Magnetic Mirroring Method with MATLAB

This MATLAB tool is a complete implementation of the magnetic mirroring method also known as method of images. The complete implementation is object oriented and includes several examples. The tool be used to compute the magnetic properties of different components, e.g., inductors, transformers, and litz wires.

The following properties can be computed:

• Magnetic field pattern (vector or norm)
• Inductance matrix between the conductors
• Energy for a given excitation

The following configurations can be computed:

• Conductors in free space (no magnetic boundary)
• Conductors surrounded by a single magnetic boundary
• Conductors surrounded by two parallel magnetic boundaries
• Conductors surrounded by a box of four magnetic boundaries

The following additional features and constraints exist:

• The magnetic boundary can feature finite permeability
• The conductors are accepted to be round with an uniform current density
• The conductors are accepted to be round with an uniform current density.
• The radius and the position of the different conductors is arbitrary
• Line conductors (without zero radius) are accepted
• No HF effects (skin or proximity) are considered (can be added in post-processing)

This tool is developed by the Power Electronic Systems Laboratory at ETH Zurich and is available under the BSD License. The code is also available on the ETH Data Archive.

Examples

The following examples are included:

• test_inductor.m - Simulation of an inductor with air gaps
• test_transformer.m - Simulation of a transformer
• test_litz.m - Current sharing problem for untwisted litz wires

Inductor Field

Transformer Field

Litz Wire Current Sharing

Compatibility

The tool is tested with the following MATLAB setup:

• Tested with MATLAB R2018b or 2019a
• No toolboxes are required.
• Compatibility with GNU Octave not tested but probably easy to achieve.

References

The following references explain the theory and applications of the mirroring method:

• Muehlethaler, J. / Modeling and Multi-Objective Optimization of Inductive Power Components / 2012
• Ferreira, J.A. / Electromagnetic Modelling of Power Electronic Converters / 1989
• Bossche, A. and Valchev, V. / Inductors and Transformers for Power Electronics / 2005.
• Binns, K. and Lawrenson, P. / Analysis and Computation of Electric and Magnetic Field Problems / 1973

Author

• Thomas Guillod, ETH Zurich, Power Electronic Systems Laboratory - GitHub Profile

License

• This project is licensed under the BSD License, see LICENSE.md.
• This project is copyrighted by: (c) 2016-2020, ETH Zurich, Power Electronic Systems Laboratory, T. Guillod.