I. Introduction
As the performance and functionality of the personal digital assistant devices are rising significantly, there has been active research for renewable and maintenance-free power sources. Harvesting energy from vibrational environments has attracted considerable attention as an alternative to conventional batteries. Three transduction mechanisms have been employed to convert kinetic energy into electrical energy: piezoelectric [1], [2], electrostatic [3], [4], and electromagnetic [5]–[8]. However, all vibration-driven energy harvesters based on these mechanisms can be analyzed as a mass-spring system within a frame, and produce a maximum power at its resonant frequency. Previous energy harvesters, whose resonant frequency is tens or hundreds of hertz, are ineffective in harvesting vibration energy at less than 10 Hz [9], [10]. Thus, it is highly desirable to make the harvester’s resonant frequency less than 10 Hz, where many commonly available vibrations such as human body motion, bridge vibration, ocean wave, etc. are occurring. For scavenging traffic-induced bridge vibrations, an electromagnetic energy harvester occupying 68 cc was shown to generate an average power of W (into 1.5 k load) from 0.54 m/ acceleration at 2 Hz (about 3.4 mm vibration amplitude) [11]. Another electromagnetic power generator with stacked multilayer magnets occupying 18 cc generated an average power of W (into load) from a root-mean-square (rms) acceleration of 0.25 m/ at 4.1 Hz [12]. To increase the power output at low vibration frequency, the energy harvesters were developed to convert low-frequency vibrations to a higher frequency by employing the frequency up-conversion technique [13], [14]. However, the resonant frequencies for these devices were still around 100 Hz, and much of the vibration energy was lost in the conversion process.