What is the relationship between the DC resistance of a wire or copper trace and...?

Question

...the resistance due to the skin effect?

There are formulas to calculate both, but I don't know how the skin effect resistance works at low frequencies where the resistance due to the skin effect is less than the DC resistance. Do they add? Rdc + Rac? Is the AC resistance ever less than the DC resistance?

Answer 1

The skin effect says that the higher the frequency, the closer to the surface of the wire the current stays.

Since the effective resistance is a function of the cross-sectional area of the wire or trace, if the signal is too high a frequency to make full use of the cross-sectional area because some of it is too deep below the surface, then the signal will see a higher resistance.

http://en.wikipedia.org/wiki/Skin_effect

So a given wire or trace will offer different resistance to signals of different frequencies.

If when you say "the resistance due to the skin effect is less than the DC resistance", you mean the additional resistance due to not using the full cross-section, then yes, you have to add it to the DC resistance.

If when you say "the resistance due to the skin effect" and mean the total resistance, then it will never be lower than the DC resistance under normal circumstances.

So I think you mean the former and they add, but only you can know for sure.