What Is Proximity Effect?

Proximity effect is the redistribution of alternating current within an electrical conductor caused by the time-varying magnetic field produced by a neighboring conductor. When two or more conductors carrying alternating current are placed in close proximity, the magnetic field of each conductor induces eddy currents in the others. These eddy currents add to or subtract from the primary current depending on their direction, pushing the net current density toward certain regions of the conductor's cross-section rather than allowing it to distribute uniformly. The result is a smaller effective current-carrying area and a higher apparent resistance than the same conductor would present under direct current.

Proximity effect is closely related to skin effect, which also concentrates alternating current toward the surface of a conductor, but the two phenomena have different origins. Skin effect is self-induced: the changing magnetic field of a conductor's own current drives eddy currents that oppose flow in the interior. Proximity effect is mutually induced, caused by the field of an adjacent conductor. Both effects increase with frequency, and in many practical designs they occur simultaneously and must be analyzed together.

Electromagnetic Mechanism

The mechanism follows directly from Faraday's law of induction. The alternating current in one conductor produces a time-varying magnetic flux that links the cross-section of a neighboring conductor. By Lenz's law, the induced eddy currents circulate in the direction that opposes the change in flux. In conductors carrying current in the same direction, proximity effect concentrates current on the faces farthest from each other. In conductors carrying current in opposite directions, as in the go-and-return conductors of a transmission line or transformer winding, the current crowds toward the facing surfaces. The magnitude of redistribution depends on conductor spacing, conductor diameter, frequency, and conductivity. The Dataforth technical reference on eddy current, skin, and proximity effects provides a quantitative treatment of how these factors combine to raise AC resistance in transformer windings.

Effect on AC Resistance

The practical consequence of proximity effect is a significant increase in the effective AC resistance of conductors at elevated frequencies. In transformer windings where multiple layers of wire are wound closely together, the combined action of skin and proximity effects can raise the winding resistance to ten times or more the DC value. This increased resistance translates directly into additional conduction losses and reduced efficiency. The Dowell method, developed in the 1960s, provides curves relating winding geometry and operating frequency to the AC-to-DC resistance ratio, and it remains the standard first-pass design tool for predicting proximity-effect losses in wound components. Research published in the journal Energies has examined proximity and skin effects in high-voltage segmented cable conductors, proposing insulation strategies to reduce the effect in underground transmission lines.

Mitigation in High-Frequency Design

Several design strategies reduce proximity effect losses. Litz wire, composed of many individually insulated strands twisted or woven together, subdivides the conductor into strands thin enough that skin and proximity effects are suppressed within each strand, restoring a more uniform current distribution. Interleaving primary and secondary windings in transformers reduces the magnetomotive force linking each layer, which lowers the induced eddy currents. Reducing the number of winding layers has a similar benefit. In power electronics and high-frequency magnetics, proximity effect analysis is an essential step in optimizing switched-mode power supply transformer designs, particularly as switching frequencies have risen above 100 kHz in modern converters.

Applications

Proximity effect analysis is relevant in a wide range of engineering contexts, including:

• High-frequency transformer and inductor design for switched-mode power supplies and resonant converters
• Underground power cable design, where closely spaced conductors in a cable bundle experience mutual induction
• Motor and generator winding design, particularly in high-speed machines with high-frequency harmonic content
• Bus bar design in power electronics modules, where wide parallel conductors carry large alternating currents
• Induction heating systems, where proximity between coil turns determines heating uniformity