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This paper presents a new inertial power generator for scavenging low-frequency nonperiodic vibrations called the Parametric Frequency-Increased Generator (PFIG). The PFIG utilizes three magnetically coupled mechanical structures to initiate high-frequency mechanical oscillations in an electromechanical transducer. The fixed internal displacement and dynamics of the PFIG allow it to operate more effectively than resonant generators when the ambient vibration amplitude is higher than the internal displacement limit of the device. The design, fabrication, and testing of an electromagnetic PFIG are discussed. The developed PFIG can generate a peak power of 163 μW and an average power of 13.6 μW from an input acceleration of 9.8 m/s2 at 10 Hz, and it can operate at frequencies up to 65 Hz, giving it an unprecedented operating bandwidth and versatility. The internal volume of the generator is 2.12 cm3 (3.75 cm3 including the casing). The harvester has a volume figure of merit of 0.068% and a bandwidth figure of merit of 0.375%. These values, although seemingly low, are the highest reported in the literature for a device of this size and operating in the difficult frequency range of ≤ 20 Hz.