Wireless power transfer (WPT) is a kind of power transmission technology with which load devices can be supported to take power from the power source in a non-contacting way. Hollow solenoidal coils are used as resonant coils extensively in engineering projects which are usually analyzed based on magnetostatic fields. In practice coils are often excited by alternating currents, and it is particularly significant to carry out studies on the time-harmonic electromagnetic solutions to solenoidal coils. In this study, the alternating magnetic vector potential is derived from Maxwell’s time-harmonic equations, and the analytic expressions are established for coaxially symmetric solenoidal coils firstly.

Then the expressions for the electric field intensity and the induced voltages of the coils are deduced, and the field-circuit coupling equations for WPT which show the specific constraint relationship between the input and output variables are obtained. Finally, the results are verified by experiment. The transmission characteristics and the variation of the input and output variables under different coils’ spans can be described by the equations when the coils’ structures and sizes are given, which have some significance for WPT design.

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