RF & High-Frequency Circuits

the skin effect

At DC, current flows evenly through the whole cross-section of a wire, using all the copper. As frequency rises, the current crowds toward the outer surface and abandons the centre, as if it were afraid of the middle. This is the skin effect. By the time you reach radio frequencies, current flows in only a thin shell near the surface, so the inside of a thick wire carries almost nothing and is, electrically, dead weight.

The mechanism is the wire's own magnetic field. Changing current creates a changing magnetic field inside the conductor, which induces little eddy currents that oppose the current in the centre and reinforce it at the edge. The depth of the conducting shell is the skin depth, and it shrinks as the square root of frequency. In copper the skin depth is about 66 micrometres at 1 MHz, about 2 micrometres at 1 GHz. Because the usable copper is a thin shell, the effective resistance rises with the square root of frequency, so a wire that is 1 ohm at DC can be several ohms at high frequency even though nothing physical about it changed.

The skin effect explains several real RF facts. It is why high-frequency conductors are often silver-plated, the current only uses the surface, so plating the surface with a better conductor helps while plating the core would be pointless. It is why RF coils are wound from many thin insulated strands (Litz wire) to give more surface, and why hollow tubing carries RF as well as solid bar. It is a major reason the Q of real inductors and the loss of cables get worse as frequency climbs. Honest caveat: the skin effect is not a small correction at RF, it can dominate a conductor's resistance, so DC resistance is a misleading guide to how a wire behaves at high frequency.

A copper wire 1 mm in radius has plenty of metal, but at 1 GHz the current only uses the outer ~2 micrometres. The effective cross-section is a thin ring, so the wire's AC resistance can be tens of times its DC value, which is why thick wire does not help much at RF.

At RF only a thin surface shell carries current, raising effective resistance.

Skin depth shrinks with the square root of frequency, so making a wire fatter barely helps at RF; surface area and surface conductivity (such as silver plating) are what matter. DC resistance badly underestimates high-frequency loss.

Also called
skin depth集膚深度趨膚效應