Mathematical equivalence of Maxwell and Voigt models

The work is devoted to the theory of transformation of resistor-capacitor two-terminal networks, the use of which simplifies the construction of electrical models of various ion-conducting media based on the data obtained by the method of impedance spectroscopy. It is shown that the fre quency characteristics of the samples can be modeled with the same accuracy by equivalent circuits (EC) with different structure. Two or more such ECs are proposed to be called mathematically equivalent two-terminal networks. The necessary and sufficient conditions for the mathematical equivalence of two-terminal networks are given. It is shown that the Voigt and Maxwell models with equal number of elements are mathematically equivalent. The theory of direct and inverse transformation of the Voigt and Maxwell schemes is considered. As an example, the formulas that allow to obtain the parameters of the three-link Voigt model from the known parameters of the Maxwell model and vice versa are given. The paper provides a printout of this algorithm from the desktop of the program Mathcad.