ALTERNATIVES TO KRONIG-KRAMERS TRANSFORMATION AND TESTING, AND ESTIMATION OF DISTRIBUTIONS

Two alternatives to Kronig-Kramers analysis of small-signal ac immitta nce data are discussed and illustrated using both synthetic and experi mental data. The first, a derivative method of approximating imaginary -part response from real-part data, is found to be too approximate in regions where the imaginary-part varies appreciably with frequency. Th e second, a distribution of relaxation-times fitting method, is shown to be valuable for testing whether a data set satisfies the Kronig-Kra mers relations and so is associated with a system whose properties are time-invariant. It also is valuable for estimating real- or imaginary -part response from the other part, usually with small error. Unlike K ronig-Kramers analysis, the second method usually requires no extrapol ation outside the range of the measured data. Finally, this discrete-f unction method also allows one to estimate the distribution of relaxat ion times or activation energies associated with a given set of freque ncy-response data. This application is described and illustrated for b oth synthetic and experimental data and is shown to yield good but som ewhat approximate results for the estimation of continuous distributio ns. It is particularly valuable for identifying response regions arisi ng from a continuous distribution and distinguishing them from those a ssociated with discrete time-constant response.