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Adiabatic quantum-flux-parametron (AQFP) logic devices can operate under extremely low bit energy approaching the thermal limit by varying their potential energy adiabatically using ac bias currents. We have proposed an on-chip ac power source, which is composed of a Josephson relaxation oscillator and a superconducting LC resonator in order to drive AQFP circuits at 5 GHz or higher frequencies. We herein experimentally confirmed the correct switching operation of an AQFP gate at 4.94 GHz using the proposed on-chip ac power source. Furthermore, we confirmed that the ac power source can drive approximately 800 AQFP gates.