Effective Conductivity Concept for Modeling Conductor Surface Roughness
Gerald Gold, Klaus Helmreich
1st January 0001
In the two-digit GHz-range, where the conventional skin depth decreases to the range of surface roughness, loss predicted assuming ideally smooth surfaces falls far behind measurement.
A new method to treat surface roughness in field solvers is introduced which employs the concept of a frequency-dependent effective conductivity as impedance boundary condition. It is deduced by solving Maxwell‘s equations for the newly introduced conductivity gradient model: Comparing signal wavelength, conductor width and
roughness feature size, one can conclude that a propagating wave does not “see“ individual peaks and pits, but rather a “mean“ plane surface, which, however, shows no abrupt border between dielectric and conductor, but a steady transition in conductivity perpendicular to the surface. Thus, roughness with the gradient model can be
characterized by one single parameter: the root mean square Rq of microscopic surface height, already provided in many PCB material data sheets. This method accurately predicts measured insertion loss responses.
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