# `Skin Depth`

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Skin Depth is a measure of how closely electric current flows along the surface of a material. At d.c. (0 Hz or a constant voltage), electric current flows uniformly through a conductor. This means the current density is the same everywhere. However, at higher frequencies, the current prefers to flow along the surface, producing surface current.

The skin depth equation is given below:

 [1]

In Equation [1], the symbols are:

• f is the frequency of the current
• is the resistivity of the material (in Ohms/meter; this is the inverse of conductivity),
• is the permeability of the material (a measure of the magnetism)

Note that (=*)

The key point to note from Equation [1] is that skin depth decreases with higher frequency.

This means that electric current flows only on the surface of a conductive material at RF frequencies (>10 MHz). For instance, the skin depth of copper at the WIFI or Bluetooth frequency (2.4 GHz = 2.4*10^9) is about 1 micron (1 micrometer = 1/1000 mm). Note that we used the resistivity for copper of 1.68*10^-8 Ohm-meters.

To illustrate skin depth in a simple figure, below is a copper conductor with an electric current flowing through it. On the left, we have the current distribution for low frequencies (i.e. DC or 0 Hz) - the current flows uniformly through the wire's cross section. On the right, we have the current distribution for the RF (radio frequency) case (that is, for wires as small as 0.1mm in diamter and frequencies as low as 10 MHz. The right side shows that the electric current only flows along the surface, and the in the center of the wire no RF electric current flows:

Figure 1. Illustration of Skin Depth

The depth of the electric current into the wire can be found from Equation [1]: it is the skin depth.

In reality, the current density actually drops off exponentially from the surface, so that if we have a wire that begins at z=0, then current flowing in the y-direction (out of the screen as shown in Figure 2), then the current density (J) will decrease away from the surface exponentially per Equation [2]:

 [1]

In Equation [1], J_0 is the current density at the surface of the material. The current drop off with distance from the surface is further illustrated in Figure 2:

Figure 2. Current Decreasing With Distance From Surface

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