Classified Foster and Cauer Circuits for the Choice of a Model

Abstract

Patrick Lagonotte, Fabien Soulier, Anthony Thomas, Sergueï Martemianov

Approximations of constant phase elements (CPE) or Warburg impedance are frequently made by equivalent electrical circuits. However, these approximating circuits generally do not take into account the boundary conditions involved by making such approximations. In this paper, we assess various models or possible topologies and classify them according to their asymptotic limits. We show that circuit topologies having the same number and the same types of elements has the same impedance (thus the same frequency behaviour). Having identical factorized impedance proves the equivalence between several proposed models (serial Foster, parallel Foster, serial Cauer and parallel Cauer). We conclude that the choice of a model for parameter identification needs to take into account the specific boundary conditions.

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