Analytical Estimation
Electromagnetic transmission models use mathematical equations to estimate the increase in conductor resistance caused by surface roughness at high frequencies. The groisse roughness model provides a calculation method that relates the surface profile measurements of copper foil to the conductor losses in printed circuit traces. This model assists designers in selecting the appropriate copper foil treatment for high speed digital designs.
High Frequency Loss
Skin effect concentrates high frequency currents along the outer boundary of the conductor, making the current path longer when the surface is rough. Standard models can underestimate this loss, but the groisse formula applies a correction factor based on the root mean square roughness height of the copper profile. This correction factor is calculated across a range of operational frequencies to generate an accurate attenuation curve.
In modern circuit boards, matching the estimated losses with actual trace measurements helps prevent signal degradation in multi gigabit transmission lines.
Substrate Interface
Conductor profile selection balances the electrical performance against the physical adhesion of the copper foil to the resin substrate. Very smooth copper reduces high frequency losses but weakens the mechanical bond, which can lead to trace delamination during thermal processing. The model helps engineers determine the maximum roughness that can be tolerated without violating the signal loss limits.
