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The performance of cantilever-beam piezoelectric energy harvester is usually analyzed with pure resistive circuit. The optimal performance of such a vibration-based energy harvesting system is limited by narrow bandwidth around its modified natural frequency. For broadband piezoelectric energy harvesting, series and parallel inductive-resistive circuits are introduced. The electromechanical coupled distributed parameter models for such systems under harmonic base excitations are decoupled with modified natural frequency and electrical damping to consider the coupling effect. Analytical solutions of the harvested power and tip displacement for the electromechanical decoupled model are confirmed with numerical solutions for the coupled model. The optimal performance of piezoelectric energy harvesting with inductive-resistive circuits is revealed theoretically as constant maximal power at any excitation frequency. This is achieved by the scenarios of matching the modified natural frequency with the excitation frequency and equating the electrical damping to the mechanical damping. The inductance and load resistance should be simultaneously tuned to their optimal values, which may not be applicable for very high electromechanical coupling systems when the excitation frequency is higher than their natural frequencies. With identical optimal performance, the series inductive-resistive circuit is recommended for relatively small load resistance, while the parallel inductive-resistive circuit is suggested for relatively large load resistance. This study provides a simplified optimization method for broadband piezoelectric energy harvesters with inductive-resistive circuits

Optimization study on inductive-resistive circuit for broadband piezoelectric energy harvesters