Dielectrics

Dielectric materials are used for Dielectric Layers and Dielectric Brick Tech Layers. When starting from a blank project, Sonnet provides an Air material and a Substrate material. The Air material may not be edited, but you may edit the Substrate material. You may add more dielectric materials to your project by selecting Circuit Settings > [Materials] : [Dielectrics] and clicking Add. This opens the Dielectric Properties dialog box.

The Dielectric Properties dialog box may also be used to edit dielectrics that are already defined. If you edit the properties of a dielectric, all uses of that dielectric material will be updated.

Dielectric Properties

Erel: The relative dielectric constant (εr). It is the ratio (ε/εo), where ε is the real part of the permittivity of the dielectric material, and εo is the permittivity of free space. The ratio is dimensionless.

Dielectric Loss Tan: The dielectric loss tangent, also called the electric loss tangent. It is the ratio (ε’’/ε’), where ε = ε’ - jε’’, and ε is the complex permittivity of the dielectric material. The ratio is dimensionless.

Conductivity/Resistivity: Dielectric conductivity or resistivity of the dielectric as determined by the value set in the Loss Type drop-down list. The EM solver converts the conductivity or resistivity you entered into a frequency-dependent electric loss tangent using the following equation.

Where,

• tan δe = The electric loss tangent.
• σ = The conductivity you entered.
• ω = The radian frequency.
• εr = The relative dielectric constant.
• ε0 = The permittivity of free space.

When both Dielectric Loss Tan and Conductivity are specified, the EM solver computes a total electric loss tangent by summing the two loss tangent terms. Please note that you may set the conductivity or resistivity to infinity by entering "INF".

Mrel: The relative magnetic permeability (μr) of the dielectric material. It is the ratio (μ/μo), where μ is the real part of the permeability of the dielectric material, and μo is the permeability of free space. The ratio is dimensionless..

Mag Loss Tan: The magnetic loss tangent, tan δm, of the dielectric material. It is the ratio (μ"’/μ'), where μ = μ' - jμ", and μ is the complex permeability of the dielectric material. The ratio is dimensionless.

Any parameter may be set to a variable in place of a constant. Either type the name of an existing variable or select <Add Variable> from the drop-down menu.

Anisotropy

If you wish the dielectric material to be anisotropic, indicating that its parameters are different in each dimension, enable the Anisotropic checkbox. The dialog box is updated so that there are three sets of entries; one for the x, one for the y, and one for the z direction. You can then enter the parameters of the dielectric material by editing the entries in the row. Any dielectric parameter (Erel, Dielectric Loss Tan, etc.) may be specified as anisotropic. 

If the dielectric is used in a Dielectric Brick, then all three specified values are used. However, if the dielectric is used in a dielectric layer, and the specified x-value is different from the specified y-value, then the x-value and y-value are set to the average of the two values.

Frequency-dependent Tables

Any dielectric parameter may use a frequency-dependent table of values in place of a constant or variable. Select <Add Table> from any parameter's drop-down menu and enter frequency/value pairs. You may also click the Import button to load a CSV file containing frequency/value pairs. An example of a CSV file is shown below.

0.1, 12.0
1.0, 12.1
3.0, 12.2

The EM solver will use linear interpolation between frequency points in the table. For frequency points above and below the frequencies in the table, the EM solver will use the first value in the table for frequencies below the minimum frequency in the table, and it will use the last value in the table for frequencies above the maximum frequency in the table.

You may also define your own custom frequency-dependent equation for any dielectric property. See Frequency Dependency.

Causality Model

The Causality Model drop list allows you apply a Debye function to the dielectric material properties to enforce dielectric causality. The choices are given below:

• No Correction: Use the No Correction option if you want the EM solver to maintain the material properties exactly as they are specified in the project file. For example,
  • If only a single value for Erel, Dielectric Loss Tangent, Conductivity, or Resistivity is specified, this value will be used for all frequencies in the analysis.
  • If a table of values is used for Erel, Dielectric Loss Tangent, Conductivity, or Resistivity, the table is handled as described in the Frequency-dependent Tables section.
• Djordjevic-Sarkar: Use the Djordjevic-Sarkar option if you want a Debye function applied to the dielectric material properties, including fixed or table-based properties and anisotropic dielectric properties. The Djordjevic-Sarkar model will compute a broadband Debye function based on the specified material properties [25]. This model requires that the specified loss tangent of the material be non-zero. The function will match the specified dielectric constant and loss tangent at the specified Reference Frequency, and then adjust those parameters at all other frequencies to enforce causality. To compare the computed Debye function versus the specified material properties, click the Graph button.

Graph: Click the Graph button to create a graph of the dielectric constant and loss tangent as a function of frequency. You may use this graph to compare the causality model to your original specified values. Solid curves are used to display the causality model and dashed curves are used for the original specified value (labeled "Raw" in the legend). The frequency range of the graph is based on your project's frequency sweeps.

The Causality Model should not be used for dielectrics that use Dielectric Bricks.

Libraries

You may also import dielectric properties from a dielectric library of commonly used dielectrics. See Material Libraries for details.

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