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Rule of thumb: Identifying skin depth of copper

21 Jan 2014  | Eric Bogatin

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This rule of thumb estimates the effective current distribution in a conductor at high frequency:

Skin depth = 2 microns at 1GHz and scales with sqrt(f)

At DC, current flows uniformly throughout a conductor. However, this is not the case when AC current flows. The redistribution of current in the signal and return path is usually referred to as the skin depth effect and associated proximity effect. These are really one and the same effect.

The figure shows a simulation of the current density in the signal and return paths of a microstrip transmission line illustrating the two behaviours: current moves to the outer surface in each conductor, and signal and return currents move closer together.

Figure 1: Current density in a microstrip at 100MHz. Blue means no current, red means a lot of current. Simulated with ANSYS SI2D.

Sometimes, the words "skin depth" refer to the current re-distribution towards the outer surface of a conductor and the "proximity effect" refers to the re-distribution of signal and return currents closer to each other. It's the combination of these two effects that give rise to the specific current distribution. These effects have the same origin and should not be considered two separate effects.

The origin of this current re-distribution can be thought of in two ways. In the fields view of the world, the changing AC current in the wire produces a changing magnetic field which induces a changing electric field which suppresses some of the currents in the centre of each conductor, and in the other conductor. In the circuits approximation of the world, the current re-distributes to reduce the loop inductance. This translates to having the current spread out as much as possible in each conductor to reduce the self inductance and having the signal and return currents move as close together as possible to increase their mutual inductance.

Other than in infinitely wide or coaxial or cylindrical shaped conductors, it is really difficult to calculate the current distribution in conductors with pencil and paper.

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