Optimal geometry of a parallelized electret-based vibration energy harvester

Electret-based vibration energy harvesters often contain electrets forming a pattern of periodically repeated strips with period L to increase the output power by parallelization. Given a gap length g between the stationary electrets and the movable electrodes facing them, the natural question is how to choose L to maximize the output power. Our analysis, based on conformal mapping, shows that the optimal ratio L/g is represented by a rapidly convergent series starting with the dominant term pi = 3: 14, followed by terms amounting to a correction of less than 0.3%. We establish the practical relevance of this finding through an experiment involving a voltage-biased energy harvester.