Arbitrary-shaped single-layer coil self-inductance using shape functions

Ishida, Koichi; Itaya, Toshiya; Tanaka, Akio; Takehira, Nobuo; Miki, Toshikatsu

doi:10.1049/iet-smt.2010.0035

Cited by 9 publications

(11 citation statements)

References 12 publications

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“…As shown in Fig. 1, the inductance L of the arbitrary-shaped single-layer coil is expressed in the integral form using the Fourier transform method as follows [7]:…”

Section: Formulas For Calculating Self-inductancementioning

confidence: 99%

“…Then, we theoretically and experimentally evaluated the appropriateness of the formulas and referred to the inductance change caused by the side number of the 'regular polygonal coil' using the calculation results of the formulas. [Correction added on 30 September 2022, after first online publication: the 'necessary (7)' has been changed to 'necessary equations [7]'. ]…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of a Calculation Formula for the Self‐Inductance of an Arbitrary‐Shaped Single‐Layer Coil (Derivation of Shape Functions and Inductance Caluculations for Regular Polygonal Coils)

Itaya

Ishida

Tanaka

et al. 2022

IEEJ Transactions Elec Engng

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In the design and production of electrical and electronic devices and circuits, it is desirable to have a calculation formula for obtaining exact inductance values, which are generally fundamental for coils. In this paper, a formula that can be applied to the exact calculations of the self-inductance of arbitrary-shaped single-layer coils is presented, and its application to the several types of coils that are technologically valuable is reported. Specifically, the formula employs a new coefficient corresponding to the Nagaoka coefficient and the shape function determined by the coil. Moreover, it realizes a versatile and convenient inductance calculation method. In addition, as the formula is derived via an analytical method, it has the advantage that it can be calculated with a short-time numerical integration. As examples of the application of the formula, rhombic, race-track, elliptic, and regular polygonal coils were discussed, and the process and result of deriving the shape function and new coefficient for each coil were presented. Furthermore, regarding the calculation formula for regular polygonal coils, we made a regular pentagonal coil and conducted an experiment, and the validity of the calculation formula was confirmed.

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“…As shown in Fig. 1, the inductance L of the arbitrary-shaped single-layer coil is expressed in the integral form using the Fourier transform method as follows [7]:…”

Section: Formulas For Calculating Self-inductancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application of a Calculation Formula for the Self‐Inductance of an Arbitrary‐Shaped Single‐Layer Coil (Derivation of Shape Functions and Inductance Caluculations for Regular Polygonal Coils)

Itaya

Ishida

Tanaka

et al. 2022

IEEJ Transactions Elec Engng

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“…A new pseudo-analytical model for calculating DC inductance of flat circular inductors with rectangular cross section was proposed by Penalver et al [20] Based on the partial inductance method, Tavakkoli et al [21] proposed a new way to calculate the mutual inductance of two planar polygonal spiral coils with arbitrary number of sides. Researchers [22], [23] also derived the equations for calculating the self-inductance of the arbitrary shaped singlelayer coils based on the shape functions.…”

Section: B Estimating Self-and Mutual-inductancementioning

confidence: 99%

Design of 3D Wireless Power Transfer System Based on 3D Printed Electronics

Hou

Elkhuizen

et al. 2019

IEEE Access

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2D coil design limits the use of wireless power transfer (WPT) in many products with freeform outer shapes. In this paper, enabled by 3D printed electronics, we propose a systematic approach to design and fabricate 3D coils for WPT. Based on the circular spiral and rectangular spiral patterns, 3D receiver and transmitter coils can be generated on an arbitrarily selected region of a product and its offset, respectively. Mathematical models are proposed to estimate the self-inductance and the mutual-inductance of the 3D arbitrarily shaped coils for 3D WPT. This leads to a new design approach of a 3D WPT system. Several sets of 3D printed WPT systems were designed, simulated, and prototyped to demonstrate the effectiveness of the proposed design approach as well as the mathematical models. The calculation speed of the proposed mathematical models is 30 times faster than the simulation, and compared with the measurement results, the calculation results have mean absolute errors of 2.63% and 4.45% regarding the self-and the mutualinductance, where the simulation results have mean absolute errors of 1.20% and 2.38%, respectively. Measurements also indicate that with a 5V input, the prototypes are able to deliver 1-watt power at an efficiency ranging between 20.9% and 25.3%. It was concluded that the proposed approach is feasible and promising for designing and manufacturing WPT using 3D printed electronics.INDEX TERMS 3D coil, WPT, IPT, 3D printed electronics, design.

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“…As shown in Fig. 9, the shape functions S 0 (ξ, η) and S 1 * ξ, η are expressed using the following equations from [14].…”

Section: Rectangular Coilmentioning

confidence: 99%

“…In a previous study, the authors obtained the magnetic fields [13] and self-inductance [14,15] of coils with arbitrary shapes. Using the results of these studies, we derived a precise numerical formula for the mutual inductance between two arbitrarily shaped single-layer coils arranged in parallel.…”

Section: Introductionmentioning

confidence: 99%