Theory of Image Impedance Matching for Inductively Coupled Power Transfer Systems

The optimum design of an inductively coupled power transfer system is accomplished by applying the Roberts's theory on conjugate image impedance. The input and output ports' impedance and the loading capacitances for maximum power transfer are obtained as functions of the self-inductances, the mutual inductance, the copper losses, and the iron loss, which are used to define the figure-of-merit of the system. It is found that the loading capacitances necessarily satisfy the resonance conditions individually in the input and output circuits. The capacitors may be connected in series or in parallel. The equivalent transform formulas between the series and parallel topologies are given for the capacitances and for the port impedances. The port impedance in the series (parallel) topology is proportional (approximately inversely proportional) to the inductive coupling coefficient. The image impedances of the lossless symmetric systems are real or pure imaginary depending on the frequency, and the image impedance patterns are classified as “Hill”, “Valley”, and “Waterfall". The reactance network approach for such lossless systems gives in-depth insight into the system behaviors and facilitates the practical design.