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Most kinetic converters for vibrations of solid objects are designed for resonance, which means they achieve their maximum electric power at a certain frequency f for an oscillating mass m. The maximum power P_max can be approximated following Roundy et al. [17]

(2.1)

where ζ_e denotes the electric damping, ζ_m the mechanic damping of the system. For a first approximation, the damping can be modeled to be ζ_m = ζ_e = 0.015 [17]. In real applications, the modeling of the damping is complex. The total damping ζ follows from ζ_m = ζ_e, with the damping coefficient d = ζ 2ωf m, where ωf = 2πf. a is the acceleration of the vibration. The oscillating mass m is damped electrically and mechanically (d). The resonance frequency depends on the feather constant k, where

(2.2)

Figure 2.1 depicts a schematic of the model.

Figure 2.1 Schematic of the basic model of a kinetic energy converter with an oscillating mass m, a feather constant k, and a damping coefficient d.

Following Eq. 2.2, both maximizing the mass m and minimizing the damping d are required for an optimization of the electric power yield. This is the reason why many converters of this type are very heavy. From the models, it also follows that for a constant amplitude, the electric yield increases with decreasing frequencies.

The acceleration of the human lower leg has been measured to be 10 m/s² [18], where the frequency f of a human walking is around 2 Hz. For a mass m = 0,2 kg, and ζ_m=ζ_e= 0.015 an electric power of 6.64W could be harvested. Decreasing the mass to a more comfortable m = 0.01 kg yields 331 mW. This would already be enough to power small transceivers with low frequencies of use, such as for paging applications in hospitals. As outlined in the introduction of this book by Joe Paradiso, those applications are more of research interest due to their low comfort for the user.

Exemplary demonstrated and commercial systems are outlined in the following sections.