Skin Depth
How deep current actually flows in a conductor at frequency.
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The engineering
AC current crowds toward the surface — 66 µm deep in copper at 1 MHz, 2 µm at 1 GHz. Past a few skin depths the metal in the middle is dead weight, which is why RF conductors are plated tubes and Litz wire exists.
Consequence: surface finish and plating decide RF loss. Silver-plating a brass cavity isn't decoration.
Where this math comes from
Horace Lamb derived the effect for spheres in 1883; Oliver Heaviside generalized it to conductors of practical shape in 1885 and named the crowding. Kelvin's 1887 work brought it to telegraph and power engineering, where it promptly complicated every large-conductor design.
The formula turned constructive at radio frequencies: if current only uses the skin, build conductors that are all skin — hence hollow waveguides, plated coatings, and stranded Litz windings.
- 1883Horace LambSkin effect derived for spherical conductors.
- 1885Oliver HeavisideGeneral conductor case; the effect named and tamed.
- 1887Lord KelvinAC resistance of practical conductors quantified.
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