Proximity Effect and Skin Effect Modeling in FEMM
David Meeker
May 4, 2008
One method of capturing proximity effect and skin effect losses is to create a finite element model in which each turn in a multi-turn winding is explicitly modeled. By modeling each turn, the changes in current distribution within each turn due to these effects can be accurately represented. However, modeling every wire individually can be very computationally expensive. An alternative approach is to replace a wound region composed many wires by a continuum with carefully selected complex-valued material properties. Although the economy of continuum methods has been well-established, the approaches described in the literature typically require preliminary magnetic field computations to determine the equivalent material properties of the wound region.
In contrast, FEMM implements a model of proximity and skin effects in magnetic problems that takes no special effort on the part of the user. The user merely specifies a wire size and material for a winding, and the program automatically takes skin and proximity effects into account in the solution for the magnetic field and in all subsequent post-processing calculations.
Under the hood, FEMM uses approximate but closed-form expressions for the equivalent conductivity and permeability of regions filled with hexagonally packed round wire, allowing proximity and skin effects to be included with ease in 2D AC field computations. A paper is available that explains the theory behind the continuum model of proximity losses and skin effects that is implemented in FEMM 4.0.
A similar model is implemented in FEMM 4.2. However, the skin/proximity effect model used in FEMM 4.2 has been tuned via the regression of a large number of finite element runs to improve the accuracy of the model at high frequencies, especially for coils with very low or very high fill factors.
- Mathematica Notebook and FEMM models used to create the figures in the paper (FEMM 4.0).
- Mathematica Notebook and FEMM models used to create the figures in the paper (FEMM 4.2).
- PDF Printout of Mathematica Notebook run with FEMM 4.0.
- PDF Printout of Mathematica Notebook run with FEMM 4.2.