How does conductor surface roughness affect RF loss and what models are used to predict it?
Surface Roughness Loss Models
All roughness correction models attempt to answer the same question: given a surface with known roughness statistics, how much additional loss does the roughness cause compared to a perfectly smooth conductor? The answer depends on the ratio of roughness to skin depth (Rq/δ), which increases with frequency as δ decreases.
| Parameter | Semi-Rigid | Conformable | Flexible |
|---|---|---|---|
| Loss (dB/m at 10 GHz) | 0.8-2.5 | 1.0-3.0 | 1.5-5.0 |
| Phase Stability | Excellent | Good | Fair |
| Bend Radius | Fixed after forming | Hand-formable | Continuous flex OK |
| Shielding (dB) | >120 | >90 | >60-90 |
| Cost (relative) | 2-5x | 1.5-3x | 1x |
Cable Selection Criteria
The Hammerstad-Bekkadal model (1980) uses a simple arctangent function of (Rq/δ)². It predicts that the roughness correction factor saturates at Kcorr = 2 (the loss doubles) for Rq >> δ. This model is conservative: it underestimates the loss at very high roughness/frequency ratios because it does not account for the complex surface topology.
- Performance verification: confirm specifications against the application requirements before finalizing the design
- Environmental factors: temperature range, humidity, and vibration affect long-term reliability and parameter drift
- Cost vs. performance: evaluate whether the application demands premium components or standard commercial grades
- Interface compatibility: verify impedance, connector type, and mechanical form factor match the system architecture
- Margin allocation: include sufficient design margin to account for manufacturing tolerances and aging effects
Loss and Phase Stability
The Huray model (2010) represents the rough surface as a dense field of hemispherical boss features with radius and density determined from surface profilometry measurements. This model more accurately captures the electromagnetic field interaction with the rough surface and predicts loss that can exceed 2× the smooth-conductor value (Kcorr > 2) at very high frequencies. The Huray model is the current standard for mmWave circuit simulation in commercial EDA tools.
Frequently Asked Questions
Which model should I use?
Below 10 GHz: Hammerstad is adequate for design-level accuracy. 10-40 GHz: either Hammerstad or Huray; verify against measurements. Above 40 GHz: Huray is recommended because the Hammerstad saturation limit (Kcorr = 2) underestimates actual loss.
How do I get the roughness parameters?
The copper foil manufacturer provides RMS roughness (Rq) and sometimes the profile parameters needed for the Huray model (ball radius and density). For a specific PCB fabrication, request roughness measurements from the PCB vendor using a profilometer. Typical values: standard ED copper Rq = 3-6 μm, VLP Rq = 0.5-1 μm, HLP Rq = 0.1-0.3 μm.
Does roughness affect both sides of the trace?
Yes. The bottom (substrate-facing) side of the copper typically has higher roughness than the top (plated) side because the roughness promotes adhesion to the laminate. Both sides contribute to loss. For microstrip, the bottom (substrate side) roughness dominates because more field energy is concentrated there.