Magnetic field of complex helical conductors

Budnik, Krzysztof; Machczyński, Wojciech

doi:10.2478/aee-2013-0043

Cited by 11 publications

(22 citation statements)

References 14 publications

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“…Based on the Biot‐Savart law, the perpendicular magnetic flux intensity ( H z ) generated by single helical coil having constant current at any arbitrary point ( x , y , z ) can be calculated as follows:

H_{z} (x, y, z) = \frac{(- a I)}{4 π} \int_{0}^{\frac{2 π L}{h}} \frac{\sin φ false(y - a \sin φ false) + \cos φ false(x - a \cos φ false)}{{[{false(x - a \cos φ false)}^{2} + {false(y - a \sin φ false)}^{2} + {false(z - L false)}^{2}]}^{\frac{3}{2}}} d φ .

…”

Section: Design Of a Stepped Helical Coilmentioning

confidence: 99%

Design of transmitting coil for wireless charging system to expand charging area for drone applications

Kim

Cho

Hong

2018

Micro & Optical Tech Letters

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This research proposes a transmitting coil structure for wireless charging which has the constant efficiency regardless of the position of the receiving coil. The proposed transmitting coil is designed to operate at 140 kHz, and to improve the uniformity of the magnetic field intensity using a stepped helical coil and ferrite core. The measured results of the charging system with proposed transmitting coil show that it has low difference in rectifying voltage and efficiency within the charging area. Therefore, it has advantages in terms of wide charging area without the charging shadow area.

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H_{z} (x, y, z) = \frac{(- a I)}{4 π} \int_{0}^{\frac{2 π L}{h}} \frac{\sin φ false(y - a \sin φ false) + \cos φ false(x - a \cos φ false)}{{[{false(x - a \cos φ false)}^{2} + {false(y - a \sin φ false)}^{2} + {false(z - L false)}^{2}]}^{\frac{3}{2}}} d φ .

…”

Section: Design Of a Stepped Helical Coilmentioning

confidence: 99%

Design of transmitting coil for wireless charging system to expand charging area for drone applications

Kim

Cho

Hong

2018

Micro & Optical Tech Letters

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“…As there is no approximation under certain conditions, these formulas can be applied to any geometric parameter of a finite-length helical coil. Inspired by H. Buchholz's works, several papers have examined the magnetic field distribution of helical coils in specific situations, but have not addressed the calculation of the mutual inductance [23][24][25][26]. expressions of the mutual inductance of finite-length coaxial helical coils using Neumann's formula [19,20].…”

Section: Introductionmentioning

confidence: 99%

Analytical Calculation of Mutual Inductance of Finite-Length Coaxial Helical Filaments and Tape Coils

et al. 2019

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Mutual inductance between finite-length coaxial helical filaments and tape coils are presented analytically. In this paper, a mathematical model for finite-length coaxial helical filaments is established, and subsequently, the mutual inductance of the filaments is derived in a series form, containing a one-dimensional integral. The mutual inductance expression of the filaments is then generalized for a tape conductor. When the tape conductor of each coil is closely wound, then the inverse Mellin transform is further utilized for transforming the generalized integral in the mutual inductance expression into a series involving hypergeometric functions, for increasing the calculation speed. Finally, the obtained expressions are compared numerically with the existing analytical solutions and finite-element simulation in order to verify the correctness and general applicability of the results. In this paper, as all the mutual-inductance analytical expressions are concise with fast convergence, it is easy to obtain the numerical results in software, such as Mathematica. The expressions presented in this paper are applicable to any corresponding geometric parameter, and are thereby more advantageous compared to the existing analytical methods. In addition, evaluation by these expressions is considerably more efficient, as compared to finite element simulation.

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“…Substituting (5) into (19), one obtains the temperature dependent effective thickness of the square-wire winding conductor The temperature dependent square-wire winding dc resistance is given by (21) and the temperature dependent normalized ac winding resistance of the square-wire is given by ( ) Figure 2 shows the 3D plot of normalized ac winding resistance of the square winding as functions of square-wire thickness and temperature at η = 0.8, f = 100 kHz, N l = 10, and l w = 12 m. It can be seen that the behaviour of the square-wire winding resistance at constant frequency is different than for the foil winding. As the thickness of the square-wire winding increases, the winding resistance decreases, reaches local minimum, then increases, reaches local maximum, and then decreases, while for the foil winding it remains constant.…”

Section: Thermal Optimization Of the Square-wire Windingmentioning

confidence: 99%

“…For the high power inductors, from aforementioned losses, significant role plays the winding losses [9][10][11][12][13][14][15][16][17][18][19][20][21][31][32][33][34][35][36]. While core and dielectric loss are decreased by selection of low-loss materials, the winding losses are significantly reduced by optimization of the winding conductor size [16,17,19].…”

Section: Introductionmentioning

confidence: 99%

Thermal analytical winding size optimization for different conductor shapes

Wojda¹

2015

Archives of Electrical Engineering

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Abstract. The aim of this paper is to derive an analytical equations for the temperature dependent optimum winding size of inductors conducting high frequency ac sinusoidal currents. Derived analytical equations are useful designing tool for research and development engineers because windings made of foil, square-wire, and solid-round-wire windings are considered. Temperature dependent Dowell's equation for the ac-to-dc winding resistance ratio is given and approximated. Thermally dependent analytical equations for the optimum foil thickness, as well as valley thickness and diameter of the square-wire and solid-round-wire windings are derived from approximated thermally dependent ac-to-dc winding resistance ratios. Minimum winding ac resistance of the foil winding and local minimum of the winding ac resistance of the solid-round-wire winding are verified with Maxwell 3D Finite Element Method simulations.

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Magnetic field of complex helical conductors

Cited by 11 publications

References 14 publications

Design of transmitting coil for wireless charging system to expand charging area for drone applications

Design of transmitting coil for wireless charging system to expand charging area for drone applications

Analytical Calculation of Mutual Inductance of Finite-Length Coaxial Helical Filaments and Tape Coils

Thermal analytical winding size optimization for different conductor shapes

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