Digital Circuit Boards: Mach 1 GHz

4.11 Skin Effect

Skin effect is usually discussed in terms of sine waves. When a conductor carries a sinusoidal current, the current is associated with a changing magnetic field. This changing magnetic field generates an emf that opposes the very current creating the field. The result is that a changing current tends to flow near the surface of a conductor. Because the inner copper has limited current flow, the conductor resistance appears to rise as a function of frequency. This rise in resistance with frequency is in addition to the reactance term that must be considered for an isolated conductor.

The equations for skin effect are often derived by applying Maxwell's equations to sinusoidal plane waves reflecting off of an infinite conducting plane. The depth where the field is attenuated by the factor 1/e is called a skin depth. This depth d is given by

4.2

where μ is the permeability of free space, σ is conductivity of copper, and f is the frequency in hertz. For copper at 1 MHz, the skin depth is 0.066 mm. At this depth, the field strength is reduced to 37% of the value at the surface. At double this depth, the field strength is reduced another 37% to 13% of its surface value. Skin depth is inversely proportional to the square root of frequency. At 100 MHz one skin depth in copper is 0.0066 mm. There is field at the center of the conductor, but it is attenuated. Field strength ...