The Piecewise Linear Model

This frequency dependence is often linear within a certain frequency range and constant outside of the frequency range, as shown below:

where:

• epsr_lower is the relative permittivity of a material below the frequency range 20 - 50 GHz.
• epsr_upper is the relative permittivity of a material above the frequency range 20 - 50 GHz.
• f_lower is the lower frequency, below which the material property is constant.
• f_upper is the upper frequency, above which the material property is constant.

In general, to account for this variance within a given frequency range, use the Piecewise Linear Material Input window to specify a material property 's values at frequencies below and above the frequency range. Based on these values, Q3D Extractor automatically creates a piecewise linear dataset that specifies the property's values at the desired frequencies during solution generation. This dataset can be modified with additional points if desired.

The piecewise linear model is quite general, and permits the relative permittivity to be specified independently from the loss tangent. As a result, it does not guarantee that the Kramers-Krönig causality conditions will be satisfied.