A numerical Kramers-Kronig transform for the calculation of dielectric relaxation losses free from Ohmic conduction losses

Abstract

A numerical Kramers-Kronig transform is described which allows the calculation of dielectric relaxation losses from dielectric constant data measured at a limited set of frequencies differing by a factor of 2. Conversion formulas for both the central frequencies and for frequencies near the edges of the experimental frequency window are derived. The approach used can be extended easily to measurement frequencies with a different logarithmic spacing. Using this conversion, relaxation and dissipative, conduction losses can be separated. In this way Ohmic conduction processes and simultaneously occurring relaxation processes like dipole or space-charge relaxations can be analysed independently. The results of some simulations and of calculations on experimental data for poly(vinyl-chloride) are used to illustrate the potentials of the ɛ′ to ɛ″ conversion.