Frequency response of unified dielectric and conductive systems involving an exponential distribution of activation energies

TLDR: In this paper, it is shown that the corresponding response of an associated conductive or dielectric system may be immediately obtained through the use of new duality relations. But the authors do not consider the relationship between the activation energy probability density and the activation frequency response.

Abstract: When the small‐signal ac frequency response of a dielectric or conductive system is known, either functionally or as data, it is shown that the corresponding response of an associated conductive or dielectric system may be immediately obtained through the use of new duality relations. A specific model is considered which involves thermally activated capacitance and/or resistance, with an activation energy probability density exponentially dependent on energy. Previous frequency response analyses of such a continuously distributed model involve inadequate approximations and lead to erroneous predictions. Correct immittance results are presented in three ways: analytically, by means of complex plane plots, and through the use of three‐dimensional perspective plots. Results are given in general form but apply to both dielectric and conductive systems which involve the same functional dependence on activation energies. Low‐ and high‐frequency‐limiting responses for a given system are found to be associated wi...