Skin, Eddy, and Proximity…All Summed Up

The simple case of a conductor carrying current can be used to demonstrate and compute the adverse effects that all circuits are exposed to known as skin, eddy, and proximity effects. Initially, to simplify and clarify the discussion, this current carrying wire will not be in close proximity to the conductor carrying the return current or in close proximity to any other current carrying conductor. As we will see later in this discussion, the close proximity of other current carrying conductors does alter the effects to be discussed.

From Electromagnetic Wave theory, a conductor that carries current will generate both internal and external electromagnetic fields. The primary field energy produced will be focused outside the conductor because all time-varying fields attenuate rapidly within a good conductor. A conductor carrying DC current or low frequency AC current will generate a field external to the conductor that is radially symmetrical. This symmetrical field forces current within the conductor to distribute itself uniformly throughout the conductor. With uniform current flow, the effects of skin and eddy are negligible. That is why skin effect and the effects of eddy currents are considered high frequency phenomena’s.

At frequencies above 50KHz, the current inside the conductor changes direction rapidly. This rapid current change causes rapid flux changes within the conductor. Flux change (df/dt) induces a voltage loop (“Eddy”) close to the surface of the conductor. The induced voltage forces a current to flow coincident with the voltage. This current is known as eddy current. This current loop will be additive to current flowing near the surface and oppose current in the center of the conductor. The result is that the current density increases at the surface and decreases toward the center of the conductor. We find an exponential decrease in the conductor current density and electric field intensity with penetration into the conductor.

Skin depth is defined as the distance from the surface to where the current density is1/e times the surface current density. In other words, one skin depth is where the current density has decreased by approximately 38% of the surface current density. To calculate the skin depth of a conductor, one can use the following expression:

where r = 2.3 X 10^-6 W-cm for 100C copper

and m = 4*p X 10^-7

Proximity, or the closeness of other current carrying conductors to the one in study, will effect the ability of that conductor to carry current. The fields of the conductors in close proximity will add and subtract depending on their direction. In circuit components such as circuit boards and magnetic devices, special attention has to be given to these effects minimizing their high frequency adverse effects. When two conductors are brought into close proximity, their external electromagnetic fields may add or subtract. The important thing to note is that high frequency current will concentrate within the wire where the fields are additive. Thus, like skin effect, proximity effect limits the effective capability of a wire to conduct high frequency currents.