Electret length optimization of output power for double-end fixed beam out-of-plane electret-based vibration energy harvesters

Thanks to miniaturization, it is now possible to imagine self-powered systems that can harvest energy from the environment to produce electrical energy. Out-of-plane electret-based vibration energy harvesters (E-EVHs) are an effective and inexpensive energy harvester type that has attracted much attention. Increasing the capacitance of variable capacitors is an effective way to improve the output power of E-EVHs. In this paper, firstly an accurate capacitance theoretical model of a double-ended fixed beam out-of-plane E-EVHs which has 97% reliability compared with FEM (COMSOL Multiphysics) results is presented. A comparison of capacitance between the double-ended fixed beam structure and a cantilever structure of the same size indicates that the double-ended fixed beam structure has greater capacitance and capacitance variation. We apply this theoretical capacitance model to the mechanical-electrical coupling model of double-ended fixed beam out-of-plane E-EVHs and study harvesters' output performances for different electret lengths by numerical and experimental method, respectively. There exists an optimal electret length to harvest maximum power in our simulation results. Enhanced electrostatic forces with increasing the electret length emphasizes the soft spring effect, which widens the half power bandwidth and lowers the resonance frequency. Increasing the length of the electret can reduce the resistance of the optimum load. The experimental results show trend consistent with the numerical predictions. The maximum output power can reach 404 μW (134.66 μW/cm²/g) at the electret length of 40 mm when the external acceleration and the frequency were 5 m/s² and 74 Hz, respectively. The maximum bandwidth reaches 2.5 Hz at the electret length of 60 mm. Therefore, the electret length should be placed between 40 mm and 60 mm, while ensuring a higher output power and also get a larger bandwidth in practical applications.