Under an in-phase assumption, the complete charging for an energy harvesting system is studied, which consists of a piezoelectric energy harvester(PEH), a bridge rectifier, a filter capacitor, a switch, a controller and a rechargeable battery. For the transient charging, the results indicate that the voltage across the filter capacitor increases as the charging proceeds, which is consistent with that reported in the literature. However, a new finding shows that the charging rate and energy harvesting efficiency decrease over time after their respective peak values are acquired.For the steady-state charging, the results reveal that the energy harvesting efficiency can be adjusted by altering the critical charging voltage that controls the transition of the system. The optimal energy harvesting efficiency is limited by the optimal efficiency of the transient charging. Finally, the relationship between the critical charging voltage and the equivalent resistance of the controller and rechargeable battery is established explicitly.
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