# Experimental Study and Parameter Optimization of a Magnetic Coupled Piezoelectric Energy Harvester
## 4 Results and Discussion
### Discussion  
* Compared with the conventional cantilever beam energy harvester, the performance has been improved in terms of amplitude and frequency bandwidth by magnetic coupling. The increased performance increases the robustness of the system, which accommodates more complex operating conditions. * This paper focuses on the peak voltage, and the peak voltage error under the optimal parameter experiments are less than 6%. Among them, the error is 3.82%, 5.30%, 5.85% under the acceleration \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Ref.**} & **Estimated Size** & **Resonance Frequency** & **Excitation** & **Voltage** & **Power** & **Power Density** \\  & **(cm3)** & **(Hz)** & **(m/s2)** & **(V)** & **(\(\upmu\)W)** & **(\(\upmu\)W/cm3)** \\ \hline
[11] & 217.5 & 17.2 & 1 & 0.16 & 7400 & 34.02 \\
[15] & 0.6 & 30 & 17.5 & 5.8 & 18.56 & 30.93 \\
[19] & 139.95 & 21.02 & 10V a  & 61.55 & 6600 & 47.16 \\
[22] & 14.4 & 21.4 & 3 & 22.35 & 429 & 29.8 \\
[23] & 3.09 & Random & 1 & 21 & 48 & 15.53 \\
[This Work] & 63.6 & 15.3 & 4 & 19.83 & 3277 & 51.53 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparisons with reported devices. Figure 13: Optimal output voltage: **(a)** 1 m/s\({}^{2}\); **(b)** 10 m/s\({}^{2}\). condition of 1, 4, 10 m/s\({}^{2}\). It can be concluded preliminarily that the error increases with the excitation, but it is still within the acceptable range. In terms of frequency, the peak frequencies of the experiments are both 0.1 Hz larger than the simulation. The main sources of the above errors are the calculation of magnetic force, experimental error, and simplified error of the lumped parameter model. * The lumped parameter model of this paper can predict the characteristics of the system within acceptable error and can be used in the structural design. Parameter optimization should be operated in applications to maximize system performance. For example, in this paper, the amplitude can be increased by 35.0% and the 5 V bandwidth is increased by 66.7%. * After parameter optimization, the structure in this paper can get more than 3 mW of energy, which is enough to provide energy for some low power consumption devices. For example, the wake-up receiver of wireless sensor networks achieves an ultra-low power consumption of 4.5 nW [38]. ADI's commercial acceleration sensor ADXL362 consumes 3.6 uW at a sampling rate of 100 Hz, and the MCU ADuCM4050 achieves a low power consumption of 40 uA/MHz. Through a comprehensive power consumption consideration, the wireless sensor system can achieve consumption at \"mW\" or even \"uW\" level. Therefore, the energy demand can be met under the settings described in this paper. If the energy is not enough in some applications, a bimorph structure can be utilized to increase the energy. * If further power is required, more advanced composite materials can be used to increase the power. For example, the novel magneto-mechano-electric material combines electromagnetic and piezoelectric mechanisms [39], and a 3D-skeletal architecture piezoelectric ceramics can get about 16 times higher energy than the conventional PZT [40]. These materials are all suitable for the structure proposed in this paper because the performance is optimized by increasing the deformation of the cantilever beam. However, it may be increased in terms of cost and additional circuits, and the durability of the new materials should be considered. * From the perspective of cost savings, ordinary PZT materials can be used. It is important to note that the magnetic flux density parameter needs to be set smaller. Since the PZT is very brittle, the large magnetic force will increase the deflection and reduce the service life. * From the perspective of practical design, the structure of this paper increases the quality and volume of the system, which is increased by about 100%. In terms of cost, since piezoelectric materials are the main cost source, the cost increase is expected to be less than 20%.