In Plane Permittivity Extraction Using Multiline Thru Reflect Line Test Vehicles
Multiline TRL stripline vehicles isolate in-plane permittivity by extracting propagation constants directly, bypassing transition discontinuities and z-axis bias.
Casual Huray Roughness
Topographic Modeling
A mathematical representation of copper foil surface topography provides a simplified method for estimating conductor losses without requiring extensive scanning electron microscopy data. The casual huray roughness model approximates the microstructural nodules on a copper trace as a collection of uniform spheres sitting on a flat surface. Designers use this model to predict high-frequency signal attenuation due to the skin effect at millimeter-wave frequencies.
The process begins with extracting a surface roughness value from standard supplier datasheets and converting it to a spherical projection. Only two parameter inputs are needed to estimate the increased resistance.
Calculation Basis
Calculation of the correction factor relies on the ratio of the surface area of the spheres to the flat hexagonal tile base. Rather than measuring every individual nodule, this approach assumes a default sphere radius and a standard treatment density. This simplification reduces the computational workload during full-wave electromagnetic simulations of transmission lines.
If the nodule size distribution is highly irregular, the model exhibits a loss of accuracy.
Model Boundary
Application of this method is limited to frequencies where the skin depth is comparable to or smaller than the nodule dimensions. When the skin depth is much larger than the roughness profile, the surface treatment has a negligible effect on the total conductor loss. Fabricators must balance the use of smoother copper foils against the need for adequate peel strength to prevent trace delamination.
This balance determines the laminate choice.