Optimization for output power and band width in out-of-plane vibration energy harvesters employing electrets theoretically, numerically and experimentally

In order to improve the performances of out-of-plane electret-based vibration energy harvesters (E-VEHs) in practical environment, we investigated the dependence of output power, resonance frequency and half power bandwidth on the load resistance for E-VEHs theoretically, numerically and experimentally. A linear analytical model is presented to describe the characteristics of E-VEHs qualitatively and the frequency response function of current versus acceleration excitation is obtained by Fourier transform when the ratio of mass amplitude to air gap is less than 0.28. In particular, the coupling effect of the electrostatic force not only changes E-VEHs’ effective stiffness but also changes it’s effective damping. The analytical and numerical investigation predicted the following results: (1) an optimum value exists in the load resistance to maximize the output power; (2) enhanced electrostatic forces with decreasing the load resistance emphasize the soft spring effect, which lowers the resonance frequency; (3) a load resistance exists to maximize the half power bandwidth. A small out-of-plane E-VEHs prototype was fabricated in this paper in order to verify our predictions. The experimental results showed behaviors consistent with the numerical predictions. The output power reach a maximum 0.028 mW during frequency up-sweep and 0.0274 mW during frequency down-sweep at optimum load resistance 60 MΩ when the external acceleration were 1 ms⁻² and 82.3 Hz, respectively. When increasing the load resistance to 330 MΩ, the half power bandwidth increased to 3.1 Hz during frequency up-sweep and 3.2 Hz during frequency down-sweep, increased 58.8 and 52.9% over optimum load resistance 60 MΩ, respectively. The peak output power at load resistance 330 MΩ was 0.0187 mW during frequency up-sweep and 0.0179 mW during frequency down-sweep, when the external acceleration were 1 ms⁻² and 82.3 Hz, respectively. Therefore, the load resistance should be placed between 60 and 330 MΩ, while ensuring a higher output power can also get a larger bandwidth in practical applications.