Dielectric Constant Measurement and Prepreg Glass Weave Selection in Multilayer Board Design
Select spread-glass prepreg and extract dielectric constants from TRL transmission line measurements to eliminate weave skew and impedance errors.
Surface Roughness Skin Effect
Loss Mechanism
High-frequency electromagnetic wave propagation concentrates electrical current within a thin superficial zone along the periphery of a metal conductor. When skin depth approaches or falls below the surface topography profile of copper foil, surface roughness skin effect drastically increases conductive attenuation along printed transmission lines. Current crowding forces electrical charges to follow the microscopic peaks and valleys of the copper tooth profile rather than a straight axial vector.
The resulting detour extends the physical path length of the circulating current, inflating effective conductor resistance above classical theoretical predictions. In addition to path lengthening, microscopic metal teeth distort internal magnetic fields, inducing localized eddy currents that dissipate signal energy as heat. Attenuation losses scale upward as signal frequencies rise toward millimeter-wave regimes.
Profile Topography
Foil manufacturing creates intentional surface tooth profiles to establish mechanical interlocking between smooth electrodeposited copper sheets and bonding prepreg matrices. In printed board analysis, surface roughness skin effect depends directly on the tooth amplitude, which standard profilometry measures through root-mean-square roughness and ten-point peak-to-valley parameters. Standard electrodeposited foils exhibit rough nodules with peak heights exceeding five micrometers, which damages signal fidelity above one gigahertz.
Very low profile and reverse-treated foils employ microscopic grain treatments with roughness values below one point five micrometers, mitigating high-frequency energy degradation. Rolled annealed copper yields the smoothest topography, but provides weaker mechanical peel strength against cured resin matrices. Chemical adhesion promoters deposited during multilayer fabrication modify outer-surface copper topography, introducing supplementary conductor losses that must be measured during signal integrity simulations.
Model Formulation
Electromagnetic modeling programs implement specialized correction formulas to predict conductor attenuation across frequency sweeps. Classical Hammerstad models scale smooth conductor attenuation through an empirical multiplier based on root-mean-square roughness, but this approach loses accuracy above ten gigahertz because it overpredicts high-frequency saturation. Advanced simulations rely on the Huray snowball model, which represents copper roughness as hexagonal close-packed spheres distributed over the conductor surface.
The Huray model accurately links microscopic scanning electron microscope surface imagery to extracted attenuation curves across microwave bands. Conductor loss calculations combining surface roughness skin effect models with dielectric dissipation factor equations dictate allowable trace lengths on high-speed circuit boards. Production acceptance tests employ time domain reflectometry and vector network analyzers to verify that completed transmission lines do not exceed loss budgets established during stackup design.