Defining Anisotropic Relative Permittivity Tensors
Eddy or Frequency Domain Solutions Only
The relative dielectric permittivity of dielectrics is assumed to be a complex quantity, expressed as the following:
where ᵋ' is the real part of the complex permittivity (the same as the usual relative dielectric constant), ᵋ" is the imaginary part of the complex permittivity, and j is the imaginary unit.
The relationship above can also be written as the following:
where tand is the dielectric loss tangent.
For anisotropic dielectrics, a tensor material property needs to be used. The anisotropic relative permittivity tensor has the following expression:
If the material property is anisotropic, its characteristics are defined by its anisotropy tensor. You must define three diagonals for anisotropic permittivity. Each diagonal represents a tensor of your model along an axis.
These tensors are relative to the coordinate system specified as the object’s Orientation property. By specifying different orientations, several objects can share the same anisotropic material but be oriented differently.
- In the Relative Permittivity row in the View/Edit Material window, select Anisotropic from the Type drop-down menu.
- Enter the material’s relative permittivity along one tensor axis in the Value box of the T(1,1) row.
- Enter the relative permittivity along the second axis in the Value box of the T(2,2) row.
- Enter the relative permittivity along the third axis in the Value box of the T(3,3) row.
Three rows named T(1,1), T(2,2) and T(3,3) are added below the Relative Permittivity row.
If the relative permittivity is the same in all directions, use the same values for each axis.
These values can also be defined as variables.
Related Topics
Creating a Relative Coordinate System
Change the Orientation of an Object
Relative Permittivity for a Maxwell Material
Defining Anisotropic Relative Permeability Tensors
Defining Anisotropic Conductivity Tensors