Groiss Surface Roughness Model

The Groiss surface roughness model is a simple function of the surface roughness and skin depth of the conductor.

The smooth surface impedance (Z_smooth) is increased by a factor (fact_R), given by the equation (1):

where:

• s is the surface roughness (in length units)
• δ is the skin depth, which is defined as (2):

  

  in which:

• f is the frequency in Hz
• μ_r is the relative permeability of the conductor
• μ₀ is the permeability of free space

  

• σ is the electrical conductivity in Siemens/m

Once the Groiss surface roughness factor is determined, the rough surface impedance (Z_rough ) is determined as (3):

Limitations of the Groiss Model:

The Groiss surface roughness model is non-causal and is therefore limited to the frequency-domain (not suitable for time-domain computations). The Groiss roughness factor is bound by the following limits:

0 < fact_R ≤ 2

Therefore, it is suitable for relatively highly polished conductors and not suitable for the much rougher copper conducting traces that are typical of manufactured PCBs.

For roughness factors greater than 2 and for time-domain computations, use the Huray Surface Roughness Model.

References:

1. S. Groiss, I. Bardi, O.Biro, K. Preis and K.R. Richter, Graz University of Technology, Kopemikusgasse 24, A-8010 Graz, Austria, "Parameters of Lossy Cavity Resonators Calculated by the Finite Element Method", IEEE TRANSACTIONS ON MAGNETICS, VOL 32. NO 3, MAY 1996