L
Admin
Above a few GHz, a perfectly smooth copper model will underestimate insertion loss on almost any real PCB. The cause is the copper foil roughness, and choosing the wrong roughness model can be as large an error as using the wrong laminate Dk.
1. Why roughness matters
Skin depth in copper is about 2.1 um at 1 GHz and about 0.66 um at 10 GHz. Standard electrodeposited foil has a tooth profile of several micrometres. Once the skin depth is comparable to or smaller than the roughness, current follows the longer surface path and conductor loss rises.
2. Common models
- Hammerstad (and Hammerstad-Jensen): a correction factor based on RMS roughness that saturates at 2. It works reasonably for mildly rough foils at lower frequencies, but underestimates loss for rough foils at high frequency because real loss keeps rising past the factor-of-two cap.
- Groiss: a smoother curve, also saturating, often closer to measurement at moderate frequency.
- Huray (snowball or cannonball model): represents the surface as stacked spheres on a flat tile. It does not saturate in the same way and usually tracks measured loss of rough foils into tens of GHz, provided the sphere radius and density are fitted.
3. Foil grades and numbers to ask for
Laminate and foil suppliers describe grades such as standard ED, RTF (reverse-treated), VLP and HVLP. Ask for the roughness value (Rz or Rq) for both the treated side bonded to the dielectric and the drum side. In multilayer boards, the inner-layer oxide or bonding treatment on the "smooth" side also adds roughness, so the two sides of a stripline trace are not identical.
4. Roughness changes delay too
Rough copper also slows the wave slightly: fitted models often show a higher "effective Dk" than the dielectric alone, because the rough surface stores more magnetic energy. If you fit Dk from measured delay with a smooth-copper model, you will fold roughness into Dk and then double count it when you add a roughness model later. Fit loss and delay together.
5. A practical fitting flow
- Build two test lines of different length on the actual stack-up and measure them on a VNA.
- Extract per-unit-length loss and delay from the difference (this removes most of the connector and launch).
- Fix dielectric Dk and Df from the laminate data at the right frequency, then fit the roughness parameters to match loss. Iterate Dk only if delay still disagrees.
- Reuse the fitted parameters for every design on that stack-up and fab.
6. Sanity checks
- Compare the smooth and rough runs; if the difference at your top frequency is under a few percent, roughness is not your main problem.
- Make sure the solver applies roughness to the right faces (top, bottom, side walls).
Which roughness model has matched your measurements best on high-speed or mmWave boards, and did you see the Dk shift?
1. Why roughness matters
Skin depth in copper is about 2.1 um at 1 GHz and about 0.66 um at 10 GHz. Standard electrodeposited foil has a tooth profile of several micrometres. Once the skin depth is comparable to or smaller than the roughness, current follows the longer surface path and conductor loss rises.
2. Common models
- Hammerstad (and Hammerstad-Jensen): a correction factor based on RMS roughness that saturates at 2. It works reasonably for mildly rough foils at lower frequencies, but underestimates loss for rough foils at high frequency because real loss keeps rising past the factor-of-two cap.
- Groiss: a smoother curve, also saturating, often closer to measurement at moderate frequency.
- Huray (snowball or cannonball model): represents the surface as stacked spheres on a flat tile. It does not saturate in the same way and usually tracks measured loss of rough foils into tens of GHz, provided the sphere radius and density are fitted.
3. Foil grades and numbers to ask for
Laminate and foil suppliers describe grades such as standard ED, RTF (reverse-treated), VLP and HVLP. Ask for the roughness value (Rz or Rq) for both the treated side bonded to the dielectric and the drum side. In multilayer boards, the inner-layer oxide or bonding treatment on the "smooth" side also adds roughness, so the two sides of a stripline trace are not identical.
4. Roughness changes delay too
Rough copper also slows the wave slightly: fitted models often show a higher "effective Dk" than the dielectric alone, because the rough surface stores more magnetic energy. If you fit Dk from measured delay with a smooth-copper model, you will fold roughness into Dk and then double count it when you add a roughness model later. Fit loss and delay together.
5. A practical fitting flow
- Build two test lines of different length on the actual stack-up and measure them on a VNA.
- Extract per-unit-length loss and delay from the difference (this removes most of the connector and launch).
- Fix dielectric Dk and Df from the laminate data at the right frequency, then fit the roughness parameters to match loss. Iterate Dk only if delay still disagrees.
- Reuse the fitted parameters for every design on that stack-up and fab.
6. Sanity checks
- Compare the smooth and rough runs; if the difference at your top frequency is under a few percent, roughness is not your main problem.
- Make sure the solver applies roughness to the right faces (top, bottom, side walls).
Which roughness model has matched your measurements best on high-speed or mmWave boards, and did you see the Dk shift?