Abstract
This paper describes the scattering matrix approach to obtain the solution to electromagnetic field quantities in harmonic multi-layer models. Using this approach, the boundary conditions are solved in such way that the maximum size of any matrix used during the computations is independent of the number of regions defined in the problem. As a result, the method is more memory efficient than classical methods used to solve the boundary conditions. Because electromagnetic sources can be located inside the regions of a configuration, the scattering matrix formulation is developed to incorporate these sources into the solving process. The method is applied to a 3D electromagnetic configuration for verification.
Highlights
The design and optimization of electrical machines and other electromagnetic applications necessitate accurate models of electromagnetic fields to precisely predict their performance
The scattering approach is applied to the electromagnetic configuration shown in Figure 2, where a rectangular slab of magnetic material is placed above three permanent magnets
The semi-analytical approach obtains the results for the electromagnetic configuration of Figure 2 faster than the finite element method (FEM); the solving time of the semi-analytical approach depends on the number of harmonics and number of regions in the model
Summary
The design and optimization of electrical machines and other electromagnetic applications necessitate accurate models of electromagnetic fields to precisely predict their performance As these systems and their structures get more complex, it is becoming more difficult to accurately model, e.g., eddy current effects [1,2] or hysteresis effects [3] in both the spatial and time domain. For more complex structures, with detailed features compared to the device size, the number of harmonics has to be increased to retain accuracy This leads to an increase in the required memory. The scattering matrix approach for harmonic models of electromagnetic configurations is described Using this approach, the memory required to obtain the solutions of the model is significantly reduced. The method is verified by application to a 3D electromagnetic configuration presented in [10], where the permeability varies in both periodic directions as a function of position
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