Analysis of the AC electrical data in the Davidson-Cole dielectric representation

The representation of the AC electrical data in the complex plane reveal two major classifications of the relaxation processes known as ideal (Debye) and non-ideal (non-Debye) types. The non-Debye relaxation has been empirically observed via Cole-Cole (C-C), Davidson-Cole (D-C), and Havriliak-Negami (H-N) responses. Each of these non-Debye relaxations is visualized with an equivalent circuit similar to the ideal relaxation. Both ideal and C-C relaxations reveal semicircular behavior in the complex plane while D-C and H-N relaxations deviate from the usual semicircular loci known as skewed behavior. The extracted equivalent circuit elements are essentially non-Debye for both D-C and H-N relaxations possessing complexity in the relaxation time. The analytical method of extracting these elements in conjunction with the empirical parameters of the D-C relaxation is described using conventional (real) domain and complex domain. The curve fitting procedure provided extremely small error for the complex domain analysis. The behavior of the D-C relaxation function and the depression parameter β are also discussed using ωτ=1 and ωτ≠1 corresponding to the maximum of the imaginary part of the impedance (Z^*) or permittivity (ε^*).