Scalar multipole expansions and their dipole equivalents

Wikswo, John P.; Swinney, Kenneth R.

doi:10.1063/1.334589

Cited by 43 publications

(41 citation statements)

References 5 publications

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“…Fig. 6 illustrates the principle to construct the dipole, quadrupole, and octupole by superposing multiple coils with different direction of current [15]. We present subsequently the characterization of these sources.…”

Section: A Standardized Sourcesmentioning

confidence: 98%

Near Magnetic Field Coupling Prediction Using Equivalent Spherical Harmonic Sources

Hoang¹,

Bréard²,

Vollaire³

2014

IEEE Trans. Electromagn. Compat.

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In the electromagnetic compatibility (EMC) behavior of power electronic converters, magnetic parasitic couplings between components are one of the main causes of dysfunctions or bad filtering (e.g., in EMC filter). These couplings could be as conducted or near-field interferences. In order to handle interaction problems, a complete knowledge of these magnetic couplings is then necessary. Our study is focused on near magnetic field's interferences. Indeed, the characterization of electromagnetic field in power electronics is still in active research. This paper details a predictive method that calculates accurately and efficiently the near magnetic field coupling between two sources. By using the near-field multipolar expansion in spherical harmonics of electromagnetic sources, the close magnetic coupling between two sources is determined from their equivalent model. It is shown that the increase in degree up to the fourth provides a more precise representation of the elements and thus a better accuracy of the near-field coupling prediction. Also, theoretical and experimental developments will be presented. The coupling between two complex sources will be considered to validate the predictive method.Index Terms-Electromagnetic compatibility (EMC), near magnetic field coupling, power electronic, spherical harmonic.

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Section: A Standardized Sourcesmentioning

confidence: 98%

Near Magnetic Field Coupling Prediction Using Equivalent Spherical Harmonic Sources

Hoang¹,

Bréard²,

Vollaire³

2014

IEEE Trans. Electromagn. Compat.

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“…where the formulas for the dipole and octupole moments ( , ) are consistent with those of Wikswo and Swinney [3].…”

Section: A Exact Multipole Imagementioning

confidence: 66%

Spatial harmonic analysis of fem results in magnetostatics

et al. 2003

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Approaches to the spatial harmonic characterization of the field due to a symmetrically shielded permanent bar magnet are presented. At first, exact spherical harmonic coefficients are obtained for a given unshielded magnet and comparisons are made with the coefficients of unshielded numerical models. In the calibration test, the scalar magnetic potential is separately calculated by the integral equation method (IEM) and finite-element method (FEM) with a layer of "infinite" elements on the interface boundary. While the values from the IEM data are nearly exact, the analysis of the FEM data demonstrates greater errors. For the selection of the coefficients from the discrete data from either unshielded or shielded magnets, discrete selective functions are additionally orthonormalized at the boundary surface. For the discrete selective functions generated for the grid of 612 points, which are uniformly distributed over the unit sphere with angular steps of 10 in and directions, the maximal error of nonorthogonality is below 10 8 .Index Terms-Finite-element method, magnetic multipole, magnetostatics, spherical harmonic analysis.

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“…However, for more complex geometries, numerical methods must be utilized. Methods such as multipole expansions using spherical harmonics [12], finite difference [13], and finite element methods [14] are available, where the later two are computationally expensive. Both the boundary element method (BEM) used in [15] and the scalar multipole expansion provide a more computationally friendly approach.…”

Section: Simulation Part 1: Static Field Pertubationmentioning

confidence: 99%

MRI simulator with static field inhomogeneity

et al. 2002

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This paper describes a new MRI simulator that provides realistic images for arbitrary pulse sequences executed in the presence of static field inhomogeneities including those due to magnetic susceptibility, errors in the applied field, and chemical shift. In contrast to previous simulators, this system generates object-specific inhomogeneity patterns from first principles and propagates the consequent frequency offsets and intravoxel dephasing through the acquisition protocols to produce images with realistic artifacts. The simulator consists of two parts. Part 1 calculates a frequency offset for each voxel. It calculates the size of the static field offset at each voxel in the image based on the known magnetic susceptibility of each of the components at all voxels. It uses a novel implementation of the "Boundary Element Method" and takes advantage of the superposition principle of magnetism to include voxels with mixtures of substances of differing susceptibilities. Part 2 produces both a signal and a reconstructed image. Its inputs include the 3D digital brain phantom introduced by the McConnell Brain Imaging Centre, frequency offsets computed by part 1, applied static field errors, chemical shift values, and a description of the acquisition protocol.

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Scalar multipole expansions and their dipole equivalents

Cited by 43 publications

References 5 publications

Near Magnetic Field Coupling Prediction Using Equivalent Spherical Harmonic Sources

Near Magnetic Field Coupling Prediction Using Equivalent Spherical Harmonic Sources

Spatial harmonic analysis of fem results in magnetostatics

MRI simulator with static field inhomogeneity

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