1 From Preliminary Design to Prototyping and Validation of Energy Harvester for Shoes 3 Fig. 1.2 Transducer layout of the transducer coils, VL(i) is the voltage on the load, and i is the current [9, 10]. An accurate modelling of the system usually requires considering non-linearity of k and œ0 that are function of the relative displacement [11, 12]. 1.2.2 Electric Interface The simplest electric load is a resistor directly connected to the ends of the coils of the transducer. This solution provides the maximum electrical power, but it does not allow energy storage; it follows that the EH can feed an electrical device only when the floating magnet of the transducer is moving. In order to store the recovered energy a capacitor is connected to the coils terminals and, as the provided current is alternating, a rectifier bridge is interposed between the capacitor and the transducer. Although this configuration represents the easiest way for storing, due to the voltage drops in the diodes of the rectifier, it implies very worst performance with respect to the previous case. Moreover, if the voltage between the ends of the rectifier is lower than the voltage of the capacitor, the transducer does not charge it. To overcome the limits characterizing the bridge rectifier, an active electronic interface consisting in a step-up and a buck converter have been developed. The electronics interface is directly connected to the positive and negative terminal of the transducer. It consists of a full wave active boost converter with a transducer current control; this provides an optimum resistive load emulation independently from the signal provided by the transducer (shape and voltage level) and from the voltage stored on the output capacitor. The interactions between the mechanical and electrical phenomena depend heavily on the power transferred by the seismic mass to the electrical load. In linear system response conditions, the optimal matching follows the well known maximum power transfer theorem. For instance, in [13] it has been demonstrated that the energy recovery in response to a sinusoidal vibration input whose frequency matches the resonant frequency of the mechanical system, is maximum in adapted load condition, namely when the resistive load RL is: RL DRADAPT DR (1.2) However, due to the nonlinear effects present in the system, mainly the mechanical dissipative effects and the limited stroke of the floating magnet, the optimal resistor value is different from the one in (1.2) and it is typically larger. A theoretical analysis of this effect is present in [14], while here the best matching resistance value is calculated according to experimental evidences of the maximum power. Thus, the following equation is adopted through experimental evidence: RL DROPT DRADAPT CRADD (1.3) 1.2.3 Application Constraints, Vibrational Input and Energy Requirements The nature of the specific application imposes very stringent dimensional constraints to the device: a cylindrical shape volume of about ˆ27 16 mm that must contain the magneto-inductive energy harvester system for the power supply, the electronic interface for the data sending and the housing for the placing and the protection of the device itself in the sole of the shoe.
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