Optimal parameters and power characteristics of piezoelectric energy harvesters with an RC circuit

A piezoelectric based energy harvesting scheme is proposed here which places a capacitor before the load in the conditioning circuit. It is well known that the impedance between the load and source contributes heavily to the performance of the energy harvesting system. The additional capacitor provides flexibility in meeting the optimal impedance value and can be used to expand the bandwidth of the system. A theoretical model of the system is derived and the response of the system as a function of both resistance and capacitance is studied. The analysis shows that the energy harvesting performance is dominated by a bifurcation occurring as the electromechanical coupling increases above a certain value, below this point the addition of an additional capacitor does not increase the performance of the systems and above the maximum power can be achieved at all point between these two bifurcation frequencies. Additionally, it has been found that the optimal capacitance is independent of the optimal resistance. Therefore, the necessary capacitance can be chosen and then the resistance determined to provide optimal energy harvesting at the desired frequencies. For systems with low coupling the optimal added capacitance is negative (additional power to the circuit) indicating that a second capacitor should not be used for. For systems with high coupling the optimal capacitance becomes positive for a range of values inside the bifurcation frequencies and can be used to extend the bandwidth of the harvesting system. The analysis also demonstrates that the same maximum energy can be harvested at any frequency; however, outside the two bifurcation frequencies the capacitor must be negative.