A Direct Approximation of Cole-Cole-Systems for Time-Domain Analysis

Abstract

Cole-Cole-systems are important in electrochemistry to represent impedances of galvanic elements like fuel cells. Fractional calculus has to be applied for system analysis of Cole-Cole-systems in the time-domain. The representation of fractional differential equations of Cole-Cole-systems is addressed in this contribution. Usually, the fractional derivation is approximated, to ensure that the fractional system can be represented by conventional differential equations of an integer order. This article presents a new opposite approach, which results by direct approximation of the Cole-Cole-systems by conventional linear time invariant systems. The method considered is based on the distribution density function of relaxation times of first order Debye-processes. This distribution density is an alternative representation of the transfer behavior of such a system. Several approximation methods, based on an analysis of the distribution density, are presented in this work. The feasibility of these methods will be demonstrated by a comparison of simulated data of the approximation models to ideal data and reference values, respectively.