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Mutual inductance calculations of non-identical n-sided planar coils with arbitrary geometry and spatial orientations

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Abstract

Planar coils are widely used in sensors, wireless chargers, robots, portable devices, medical implants, etc. An important factor in the performance of two magnetically coupled coils is the mutual inductance. However, the mutual inductance measurements between two arbitrarily positioned non-identical n-sided coils with lateral and angular misalignments have not been solved. In this paper, we calculated the mutual inductance between two arbitrarily positioned, non-identical n-sided planar spiral coils by the partial inductance method. The proposed model can adapt the calculations for any planar coil configurations including rectangle, pentagon, hexagon, or any other regular n-sided coils. Even the circular coils are approximated by multiple sides. In addition, measurements can cover lateral displacement, angular rotation, and both simultaneously. The theoretical calculation results are verified with the results of Ansys Maxwell simulations and previously published works in the literature. The relative errors of the presented method with simulation results are less than 0.1% in selected cases. Finally, the superiority of the proposed method over simulation in terms of time consumption is investigated. For the samples studied in this paper, more than 90% of the time could be saved compared to 3D finite element method simulations.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request].

Abbreviations

A:

End point of AB line segment

B:

End point of AB line segment

C:

End point of CD line segment

D:

End point of CD line segment

l:

Length

M:

Mutual inductance

n:

Number of sides

N:

Number of turns

O:

Transmitter coil vertices

P:

Receiver coil vertices in parallel with the transmitter coil

Q:

Receiver coil vertices

R:

Distance

r:

Circumcircle radius

RM:

Rotation matrix

s:

Space between each turn

V:

Relative position vector

w:

Width of coil wire

x:

Cartesian coordinate

y:

Cartesian coordinate

z:

Cartesian coordinate

Δ:

Constant

θ:

Rotation around y-axis

μ:

Magnetic permeability coefficient

φ:

Rotation around x-axis

ψ:

Rotation around z-axis

Ω:

Constant

R:

Receiver coil

T:

Transmitter coil

A:

Point A

AB:

AB line segment

B:

Point B

C:

Point C

CD:

CD line segment

D:

Point D

i:

Turn number of the transmitter coil (the outermost equals 1)

j:

Turn number of the receiver coil (the outermost equals 1)

k:

Vertex number of the receiver coil

m:

Vertex number of the transmitter coil

t:

Total

V:

Relative position vector

AC:

Alternating current

FEM:

Finite element method

WPT:

Wireless power transmission

B:

Byte

H:

Henry

Hz:

Hertz

m:

Meter

min:

Minute

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Urmia University, Urmia, 57561-51818, Iran

    Ata Ollah Mirzaei & Amir Musa Abazari

  2. Department of Energy Systems Engineering, School of Advanced Technology, Iran University of Science and Technology, Tehran, 16846-13114, Iran

    Mahdi Asadi

  3. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Hamed Ghanbarpour

  4. Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology (HKUST), Clear Water Bay, Hong Kong

    Hadi Tavakkoli

Authors
  1. Ata Ollah Mirzaei
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  4. Amir Musa Abazari
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  5. Hadi Tavakkoli
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Correspondence to Amir Musa Abazari or Hadi Tavakkoli.

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Mirzaei, A.O., Asadi, M., Ghanbarpour, H. et al. Mutual inductance calculations of non-identical n-sided planar coils with arbitrary geometry and spatial orientations. Eur. Phys. J. Plus 138, 869 (2023). https://doi.org/10.1140/epjp/s13360-023-04493-1

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