The Differences Between Equivalent Foster and Cauer Circuits and Factorised Impedance

Abstract

Approximations of non-integer order elements as Warburg impedance or constant phase element (CPE) are frequently made with equivalent electrical circuits. We can show that 5 various models are impedances mathematically equivalent for their frequency behavior. However, if we look closer at these models according to their various properties: model available in all cases, number of optimum, transient simulation, integration time, it seems that only one of the 5 models have all the qualities. This result is fundamental for the good choice of a model used for transient identification or for on-line identification.