Skin Effect

RF/Photonics Lab
Jared Alves
November 2019

Skin Effect

                The skin effect is an important characteristic of alternating current within conductors. With direct current, charges are distributed evenly when flowing through a conductor. However, due to the Skin Effect as the frequency of the conduction current is increased, the charges distribute in greater quantities towards the surface of the conductor. In other words, the current density (J) decreases with greater depth in the conductor.   As shown, the current density is per area.

skin1

The skin depth of the conductor is the length from the surface of the conductor inward in which the majority of the charge is contained at frequencies higher than DC.

skin2

As shown in the equation above, skin depth is inversely proportional to frequency so at higher frequency values, the effective resistance of the conductor increases which reduces the cross-sectional area, as shown below.

skin3

The figure demonstrates that the conductor becomes more “hollow” at higher frequencies as the electric charges avoids traveling through the center. This is because the back EMF is strongest towards the center of the conductor. Maxwell’s equations explain that magnetic field strength is proportional to current and therefore as current intensity changes, so does magnetic field strength. The changing magnetic field creates an electric field opposing this change in intensity which causes the counter EMF effect. This creates an almost “Faraday cage” effect with the electrons at the center of conductor as the electric field cannot penetrate as deep into the conductor with increasing frequency.

skin4

The skin depth is technically defined as the length from the surface to the inside of a conductor in which J (current density) decays to 1/e of Js (current density at the surface). The imaginary part of the above equation shows that for each skin depth of penetration, the current density phase is delayed by 1 radian.