Frequency dependent resistance calculation of multiple conductors

The purpose of this paper is to present a method for calculating frequency-dependent resistance when multiple current-carrying conductors are present.

Analytical and numerical formulations are presented. Both skin- and proximity-effects are considered in the numerical approach, whereas only skin-effect can be taken into account in analytical equations. The calculation is done using a self-developed integral equation-based field solver. The results are benchmarked using professional software based on the finite element method (FEM).

Results from the numerical approach are in agreement with FEM-based software throughout the whole frequency range. Analytical formulations yield unsatisfactory results in higher frequency range. When multiple conductors are mutually relatively close, the proximity-effect has an impact on effective resistance and has to be taken into account.

The methodology is presented using axially symmetrical conductors. However, the same procedure can be developed for straight conductors as well.

Presented fast and stable procedure can be used in most electromagnetic devices when frequency-dependent resistance needs to be precisely determined.

The value of the presented numerical methodology lies in its ability to take both skin- and proximity-effects into account. As conductors are densely packed in most electromagnetic devices, both effects influence the effective resistance. The method can be easily implemented using a self-developed solver and yields satisfactory results.