Surface Roughness for SBR+

HFSS SBR+ provides the option to simulate the scattering impact of surface roughness applied to object boundaries. The surface roughness model includes two additional physical effects into the SBR+ simulation: coherent field attenuation and diffuse incoherent scattering. These effects are wavelength dependent. As the surface height deviations become large relative to the simulation wavelength, coherent specular reflections are converted into a diffuse response that has an incoherent (random) phase.

The SBR+ model characterizes surface roughness as a random process which is defined by two parameters: 1) the standard deviation of surface heights (H), and 2) a surface correlation length (L).

The surface height deviations are modeled as a Gaussian distribution with mean zero and standard deviation H. The surface correlation (i.e., its auto-correlation function) is also assumed to follow a Gaussian distribution with standard deviation . The correlation length L may be thought of as the average lateral distance between neighboring peaks on the surface.

For user inputs, the correlation length is replaced with a dimensionless parameter called roughness, which is defined as R = H / L. A roughness value of 0 produces a flat surface. The surface roughness increases with R and has typical values in the range [0.,0.5]. As the figure illustrates, the parameter R provides an intuitive measure of roughness that is independent of the magnitude of the height fluctuations (H).

Figure: Explicit rough surfaces with different roughness values R and height standard deviation H=1mm.

Prerequisites

• The feature is for SBR+ Solution Setups with Fast Frequency Looping (FFL) enabled in the SBR+ Solution Setup Options. If FFL is not enabled, an error message is issued to the Message window.
  
• The roughness model may only be applied to non-penetrable surface boundaries: Perfect E, Perfect H, Layered Impedance (one-sided), Impedance Boundary, and Finite Conductivity.
  
• The SBR+ rough surface model requires GPU acceleration to initialize the model. If this criteria is not met, an error message is issued during SBR+ pre-processing. An HPC license is not required to enable the model.

Setting up an SBR+ Simulation with Surface Roughness

1. Create an HFSS design and set the Solution type to SBR+.
2. Add geometry objects.
3. Assign object boundaries. For the Finite Conductivity Boundary, Impedance Boundary, Perfect E Boundary and Perfect H Boundaries, you can set the SBR+ Rough Surface properties as shown. Typical values for rough asphalt are H=1mm for height deviation, with a roughness of R=0.2 so the corrolation length L = 5mm.
   
   For the Layered Impedance Boundary, select the Layers tab and select One sided and edit the properties under the “SBR+ Rough Surface for Top Layer” panel.
   
   
4. The “SBR+ Rough Surface” properties can also be edited after creating the boundary by selecting the boundary in the project tree and editing values in the property window.
5. Add an excitation, such as Parametric Antenna under 3D components.
6. In the “Options” tab of the “SBR+ Solution Setup” dialog box, select “Enable Fast Frequency Looping”.
7. Run validation
8. Run simulation