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Limitations of Kramers-Kronig transform for calculation of the DC conductance magnitude from dielectric measurements

Chalashkanov, N. M., Dodd, S. J. & Fothergill, J. (2012). Limitations of Kramers-Kronig transform for calculation of the DC conductance magnitude from dielectric measurements. Paper presented at the IEEE Conference on Electrical Insulation and Dielectric Phenomena, 14 - 17 October 2012, Montréal, Canada.


The Kramers-Kronig (K-K) transform relates the real and imaginary parts of the complex susceptibility as a consequence of the principle of causality. It is a special case of the Hilbert transform and it is often used for estimation of the DC conductance from dielectric measurements. In this work, the practical limitations of a numerical implementation of the Kramers-Kronig transform was investigated in the case of materials that exhibit both DC conductance and quasi-DC (QDC) charge transport processes such as epoxy resins. The characteristic feature of a QDC process is that the real and imaginary parts of susceptibility (permittivity) follow fractional power law dependences with frequency with the low frequency exponent approaching -1. Dipolar relaxation in solids on the other hand has a lower frequency exponent <1. The computational procedure proposed by Jonscher for calculation of the K-K transform involves extrapolation and truncation of the data to low frequencies so that convergence of the integrals is ensured. The validity of the analysis is demonstrated by performing K-K transformation on real experimental data and on theoretical data generated using the Dissado-Hill function. It has been found that the algorithm works well for dielectric relaxation responses but it is apparent that it does not work in the case of a low frequency power law in which the low frequency exponent approaches -1, i.e. in the case of QDC responses. In this case convergence can only be guaranteed by extrapolating the low frequency power law over many decades towards zero frequency.

Publication Type: Conference or Workshop Item (Paper)
Additional Information: © 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Departments: Presidents's Portfolio
School of Science & Technology > Engineering
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