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Wireless sympathetic connection systems are proposed which employ a single resonator located between two electrically small non-resonant antennas. Symmetric configurations consisting of two equal transmitting and receiving antennas and a resonator are characterized by the equivalent reactive circuits with two inductors and one capacitor in the case of closed path type antennas and with two capacitors and one inductor in the case of open path type antennas. The equivalent circuit constants are identified by the series and parallel resonance frequencies for the even mode excitation and by the low frequency inductance or capacitance for the odd mode excitation. The power transfer efficiency evaluated by the equivalent circuit analysis agrees well with the full wave analysis result, and is 100 percent when the port impedances are matched to the image impedance and the structures are assumed to be lossless. Asymmetric cases of unequal transmitting and receiving antennas are treated, and the theory is applied to the simplified design of HF-RFID systems, where the reader/writer port impedance is 50Ω and the tag port impedance is 3 KΩ. The power transfer efficiency is evaluated in case the antennas and the resonator are made of cupper. It keeps the efficiency larger than -10 dB when the tag antenna moves from the home position by 15 cm horizontally or vertically.