A Debye dispersion model of a two-layered material

Debye formulas are widely used to describe the electrical dispersion characteristics of a uniform lossy material. Debye model uses some empirical coefficients to control the shape and position of spectroscopy curves. It can fit most of the data from experiments. A two-layered model is investigated through its equivalent Debye circuit model. A Finite Difference Method (FDM) is developed to extract the effective permittivity and conductivity of a two-layered model as the verification of the analytical derivation. The computation results indicate the results obtained from FDM and the layered Debye formulas agree very well, which shows the validity of the layered Debye formulas in terms of the original circuit parameters. The derived formulas are used to analyze the relationship between the effective electrical spectra and the electrical parameters of each layer. A few examples are given in the discussions. And it can be concluded that: (1) with the increase of the average value of the conductivity of the two layers, the spectra of effective permittivity transition area shifts to higher frequencies; while the spectra of effective conductivity transition kept the same with the values decrease; (2) with the increase of the average value of the relative permittivity of the two layers, the transition area of the spectra of effective permittivity kept the same with values increase; and the transition area of the spectra of effective conductivity shifts to the lower frequencies; (3) the effective permittivity enhances at the lower frequency region as the ratio between the conductivity of two layers increase.