CST – Computer Simulation Technology

Effective Conductivity Concept for Modeling Conductor Surface Roughness

Effective Conductivity Concept for Modeling Conductor Surface Roughness
Gerald Gold, Klaus Helmreich
DesignCon 2014
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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