# Development of a Nonlinear Piezoelectric Energy Harvester for Alternating Air Load
## 7 Results and Discussion
Thus, the root mean square (RMS) voltage can be decreased as the cycle time increases. Therefore, the cycle time of 2.5 s is used to research the performance of the RMS voltage and effective power. Figure 11 shows that the peak voltage and output power are tested at different load resistances. The conditions of these curves are tested using the above excitation process pressure of 200 kPa, at a cycle time of 2.5 s and a flow of 150 L/min. At the down-warping stage of the PZT patch, the output voltage and the power against the external load resistance are measured, and it is found that the peak voltage increases monotonically with increasing load resistance. The maximal peak voltage is 24.7 V, and the optimal output power is 1.06 mW, as shown in Figure 11a. At the spring-back stage of the PZT patch, the maximal peak voltage is 19.5 V, and the optimal output power is 0.97 mW, as shown in Figure 11b. Figure 10: Comparison of the different instantaneous curves: (**a**) the relationship between displacement and time; (**b**) the speed–time curve; (**c**) the relationship between pressure and time; (**d**) the voltage–time curve. The RMS voltage and the effective power are measured through the resistor load. Figure 12a shows the RMS voltage that is generated by the harvester, which can be changed with different pressures and resistive loads. As a result, effective power can be influenced by the compressed air pressure. In different pressure conditions, the effective powers are also different. Figure 12b shows that the optimal effective power is 0.28 mW through the 200 k\(\Omega\) resistor at a pressure of 200 kPa and cycle time of 2.5 s.  
The most classical energy collection technology is to only use the bridge rectifier and filter capacitor, and the nonlinear power can be adjusted and filtered by the classical energy collection circuit. Figure 13 shows the schematic of the standard rectifier circuit. The alternating electric energy can be adjusted by the bridge rectifier (\(D_{1}\), \(D_{2}\), \(D_{3}\) and \(D_{4}\)). The electric power can be stored in the capacitor \(C_{1}\). At last, the load \(R_{L}\) can consume the electric power. Figure 11: Peak voltage and output power versus load resistance: (**a**) the voltage and power in down-warping stage of PZT patch; (**b**) the voltage and power in the spring-back stage of PZT patch. Figure 12: Root mean square (RMS) voltage and effective power versus load resistance: (**a**) the RMS voltage; (**b**) the optimal effective power. Figure 13: Schematic of the standard rectifier circuit. Figure 14 shows the relationship between the storage voltage and time. The power has been stored in the capacitance. As the time increases, the storage voltage also increases. Figure 15 is the relationship between the energy and time. As the time increases, the energy is increasing, too. At the beginning, the energy is nearly the same in the differently compressed air. As the time increases, the energy is stabilizing. It is clear that the energy increases with the increase of the compressed air after 100 s.  
This phenomenon depends on the optimal output voltage on the capacitor. The capacitor has a starting voltage. Energy can be consumed due to the internal resistance in the capacitor when the energy is less than the starting voltage. After 100 s, the voltage is larger than the starting voltage. As a result, energy increases rapidly after 100 s.