of systems can be approximated by serially connected RC elements and from that to conclude for which electrochemical systems the mentioned class of validity tests is applicable. Moreover, the results will yield theoretical justification for generalizing the concept of distribution function of relaxation times (DRT) by using positive and negative RC elements so that its benefits can be utilized not only for strictly capacitive, but for any possible non-oscillating electrochemical system.