Proximity Effect
Proximity Effect: Theoretical Foundations
What is the Proximity Effect?
Professor, what's the difference between the proximity effect and the skin effect?
The skin effect is the current crowding caused by "one's own magnetic field." The proximity effect is the current crowding caused by "the magnetic field from a neighboring conductor."
An external magnetic field $H_{ext}$ created by an adjacent conductor induces additional eddy currents within the conductor. Loss according to Dowell's formula:
So it becomes a problem in multi-layer windings, right?
Exactly. The external magnetic field experienced by a conductor in the $m$-th layer is proportional to $H = (m-1) \cdot n \cdot I$. Since inner layers receive a larger external magnetic field, the loss in inner layers is overwhelmingly greater than in outer layers. The AC resistance factor $F_r$ in Dowell's formula increases proportionally to $m^2$.
Summary
- Magnetic field of adjacent conductors — Additional eddy current loss
- $F_r \propto m^2$ — Loss increases with the square of the number of layers
- Multi-layer windings — Dominant in transformers and inductors
"The Neighbor's Wire Gets in the Way" — Why the Proximity Effect Complicates Coil Design
The skin effect is a phenomenon where the current distribution becomes uneven due to "the magnetic field created by its own current," while the proximity effect is the unevenness caused by "the magnetic field created by a neighboring conductor's current." When currents flow in the same direction, the current is pushed to the outer side of the conductor; when they flow in opposite directions, it concentrates on the inner side. When this occurs in transformer windings or inductor coils, the effective resistance can become several times the design value. In multi-layer coils, the effects of each layer accumulate, making it impossible to handle with analytical formulas for a single conductor. One of the main reasons FEA has become essential in modern power electronics coil design is to accurately predict this proximity effect.
Computational Methods for Proximity Effect
Proximity Effect Analysis with FEM
How do you capture the proximity effect with FEM?
Perform eddy current analysis by meshing each conductor individually. The magnetic interaction between conductors is automatically included.
2D cross-section analysis is efficient: If the coil's longitudinal direction is uniform, 2D provides sufficient accuracy. You can visualize the current density distribution in each conductor and confirm the current crowding due to the proximity effect.
Can the proximity effect be reduced with interleaved winding?
Yes. By alternately arranging primary and secondary windings, the MMF (Magnetomotive Force) distribution is flattened, significantly reducing the proximity effect. Comparing losses before and after interleaving with FEM clearly shows the effect.
Summary
- Individual conductor meshing — Directly calculates proximity effect
- 2D cross-section analysis — Efficiently visualizes current distribution
- Interleaved winding — Reduces proximity effect by flattening MMF
The Compromise of 2.5D Analysis — Why Approximate Calculations for Proximity Effect Survive
Attempting a strict 3D analysis of a multi-layer coil can sometimes take hours just for mesh generation. Therefore, in practice, "2.5D analysis"—that is, an approximate method that precisely analyzes the cross-sectional shape in 2D and extrapolates in the length direction using a multiplier—remains widely used. This method can evaluate current distribution including the proximity effect with high accuracy while reducing computation time to less than 1/100 of 3D. While end effects and three-dimensional magnetic field wrapping are ignored, the empirical rule that the main losses in the winding section are largely governed by the 2D cross-section provides sufficient accuracy for many practical designs. "Knowing where to approximate" is also an important skill for design engineers.
Proximity Effect in Practice
Countermeasures in Practice
Related Topics
Experience the theory firsthand with the interactive simulator for this field
All Simulators