Frequency domain analysis of a piezoelectric energy harvester with impedance matching network

Piezoelectric energy harvesters are electromechanical systems, capable to convert ambient dispersed mechanical vibrations into usable electrical energy. They can be used for supplying power to sensors and actuators that are wireless connected, miniaturized and remote located. In this work, we analyze piezoelectric energy harvesters for mechanical vibrations in the frequency domain. White Gaussian and colored noise models for random vibrations are considered. The governing equations for the harvester are derived from mechanical properties, the characteristic relationships of piezoelectric materials, and circuit description of the electrical load. We show that the energy harvester can be modelled by cascade connected electromechanical two-ports, and that frequency domain methods are the perfect tool for analysis. Formulas for the harvested power and power efficiency are derived. We also show that application of matching networks reduces the impedance mismatch between the mechanical and the electrical parts, significantly increasing the harvested power and power efficiency. The matching network solution is compared to others, previously proposed solutions, such as application of power-factor correction. We show that the matching network offers nine times more average power and better power efficiency than the unmatched resistive load, and increases by more than 10% the harvested power and efficiency, with respect to the power-factor corrected solution.