Document Type : Research Article


1 Department of Mechanical Engineering, Faculty of Engineering, Urmia University, Urmia, Iran

2 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran

3 Department of Energy Systems Engineering, School of Advanced Technologies, Iran University of Science and Technology, Tehran, Iran

4 Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong


The calculation of mutual inductance has widespread applications in microelectromechanical systems (MEMS) sensors and wireless power transfer in microchips. Flat coil structures are commonly employed for implementing coils in micro dimensions. MEMS sensors and microchips with flat coil structures have found applications in various industries, including medical, robotics, and aerospace, in the electromagnetic systems field. Mutual inductance is a crucial factor in the design of flat coil windings used in these sensors, significantly affecting their performance quality. In this paper, a comprehensive analytical solution based on the partial inductance method is presented for calculating the mutual inductance between two co-centric flat coils with an arbitrary angular orientation relative to each other. Using the partial inductance method and rotation matrices, the mutual inductance relations for two flat coils with arbitrary angular orientation in space are derived. The proposed method's results are validated against ANSYS Maxwell software simulations, demonstrating acceptable computational errors. The error for six-sided and eight-sided flat coils is, respectively, a maximum of 13.3% and 1.52%, affirming the accuracy of the proposed method.


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