E. Tuncer et Sm. Gubanski, On dielectric data analysis - Using the Monte Carlo method to obtain relaxation time distribution and comparing non-linear spectral function fits, IEEE DIELEC, 8(3), 2001, pp. 310-320
Citations number
65
Categorie Soggetti
Eletrical & Eletronics Engineeing
Journal title
IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION
In this paper, we present a technique for analyzing dielectric response dat
a in the frequency domain, chi(omega) = epsilon(omega) - epsilon (infinity)
= epsilon '(omega) - epsilon (infinity) - i epsilon "(omega). We use a pre
distribution of relaxation times and reconstruct the original data by singl
e Debye relaxations using a box constraint, least squares algorithm. The re
sulting relaxation times tau (Di), and their amplitudes Delta epsilon (i),
yield the relaxation time spectrum, where i is equal or less than the numbe
r of data points. Two different predistributions of relaxation times are co
nsidered, log-uniform and adaptive. The adaptive predistribution is determi
ned by the real part of the dielectric susceptibility chi ', and it allows
for the increase of the number of effective relaxation times used in the fi
tting procedure. Furthermore, since the number of unknowns is limited to th
e number of data points, the Monte Carlo technique is introduced. In this w
ay, the fitting procedure is repeated many times with randomly selected rel
axation times, and the number of relaxation times treated in the procedure
becomes continuous. The proposed method is tested for 'ideal' and measured
data. Finally, the method is compared with a nonlinear curve fitting by a s
pectral function which consists of three contributions, i.e. the Havriliak-
Negami relaxation polarization, low frequency dispersion and de conductivit
y It has been found that more information can be obtained from a particular
data set if it is compared with a nonlinear curve fitting procedure. The m
ethod also can be used instead of the Kramers-Kronig transformation.