Abstract
The general solution for resonant inductive coupling circuits has not been obtained because the roots of the characteristic equation of the circuits are too complicated. In order to overcome the difficulty of solving the circuit equation, we have introduced a new method that is converting the second-order differential equation for the charges to the first-order differential equation for the vector whose elements are currents and charges, and incorporating the characteristic equation into the structure of the eigenvectors of the differential coefficient matrix. We thus obtained the general solution for the circuits. In addition, we derived formulas for power transmission and power reception. Results of numerical calculation in the time and frequency domains always satisfy the low of conservation of energy. We thus obtain a number of interesting results. For example, 1/4 cycle delay between power transmission and power reception is very interesting because it shows that the power transition from the primary coil to the secondary coil resembles the peristaltic motion of the magnetic field energy.
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