Surface Roughness Modeling
Surface roughness plays an important role in accurately modeling radio frequency components (RFC), such as resonators and signal integrity projects (e.g., microstrips, printed circuit boards (PCBs)). The increase of the surface resistance due to surface roughness results in lower quality factor (Q) in resonators and higher insertion losses for microstrips and PCBs. The scale of the roughness is different in the different application areas so different surface roughness models are used. The common theme in the different models is that an effective frequency dependent conductivity is defined depending on the type and magnitude of the roughness, which shows the increase of the surface resistance compared to the smooth surface resistance.
For HFSS and HFSS 3D Layout designs, Groiss [6] or Huray [2] surface roughness models may be employed, the latter being a complex-value-based causal modification of the original real-value-based model. For SIwave and 2D Xtractor designs, the original Hammerstad-Jensen [4] or modified Huray [2] model may be employed.
Impedance at a rough surface is higher than the impedance at a smooth surface by a factor factR as shown in the general equation below:
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(13) |
where Zrough is the impedance at the rough surface and Zsmooth is the impedance at the smooth surface.
For the Groiss model, the surface roughness factor is given by the equation:
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(14) |
where d is the skin depth and s is the surface roughness.
The Groiss surface roughness model is not causal, and therefore, it is only suitable for frequency-domain computations, not for the time-domain.
Additionally, you can see, from equation (14), that the maximal roughness factor is 2. So this model is only applicable to RFC problems when the surfaces are highly polished to avoid lower Q. A surface roughness model of higher losses is necessary to model the fabrication effects in PCBs, where the roughness of the deposited metal is considerably higher.
The alternative modified Huray [2] surface roughness model, available in the Ansys Electronics Desktop software, is a complex-value-based causal model that is suitable for both frequency-domain and time-domain computations. It also overcomes the factor of 2 limitation of the Groiss model, as it supports rougher surfaces with factors greater than 2:
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Refer to the Technical Note: Huray Surface Roughness Model for the equations and definitions that are applicable to this model. The Huray roughness factor adjusts the surface impedance in the same manner as shown in equation (13) except that the roughness factor variable is referred to as Hc instead of factR. |
(15) |
All SIBCs depend on the material conductivity too, because the skin depth varies with conductivity.
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