# Huray Surface Roughness Modeling Approaches

### Key Takeaways

• The Huray surface roughness model is a physics-based roughness model that is useful in calculating increased losses due to surface roughness.

• Huray surface roughness models are effective in determining analytical solutions for the fields surrounding a hemispherical ball attached to a metal surface.

• There are two modeling approaches in the Huray surface roughness model: the Huray snowball surface roughness model and the Huray cannonball surface roughness model.

In printed circuit boards, conductor surface roughness incurs losses in high-speed circuit designs. Understanding the smoothness of the conductor helps engineers calculate losses in PCB interconnects. Several models—such as the Hammerstad and Jensen model, hexagonal close-packing of equal spheres model, and the Huray surface roughness model—help engineers predict signal degradation effects due to conductor surface roughness. In this article, we will explore the skin effect on PCB interconnect losses and the Huray surface roughness model in further detail.

## The Skin Effect

In PCB manufacturing, copper conductors are used as interconnects. The copper used in the PCB industry is usually one of two types: rolled-annealed (RA) copper or electro-deposited (ED) copper. The surface roughness of ED copper conductors is greater than RA copper. However, due to its low-cost, ED copper is extensively used in PCB interconnects.

PCB interconnects or conductors are subjected to losses at high frequency and add to the total losses in the PCB interconnect, along with dielectric losses. The skin effect in a conductor redistributes the current towards the outer surface and increases the effective resistance of the conductor, thereby increasing the conductor loss. The skin effect in a PCB conductor is frequency-dependent.

The impact of the skin effect increases in proportion to the square root of the frequency. The skin effect in PCB interconnects is influenced by the conductor surface roughness. In perfectly smooth PCB interconnects, the skin effect is marginal. With the increase in frequency and conductor surface roughness, the skin effect on a PCB interconnect worsens.

## Conductor Surface Roughness

The surface roughness of a conductor is an important parameter to be considered while calculating the actual conductor losses. The tooth-like projections on the conductor surface increase the surface area, increasing the conductor losses.

The surface roughness of PCB interconnects adversely influences the signal integrity performance of transmission lines. The conductor surface roughness exacerbates the bit error in data channels on PCBs and leads to severe signal integrity issues in the PCB interconnects. The increase in the conductor losses due to surface roughness causes attenuation and dispersion in the transmitted signal. The surface roughness is crucial in increasing the signal losses and degradation in PCB interconnects.

Neglecting conductor surface roughness can cause incorrect conductor loss calculation in PCBs. It is necessary to model the surface roughness of the PCB interconnects to obtain the roughness value of the surface. Surface roughness models help in calculating the increased conductor losses and also aid in differentiating the loss variations with the change in smoothness of the conductor surface.

## The Huray Surface Roughness Model

The Huray surface roughness model is a physics-based roughness model that is useful in calculating the increased losses due to surface roughness. This model is effective in determining analytical solutions for the fields surrounding a hemispherical ball attached to a metal surface. The Huray surface model applies frequency-dependent correction on the surface impedance of smooth conductors to calculate the losses due to rough-surfaced conductors.

There are two modeling approaches in the Huray surface roughness model: the Huray snowball surface roughness model and the Huray cannonball surface roughness model.

### Huray Snowball Surface Roughness Model

The Huray snowball surface roughness model is based on the non-uniform distribution of spherical shapes that resemble snowballs. The snowballs are arranged to form pyramidal geometry. The superposition of sphere losses gives the total losses in the structure, and electromagnetic wave analysis is applied to the model for calculating the total losses. The Huray snowball model analytically solves the problem of accurately estimating the roughness correction factor, which is a function of frequency. The Huray snowball surface roughness model is impractical when the data available is only the roughness parameters from the manufacturer’s datasheets.

### Huray Cannonball Surface Roughness Model

The Huray snowball surface roughness modeling approach requires parameters–the roughness factor and ball radius–to define the surface roughness accurately. If these parameters are not available, engineers can use Huray cannonball surface roughness modeling. This model easily estimates the sphere radius and flat base area parameters from the roughness parameters given in the manufacturer’s datasheet. The Huray cannonball surface roughness model can predict conductor losses without any information about the shape of the conductor.

## Using Field Solvers to Compute the Effects of Surface Roughness

Huray surface roughness models are instrumental in describing the attenuation and dispersion of transmitted signals over PCB interconnects. The accuracy of these models is much better than earlier modeling approaches. Cadence software provides full-wave and quasi-static solver technology for PCBs that is capable of accurately analyzing complex 3D structures. With Cadence field solvers, you can compute the effects of surface roughness by defining the type of model, such as the Hammerstad model, exponential model, or Huray model.

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