# A Review of MEMS Scale Piezoelectric Energy Harvester
## 2 Research Progress of PEH
### Optimization of Energy Harvesters' Structure
#### 2.4.1 Adjusting the Resonant Frequency  
The frequency of vibration energy available in environment is mostly below 200 Hz. However, most of the PEHs reported have a higher resonant frequency(above 200 Hz) [63]. To match the resonant frequency of the energy harvester and the external excitation frequency, an available scheme is to reduce the resonant frequency of the PEH.  
For the traditional cantilever PEH, the resonant frequency can be determined by the following equation:  
\[f=\frac{1}{2\pi}\sqrt{\frac{k}{m}} \tag{9}\]  
where \(k\) is the effective spring stiffness coefficient (inversely proportional to the effective length of the cantilever beam) and \(m\) represents the effective mass.  
According to Equation (9), it is possible to reduce the spring stiffness coefficient or to increase the mass to reduce the resonant frequency of the PEH and match the external excitation frequency. However, the length of the cantilever beam is limited in MEMS devices. To solve this problem, [PERSON] et al. [63] designed the S-shaped cantilever beam PEH in 2012. The structure is shown in Figure 5a. Figure 5b is a top view of the PEH and gives some dimensions. It can be found that the S-shaped cantilever beam reduces the spring stiffness factor in this design. A commonly used vibration testing system for the dynamic characterization of the PEH is shown in Figure 6. The assembled mechanism is fixed on a shaker. The vibration frequency and amplitude of the shaker are controlled through an amplifier. Then, the output voltage of the PEH is collected and recorded by the dynamic signal analyzer. The experimental results showed that the resonant frequency of the PEH was 27.4 Hz and the maximum output voltage was 42.1 mV for an acceleration of 0.06 g.  
Similar to [PERSON]'s design, [PERSON] et al. [64] declined the resonant frequency of the PEH by using S-shaped cantilever beam as well. A disk proof mass was attached to two or three PZT S-shaped spring flexures as shown in Figure 7a,b, respectively. The resonant frequency of the PEH could be tuned by adjusting the diameter of the proof mass. The simulation results showed that the resonant frequency of the PEH is related to the number of S-shaped spring flexures. The two-spring sensors had lower resonant frequencies than those of the three-spring sensors at the same dimension. However, as the number of springs increased, Q-factor of the device also increased.  
Figure 5: (a) Schematic of S-shaped cantilever PEH; (b) The top view of S-shaped cantilever PEH. Reprinted by permission from [PERSON] et al. Microsyst. Technol. 18, 497 (2012). Copyright 2012 Springer Nature.  
Figure 6: Experimental setup for the dynamic characterization. Reprinted by permission from [PERSON] et al. Microsyst. Technol. 18, 497 (2012). Copyright 2012 Springer Nature.  
Figure 7: Schematic view of the low-frequency PEH design: (a,b) two- and three-spring sensor structures, respectively. Reprinted by permission from [PERSON] et al. Rev. Sci. Instrum. 87, 085005 (2016). Copyright 2016 AIP Publishing LLC.  
In 2011, [PERSON] and [PERSON] [65] proposed a zigzag-shaped PEH. The structure was modeled as a collection of straight beams, with rectangular cross-sections, placed next to each other on the main plane. Each beam was connected to its neighbor beams at its ends by the link portions. The maximum power increased by adding the number of beams, but only to some extent (roughly by 2.5 times). The simulation results showed that when the number of beams reached to 9, the power it produced barely increased since the bending deformation in the structure was limited.  
Compared with the conventional straight cantilever, wavy cantilever beam had better bending stiffness [66]. The simulation showed that the resonant frequency of the harvester was lower than that of the conventional cantilever energy harvester. In addition, the output voltage of the PEH increased with the rising number of the corrugations and the ripple height.