Magnetic Field of Coaxial Square Coils Enclosed with High-Permeability Material (original) (raw)
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IEEE Transactions on Magnetics, 2000
A method is presented to determine the magnetic reluctance of a thin or a thick magnetic layer of permeability underneath a planar coil based on inductance measurements. The procedure is substantiated on the basis of the linear electromagnetic network model. The influence of the involved magnetic reluctances on the inductance is analyzed by a transformation into the electrical domain applying linear network theory. From inductance measurements the individual contributing inductances can be calculated and from the back transformation into the magnetic domain the reluctances and further parameters, such as the magnetic field strength for a given electrical current or the permeability. Analytical results are compared with FEM simulations and with measurements obtained from a magnetostrictive bending sensor.
Helmholtz Coils and Magnetic Fields
2020
The objectives of the experiment are to determine the magnetic field along the horizontal x-axis that passes through the centre of a single solenoid coil, and to determine the magnetic field along the horizontal x-axis that passes through the centre of the Helmholtz coil. Helmholtz coil is a device that produces a region of a nearly uniform magnetic field. It consists of two solenoids that are parallel to each other on the same axis. Both solenoids are separated by a distance, d. Each coil carries an equal electric current in the same direction. The entire experiment is conducted via a simulator software provided. For Experiment I, the graph of B vs x is obtained alongside with the logarithmic graph of B vs the square of x. The comparison of the experimental and the theoretical logarithmic graphs allows the determination of the turns of wire, N of the hypothetical single coil. That is, N = 1717.5. It is managed to obtain the best value for B_0 through the standard deviation as the uncertainty in a single measurement with 70% confidence. That is, B_0 = (4.1267 x 10-3) ± (9.2236 x 10-5) T. The experimental μ_0 is deduced and it is given by μ_0 = (2.5292 x 10-7) T m A^-1. The determination of the experimental μ0 yields a percentage error of 79.9%. For Experiment II, the graph of B vs x is obtained for all d = R, d = 1.5R and d = 0.5R. Two major things found out in this part are, firstly, the mathematical erratum in either the simulator or in the laboratory manual is very substantial, and secondly, the erratum has caused such an ambiguity that a thorough quantitative analysis has become cumbersome given the time constraint as the deviation between the experimental and the theoretical values are of logarithmic. Next, the graph of B_0 vs d is also obtained for both the experimental and the theoretical values. Nothing much could be done on the quantitative aspect of it. However, qualitatively, it is observed that as d increases, B decreases. This may explain the lesser incident flux density as the coils move further apart. Lastly, the slope of the experimental data has a greater rate of change as opposed to that of the theoretical values.
Investigation of high frequency effects on layered coils
2008 13th International Power Electronics and Motion Control Conference, 2008
Copper losses in magnetic coils depend on several geometrical parameters, as well as on frequency, in a way that makes their modeling a quite difficult task. In this paper a Finite Element Analysis (FEA) software is utilized for the investigation of a series of issues critical for the accurate determination of copper losses in layered coils with round wires or foils. Some of the issues investigated are the edge effect in foil and round wire windings as well as the effect of the winding pitch on the copper losses. The results that come up from this work help to fully understand the real impact of two dimensional (2D) effects in layered windings of real rather than ideal magnetic components and they consist a tool for the accurate calculation of the encountered losses, which is necessary for an optimized magnetic component design.
Ab st ra c t-This paper describes a design methodology of a square Helmholtz coil with finite cross-sectional area to be used as a magnetic flux density standard up to 50 mT at NIMT. Magnetic field inside the square Helmholtz coil was considered to be assembled from the magnetic fields produced by every pair of square loops, which were analytically derived from the Biot-Savart law. This design technique, based on physical properties of the copper wires, allows the coil resistance to be easily predicted to match the output characteristics of the DC power supply. Temperature rise in the coil and the decrease of the coil constant due to thermal expansion were also taken into account. The calculated magnetic field was found to be closely agreed with finite element modelling (FEM). A design prototype was constructed and results showed good agreements with the numerical calculation.
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IEEE Transactions on Magnetics, 2000
ABSTRACT This paper presents a synthesis of analytical calculations of magnetic parameters (field, force, torque, stiffness) in cylindrical magnets and coils. By using the equivalence between the amperian current model and the coulombian model of a magnet, we show that a thin coil or a cylindrical magnet axially magnetized have the same mathematical model. Consequently, we present first the analytical expressions of the magnetic field produced by either a thin coil or a ring permanent magnet whose polarization is axial, thus completing similar calculations already published in the scientific literature. Then, this paper deals with the analytical calculation of the force and the stiffness between thin coils or ring permanent magnets axially magnetized. Such configurations can also be modeled with the same mathematical approach. Finally, this paper presents an analytical model of the mutual inductance between two thin coils in air. Throughout this paper, we emphasize why the equivalence between the coulombian and the amperian current models is useful for studying thin coils or ring permanent magnets. All our analytical expressions are based on elliptic integrals but do not require further numerical treatments. These expressions can be implemented in Mathematica or Matlab and are available online. All our models have been compared to previous analytical and semianalytical models. In addition, these models have been compared to the finite-element method. The computational cost of our analytical model is very low, and we find a very good agreement between our analytical model and the other approaches presented in this paper.
Magnetic field of paired coils in Helmholtz arrangement
Principle The spatial distribution of the field strength between a pair of coils in the Helmholtz arrangement is measured. The spacing at which a uniform magnetic field is produced is investigated and the superposi-tion of the two individual fields to form the combined field of the pair of coils is demonstrated.
IEEE Transactions on Magnetics, 2006
In this paper, we present analytic-numerical expressions for the calculation of the mutual inductance of two axisymetric circular coils with rectangular cross section in air. This original and new method may seem complicated but it is explicit, accurate, and fast, even though all expressions are obtained by the complete elliptic integrals of the first and second kind, Heuman's lambda function, and three terms that must be solved numerically. We confirm the validity of this approach by comparing it with other approaches (filament method and previously published data). We also compare the accuracy and the computational cost of this approach and that of the filament method. All results obtained by the various approaches are in excellent agreement.