Coupling coefficient is a key parameter for the coil design of wireless power transfer (WPT) systems. The accurate calculation of coupling coefficient is an important theoretical basis for optimizing the coil structure and improving the transmission efficiency in WPT systems. In this paper, the magnetic flux density distribution of rectangular spiral coils with double magnetic shielding is studied, and an analytical model of coupling coefficient between arbitrarily positioned rectangular spiral coils is established. First, the incident magnetic flux density is obtained based on the dual Fourier transformation and the relationship between the magnetic flux density and magnetic vector potential. Second, the reflected magnetic flux density in the region of the receiving coil is solved by using Poisson's equation, Laplace's equation and boundary conditions. Finally, the formula for the coupling coefficient between rectangular spiral coils is derived by the spatial frame transformation method and the integral method. The calculation results agree well with the finite element simulation value and experimental measurements, which verifies the correctness of the calculation formula of the coupling coefficient.
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