Some simple equivalent circuits for ionic conductors

Abstract

Some equivalent circuits which involve one or two distributed circuit elements are discussed. These circuits are useful in fitting small-signal frequency response data for solids and liquids. A fitting circuit recently proposed by Bruce to represent distributed bulk effects in conducting materials is shown to be closely related to earlier work. Although Bruce demonstrated that his circuit fitted certain data better than a simple alternative circuit, it is not physically realistic in the high frequency region. We investigate how well the response of the Bruce circuit (which involves one distributed circuit element and three ideal elements) can be simulated by that of simpler circuits, ones which involve a single unified distributed element, possibly in parallel with a single ideal capacitor. The usefulness of several different distributed elements, most of which have been widely used for data fitting in the past , is compared. Complex nonlinear least squares fitting results suggest that several of the simpler circuits considered are preferable to the proposed Bruce circuit for fitting of most ionic-conductor frequency response data. Finally, two structurally different equivalent circuits which involve two distributed elements each, so they can represent distributed interface as well as bulk effects, are compared and found to be able to simulate each other quite well under certain conditions. Problems which thus arise in choosing the best equivalent circuit for data fitting are discussed.