Huray Surface Roughness Model

Surface roughness can increase conductor power losses by more than two times the loss associated with smooth conductors. In Ansys Electronics Desktop, a modification of the standard real-valued Huray surface roughness model is implemented to accurately account for these losses in both the frequency and time domains.

This modification fixes a causality problem with the original Huray model by adding some frequency-dependent reactance to the roughness-enhanced surface impedance. The purpose is to provide a complex-valued causal analytic model that exactly matches the loss results of the original model but is also suitable for time domain computations.

The original Huray model was limited to calculations in the frequency domain and did not account for the effects of roughness on the phase of the transmitted signal. These limitations have been eliminated. The enhanced causal model not only provides accurate broadband modeling of the losses in very rough copper foils (typically used in PCB manufacturing) but also accurately predicts increased phase delay due to the surface roughness.

Essentially, the smooth surface impedance (Z_smooth) is increased by a complex “Huray” factor (H_c), a function of frequency, given by the following equation (1):

where:

• ω is the frequency in radians/second
• ω₀ is a corner frequency represented by the equation (2):

  

• K is a derived constant used to simplify the equation (3):

  

  in which:

  • SR is the Hall-Huray surface ratio:

    

  • a is the radius of a spherical nodule
  • μ_r is the relative permeability of the conductor
  • μ₀ is the permeability of free space

    

  • σ is the electrical conductivity in Siemens/m
  • N is the number of nodules
  • A_f is a unit cell area
  Note:

  aandSRare the two parameters you must enter in theSurface Roughness Modeldialog box when you select the Hurayoption:

  

For more information about this complex causal Huray model (its necessity, background, derivation, proof of accuracy, and consistency with the original real-valued model), see Reference 6 below.