Dielectric Roughness
Electromagnetic signal attenuation in high frequency printed circuit boards arises from surface irregularities on copper foil. The cannonball huray model quantifies this power loss by approximating the copper topography as a collection of stacked spheres. It calculates the effective impedance change caused by current flow through these microscopic obstacles.
This geometric representation allows engineers to predict insertion loss in transmission lines where skin effect dominates signal behavior.
Calculated Impedance
Surface morphology parameters derived from profilometry provide the inputs for this mathematical framework. Each sphere represents an individual grain or nodule found on the treated side of the copper foil. Summing the contribution of these segments provides a correction factor that adjusts the standard conductor loss equations.
Software tools utilizing this approach simulate the impact of various foil profiles on signal integrity before fabrication begins. Design teams use these simulations to select appropriate copper treatments for specific speed requirements. High frequency signals undergo significant phase shifts when encountering uneven surface profiles during propagation.
Signal Propagation
Mathematical integration of the sphere arrangement describes how current density distributes across the irregular copper surface. Increased roughness lengthens the actual path length for electrons as they navigate around the spheres. This longer path forces current into a greater volume of copper, increasing resistive heating at specific frequencies.
Effective roughness values correlate with the measured return loss observed during vector network analyzer testing. The model remains valid for copper surfaces where the grain size represents a significant fraction of the skin depth. Accurate prediction of transmission line performance relies on the precision of the input geometry.
