Skin Effect:

[Styx]

Consider a single conductor shown in Fig1a, which is carrying a time-varying current: i(t). This current generates the magnetic field shown in fig1a, and they in turn generate the eddy currents illustrated in fig1b.

These eddy currents flow in the opposite direction to the applied current i(t) in the core of the wire and thus tend to shield the interior of the conductor from the applied current and the resultant magnetic field.

 

[Styx]

As a result the total current density is largest at the surface of the conductor as shown in fig1c.

Table 1 shows the skin depth in copper at several different frequencies at a temperature of 100C.

Freq: 50hz		5khz			20khz		500khz
δ	10.6mm		1.06mm		0.53mm		0.106mm

Table 1


If the cross-sectional dimensions of the conductor used in the windings are significantly larger then the skin depth, most of the current carried by the conductor will be constricted to a relatively thin layer at the surface approximately one skin depth in thickness as illustrated in fig1c. The net effect of this is that the effective resistance of the conductor will be far larger then the DC resistance because the effective cross-sectional area for current flow is small compared to the geometric cross section of the conductor. This will cause the winding losses to be much larger then if it were a DC current.

The solution to this problem is to use conductors with a cross-sectional dimension on the order of the skin depth in size. IF d is the diameter of a round conductor or the thickness of a rectangular conductor, calculations have shown that if d<2xδ the consequences of the skin effect can be neglected.