# Foil coil windings

## Overview

The current density distribution in a foil-wound coil fed by a time-varying source depends on skin and proximity effects. Since the foil is usually very thin and made from a material with a high electrical conductivity, the skin effect along its thickness is negligible (i.e., the current density in each turn results practically uniform along a radial direction). On the other hand, the current density in each foil turn may greatly vary along the axial direction of the coil as a function of both position and frequency.

This anisotropic behavior is specific to foil coils and influences the Joule losses developed in the bulk of the coil material. Thus, Flux now provides a new subtype of the coil conductor region with losses and detailed geometric description that implements a homogenization technique to represent this type of coil efficiently in its 2D Steady State AC application. This technique is exclusive to foil coils and differs from the approach used in the other subtypes of coil conductor regions with losses and detailed geometric description representing stranded coils.

Using this new coil conductor region subtype spares the user from representing each turn of the foil coil with an individual solid conductor region (linked to its corresponding FE coupling component in a complicated electric circuit). While this latter approach is also legitimate and rigorous, it is usually very time consuming to set up in Flux due to the elaborate geometry and the refined mesh required. Moreover, the solving time with the new foil-wound coil conductor region subtype is significantly reduced when compared to the alternate solid conductor approach.

## Example of application

**Calculation of Current Distribution and Optimum Dimensions of Foil-Wound Air-Cored Reactors**by M.M. El-Missiry (

*Proceedings of the Institution of Electrical Engineers*, vol. 124, no. 11,November 1977, DOI: 10.1049/piee.1977.0218 ). In that work, the author presents a circuit-based, semi-analytical method to compute the current density distribution and several other electromagnetic quantities of a foil coil. The coil in Figure 2 may be easily modeled in Flux 2D with the foil coil template available for coil conductor regions with losses and detailed geometrical description. Figure 3 shows the results obtained with an axisymmetric Steady State AC Magnetic application at 50 Hz and with an additional horizontal symmetry (i.e., only one quarter of the foil coil is represented). The development of a non-uniform current distribution pattern characteristic to foil coils may be verified in the color plot available in that figure. A comparison between the current density results obtained with the approach described in that article and the solution evaluated with Flux 2D is provided in Figure 4. The graph in this figure displays the real and imaginary parts of the current density phasor (in RMS values) on a path from its upper extremity (0.0 p.u.) to its center (0.5 p.u.) along one of the centermost turns of the coil (as depicted in Figure 3).

Lumped circuit parameter at 50 Hz | Measurement | Flux 2D | Deviation |
---|---|---|---|

Reactance | 1.802 Ω | 1.827 Ω | 1.39% |

Resistance | 0.382 Ω | 0.376 Ω | 1.57% |