Skin Depth and High-Frequency Current Distribution

Skin effect is the tendency of alternating current to crowd near the surface of a conductor as frequency increases. At DC, current density is approximately uniform through the cross section of a round wire or PCB trace. At high frequency, the changing magnetic field induces internal fields that oppose current flow in the center of the conductor. The result is an exponential current-density profile, with most current flowing within a shallow layer near the surface. The characteristic depth of that layer is called skin depth.

For a good conductor, skin depth is calculated as delta = sqrt(2 / (omega x mu x sigma)), where omega is 2πf, mu is magnetic permeability, and sigma is conductivity. Higher frequency reduces skin depth. Higher conductivity also reduces skin depth because the induced opposing currents are stronger. Higher permeability reduces skin depth as well, which is why magnetic materials behave very differently from copper or aluminum at AC.

This calculator uses common conductivities for copper, aluminum, silver, and gold and allows relative permeability to be entered separately. Nonmagnetic conductors are usually close to mu-r = 1. Ferromagnetic materials can have much higher effective permeability, although the value may vary strongly with frequency, field strength, alloy, heat treatment, and geometry. For precision magnetic-material work, manufacturer data is required.

Manual Calculation Steps

Consider copper at 100 MHz. Copper conductivity is approximately 5.8 x 10^7 S/m. The angular frequency is 2π x 100,000,000 rad/s. Free-space permeability is 4π x 10^-7 H/m, and copper relative permeability is close to 1. Substituting those values gives a skin depth of roughly 6.6 micrometers. That means a large fraction of the RF current flows within only a few micrometers of the surface, even though standard 1 oz PCB copper is about 35 micrometers thick.

At 1 MHz, the same calculation gives a skin depth about ten times larger because skin depth scales with the inverse square root of frequency. This square-root behavior matters. Increasing frequency by 100 times reduces skin depth by 10 times, not 100 times. That is why skin effect gradually becomes important across switching supplies, RF circuits, fast digital edges, and high-current AC conductors rather than appearing as a sudden threshold.

PCB and Wire Design Implications

Skin effect increases AC resistance because less conductor area effectively carries current. In PCB traces, this interacts with copper thickness, trace width, surface roughness, solder plating, return-current path, and dielectric loss. At RF, current also crowds according to proximity effect, where neighboring conductors and return planes shape the magnetic field. A simple skin-depth number does not fully describe controlled-impedance loss, but it is a useful first estimate of whether conductor thickness is being used effectively.

In magnetics, skin depth influences transformer windings, inductors, and high-current switching converters. Litz wire uses many individually insulated strands so each strand has a small diameter relative to skin depth. Foil windings and planar magnetics must be checked for AC loss because wide conductors can suffer severe proximity-effect losses. A winding that looks efficient at DC can run hot at switching frequency if AC current distribution is ignored.

Surface Resistance and Loss

The calculator also reports an approximate surface resistance using 1 / (sigma x delta). Surface resistance is a useful RF concept because once a conductor is many skin depths thick, making it thicker provides limited benefit for high-frequency current on that surface. Plating quality and surface condition can matter because current is concentrated near the exterior. Silver plating improves RF conductivity, while rough copper can increase loss in high-speed PCB traces.

Engineers use skin-depth estimates in RF feed lines, antennas, PCB impedance design, switch-mode power supplies, bus bars, inductors, transformers, shielding, and grounding structures. The formula gives a physics-based starting point. A production design should also consider temperature, surface roughness, plating, conductor geometry, return-current path, dielectric loss, and measured performance across the actual frequency spectrum.

Edge rate is another practical reason to use this calculation outside traditional RF work. A digital signal with a fast rise time contains harmonic energy far above its clock frequency, so current distribution can be shaped by skin effect even when the fundamental toggle rate looks modest. Power converters have the same issue because rectangular switching waveforms contain high-frequency components. When estimating loss, use the frequency content that actually carries current, not only the repetition rate printed on the schematic.