Dielectric Modelling

Frequency Independent

The media is defined in terms of the relative permittivity ( ${\epsilon }_{\text{r}}$ ), relative permeability ( ${\mu }_r$ ), magnetic loss tangent ( $\tan {\delta }_u$ ), and the dielectric loss tangent ( $\tan \delta$ ) or conductivity ( $\sigma$ ).

For example, low loss dielectric substrates are typically specified in terms of the loss tangent, while human tissue (used in specific absorption rate studies) are specified in terms of conductivity.

The effective permittivity of the dielectric is given by:

Debye Relaxation

The Debye relaxation¹ describes the relaxation characteristics of gasses and fluids at microwave frequencies. It has been derived for freely rotating spherical polar molecules in a predominantly non-polar background. The method is defined in terms of the relative static permittivity ( ${\epsilon }_s$ ), relative high frequency permittivity ( ${\epsilon }_{\infty }$ ) and the relaxation frequency ( $f_r$ ).

Cole-Cole

The Cole-Cole² model is similar to the Debye model, but uses one additional parameter to describe the material. The model is defined in terms of the relative static permittivity ( ${\epsilon }_s$ ), relative high frequency permittivity ( ${\epsilon }_{\infty }$ ), relaxation frequency ( $f_r$ ) and the attenuation factor ( $\alpha$ ).

Havriliak-Negami

The Havriliak-Negami³ is a more general model and should be able to successfully model liquids, solids and semi-solids. It is defined in terms of the relative static permittivity ( ${\epsilon }_s$ ), relative high frequency permittivity ( ${\epsilon }_{\infty }$ ), relaxation frequency ( $f_r$ ), attenuation factor ( $\alpha$ ) and the phase factor ( $\beta$ ).

Djordjevic-Sarkar

The Djodervic-Sarkar⁴ model is particularly well suited as a broadband model for composite dielectrics. It is defined in terms of the variation of real permittivity ( $\Delta \epsilon$ ), relative high frequency permittivity ( ${\epsilon }_{\infty }$ ), conductivity ( $\sigma$ ), lower limit of angular frequency ( $\omega {}_1$ ) and the upper limit of angular frequency ( $\omega {}_2$ ).

Frequency List (Linear Interpolation)

Data points at a range of frequencies are specified. Values for the dielectric properties are then linearly interpolated to obtain the dielectric properties at frequency points other than specified. Parameters required are frequency, relative permittivity ( ${\epsilon }_{\text{r}}$ ) and either the loss tangent ( $\tan \delta$ ) or conductivity ( $\sigma$ ).