Generalization of transmission line models for deriving the impedance of diffusion and porous media

System simulation and system identification are common problems in science and technology. In the field of electrochemistry this is of interest for systems, such as porous electrodes and mechanisms, such as diffusion. These are relevant for technical applications, such as energy storage and corrosion protection. Models describing the electrical behavior of such systems are based not only on schematics, physical and chemical approaches but also on equivalent circuits. Sometimes simplifications are applied to the conduction path and the spatial distribution of parameters. Due to the availability of many different models, the selection of a suitable model for a specific application is very difficult. Hence, identifying model similarities allows for a better understanding of each mechanism, reducing the number of mathematical calculations, simplifying model evaluation and thereby reducing the complexity. In this paper, a more general point of view of impedance in terms of a generalized transmission line model is considered. The differential equation of the transmission line model and its general solution is discussed. Furthermore, different boundary conditions are applied to obtain the solution for different electrochemical systems. The results for diffusion and porous electrodes are discussed in more detail, the solution of the differential equations are compared with the established models and the impedance behavior is analyzed. An effort has thus been made to analyze and remove ambiguity from impedance model equations. Removing ambiguity simplifies the analysis of model parameters influencing impedance behavior and additionally improves the robustness of nonlinear parameter optimization techniques.