How does surface roughness on a PCB trace affect insertion loss at millimeter wave frequencies?
Roughness and mmWave Loss
At microwave and millimeter wave frequencies, the skin depth becomes comparable to or smaller than the copper surface roughness features. At 10 GHz, the skin depth in copper is about 0.66 μm. Standard electrodeposited (ED) copper has RMS roughness of 1-6 μm, meaning the surface features are larger than the skin depth. The RF current flowing in this thin skin layer must follow the rough surface topology, increasing the effective path length and resistance.
Several models quantify the roughness effect. The Hammerstad-Bekkadal model uses a correction factor: Kcorr = 1 + (2/π)·arctan(1.4·(Rq/δ)²), where Rq is RMS roughness and δ is skin depth. For Rq = 2 μm at 30 GHz (δ = 0.38 μm): Kcorr = 1.94, nearly doubling the conductor loss. The Huray model provides better accuracy by modeling the rough surface as a field of hemispherical boss features.
For millimeter wave designs, substrate and copper selection is critical. Rogers RT/duroid 5880 with rolled copper (Rq < 0.5 μm) provides the lowest loss. Megtron 6 and 7 offer good electrical performance with standard PCB processing. FR4 with standard ED copper is entirely impractical above 20 GHz due to excessive conductor and dielectric loss.
Frequently Asked Questions
Can I specify copper roughness to my PCB vendor?
Yes. Request low-profile (LP), very-low-profile (VLP), or hyper-low-profile (HLP) copper foil. Specify the maximum RMS roughness (e.g., Rq < 1 μm). Not all PCB vendors stock low-roughness copper, and it costs more. Plan this into the board quotation.
Does roughness only affect the trace side?
No. Roughness on both sides of the conductor contributes to loss. The side facing the dielectric (bonding side) is typically rougher than the polished side (air side) because roughness improves adhesion to the laminate. For microstrip, the trace-substrate interface roughness dominates.
What about gold plating?
Gold plating adds a thin (0.5-5 μm) layer over the copper. If the gold fills in the surface roughness features, it can slightly reduce the effective roughness. However, gold has higher resistivity than copper, so thick gold plating increases loss. ENIG (electroless nickel immersion gold) adds both nickel (magnetic, lossy) and gold, significantly increasing loss at mmWave frequencies.