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Rule of thumb: Identifying skin depth of copper

21 Jan 2014  | Eric Bogatin

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Planar geometries like stripline or microstrip require a 2D field solver to calculate their current distribution at a specific frequency. But, it can be roughly approximated. In general, the current density will drop off exponentially into the surface of the conductor. The depth at which the current density has dropped by 1/e is called the skin depth.

If the geometrical thickness of the conductor is large compared to the skin depth, the conductor resistance is equivalent to having all the current uniformly distributed in a thickness equal to the skin depth. This makes the skin depth a useful figure of merit to describe the effective thickness of the current distribution.

For the case of wide and thick conductors, the skin depth can be analytically calculated as

For the special case of Copper, the skin depth is

This is a very powerful rule of thumb. The skin depth for copper is about 2 microns at 1GHz and scales inversely with the sqrt(f).

For example, if the skin depth is thinner than the rms roughness of the copper, most of the current will be traveling in the rough part of the copper, so the series resistance, and conductor loss, will increase more rapidly than the sqrt(f). A typical rms thickness is about 2 microns. Surface roughness will increase the series resistance of copper traces above 1GHz.

Try these two simple examples:

1. At what frequency is the skin depth about the geometrical thickness of ½ oz copper, 17 microns? Above this frequency, the resistance of a trace will be frequency dependent.

2. At 100Hz, close to the line frequency, what is the skin depth of copper?

About the author
Eric Bogatin is Signal Integrity Evangelist at Teledyne LeCroy.

To download the PDF version of this article, click here.

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