Updated October 29, 2012: ADS now includes a measurement-hardened surface roughness model called multi-level hemisphere. Please see my later posting Conductor Surface Roughness. Thanks!

In serial links, you hit the “skin effect crisis” when high frequency components of the EM waves in the dielectric induce eddy currents in the metal traces and can’t penetrate the whole thickness of conductor. The effective cross section is thus reduced, and the resistance at those high frequencies goes up compared to lower frequency components. Here is an order-of-magnitude calculator that illustrates the effect in terms of relative attenuation at DC and the high frequency end of the spectrum.

The above JavaScript assumes:

Copper traces (16.78×10^{-9}Ω.m resisitivity) in a differential pair, with equal length of positive and negative polarity, driving a 100 Ω load.

The resistance given assumes the round trip (i.e. double the resistance R_{trace} of one of the pair of traces).

Attenuation is that of a voltage divider: 20*log_{10}(R_{load}/(2*R_{trace}+R_{load})).

f_{knee} is 0.5/rise time.

The width is greater than the skin depth (i.e. fringing effects are ignored).

If the skin depth is about equal to the thickness, this simple calculation won’t be very accurate.

At f_{knee} and for smooth surfaces, the current flows on the upper and lower skin of the trace i.e. the effective cross section is twice the skin depth times width.

The empirical roughness model is from Microstrip Handbook, E. O. Hammerstad, Edited by F. Bekkadal, ELAB Report No. STF44 A74169, University of Trondheim, Norway, 1975. Hammerstad depth is the actual skin depth divided by a unitless loss factor = (1 + (2/π) arctan(0.7 * variance / (skin depth)^{2}). (Variance is the square of the RMS roughness.) The loss factor varies between 1 (perfectly smooth) and approaches 2 in the limit of roughness >> skin depth. For one rough surface (the solution side) and at f_{knee}, the current flows in a effective cross section of (Hammerstad depth plus skin depth) times width. Assumes RMS roughness << thickness. Eric Bogatin has an article on smooth copper foils for extra low loss. Eric pointed out to me an error in an earlier version: the roughness is one-sided, not two-sided. The drum side is assumed to be smooth. Only the solution side that is rough.

Its true that the drum side is assumed to be smooth but it does have some amount of roughness and would be good to include. I had measured data of 0.066mils on the drum side and 0.465mil on solution side. I was reading about the Hurray method, are you planning to add that as a calculator.
Thanks for the good work.
Bhavesh

Tim Coyle// Jul 25, 2008 at 9:38 amHi Colin,

Thanks for the cool skin effect calculator! I think a lot of engineers are going to need this for their PCIe Gen2 designs.

By the way, I like your new blog, keep up the good work!

woz2// Jul 26, 2008 at 9:18 pmThanks, Tim. Keep up the good work with XrossTalk Magazine. I enjoyed your article on the emerging IBIS AMI project http://www.xrosstalkmag.com/images/magazine/serdes_modeling_with_ibis_ami.pdf

Bhavesh// Oct 19, 2009 at 10:42 amIts true that the drum side is assumed to be smooth but it does have some amount of roughness and would be good to include. I had measured data of 0.066mils on the drum side and 0.465mil on solution side. I was reading about the Hurray method, are you planning to add that as a calculator.

Thanks for the good work.

Bhavesh

Top Ten Postings// Jun 23, 2010 at 3:39 am[…] Skin Effect Crisis […]