**4. Results and Discussions**

#### *4.1. Fabrication Results of the EVEH Device*

The designed EVEH device (T1 device) was successfully fabricated and assembled, as shown in Figure 7a. Additionally, for the T2 device, the difference is the spring type shown in Figure 1c. The NdFeB disc magnet was glued to the bottom of the circular silicon microplate as the proof-mass (not visible in the photo). The magnet proof-mass was suspended by a long torsional beam above a stack of flexible coils. Under external vibration excitation, the relative position of the magnet and the coil changed to generate a changing magnetic field, and an electrical voltage was induced in the coil. The stacked flexible coils (clamped between two rigid FR4 frames) were mounted on the bottom of the EVEH device. Additionally, for a large number of turns, the thickness of the stacked flexible coils is reasonable. The thin substrates make it possible to have high-density coils close to the magnet. This is essential for the miniaturized device, as the magnetic field decays exponentially from the outer surface of the magnet. Through this coil design, the EVEH device can achieve high output power with a minimum footprint. The proposed technology is a general technology that can address the limitations of planar coils widely used in MEMS devices. This method is simple and cost effective because the coil stack is composed of repeating low-cost flexible layers. In addition, the distance between the magnet and the coils could be adjusted by the spacers between them. The flexible coil had an identical spiral coil on each side but with opposite winding directions, connected by the via in the center of the coil, as shown in Figure 7b. The electrode and dummy electrode were located at the edge of the film, and the positions were reversed on the other side of the coil layer. When two layers were clamped together (the electrodes were connected), a coil with four windings connected in series was formed. The dummy electrodes were patterned on each side of the coil layer to maintain the mechanical symmetry of the coil layer during stacking and clamping. For comparing the performance of four types of spring design, the coil size and the overall footprint of the EVEH in this work is the same as the device reported in [20], but the functional area of the silicon layer is greatly reduced, which has the potential to the goal of miniaturization. *Micromachines* **2021**, *12*, x FOR PEER REVIEW 8 of 13 (clamped between two rigid FR4 frames) were mounted on the bottom of the EVEH device. Additionally, for a large number of turns, the thickness of the stacked flexible coils is reasonable. The thin substrates make it possible to have high-density coils close to the magnet. This is essential for the miniaturized device, as the magnetic field decays exponentially from the outer surface of the magnet. Through this coil design, the EVEH device can achieve high output power with a minimum footprint. The proposed technology is a general technology that can address the limitations of planar coils widely used in MEMS devices. This method is simple and cost effective because the coil stack is composed of repeating low-cost flexible layers. In addition, the distance between the magnet and the coils could be adjusted by the spacers between them. The flexible coil had an identical spiral coil on each side but with opposite winding directions, connected by the via in the center of the coil, as shown in Figure 7b. The electrode and dummy electrode were located at the edge of the film, and the positions were reversed on the other side of the coil layer. When two layers were clamped together (the electrodes were connected), a coil with four windings connected in series was formed. The dummy electrodes were patterned on each side of the coil layer to maintain the mechanical symmetry of the coil layer during stacking and clamping. For comparing the performance of four types of spring design, the coil size and the overall footprint of the EVEH in this work is the same as the device reported in [20], but the functional area of the silicon layer is greatly reduced, which has the potential to the goal of miniaturization.

**Figure 7.** Photos of (**a**) assembled EVEH device (T1) and (**b**) a layer of the flexible coil. **Figure 7.** Photos of (**a**) assembled EVEH device (T1) and (**b**) a layer of the flexible coil.

#### *4.2. Open-Circuit Frequency Domain Response of the EVEH Device*

*4.2. Open-Circuit Frequency Domain Response of the EVEH Device*  Figure 8 shows the open-circuit peak-to-peak output voltage of the assembled EVEH device as a function of frequency, under a sinusoidal excitation (the most common vibration signal existing in both nature and industry), with an amplitude of ±0.5 g. The output voltage of the EVEH increases gradually as the frequency of the excitation vibration increases toward the resonant frequency, reaches a maximum value at resonance and then Figure 8 shows the open-circuit peak-to-peak output voltage of the assembled EVEH device as a function of frequency, under a sinusoidal excitation (the most common vibration signal existing in both nature and industry), with an amplitude of ±0.5 g. The output voltage of the EVEH increases gradually as the frequency of the excitation vibration increases toward the resonant frequency, reaches a maximum value at resonance and then decreases again as the frequency further increases. For device T1, at the resonant

decreases again as the frequency further increases. For device T1, at the resonant fre-

the resonant frequency of 96 Hz. It is known that most of the ambient vibrations concentrate in the frequency band of 1–200 Hz, the resonant frequency around 100 Hz of the devices T1 and T2 may find applications in several industrial scenarios such as power transformers, transmission lines, and power inductors. In comparison, the open-circuit peak-to-peak output voltage of the EVEH devices presented in [20] is 208.3 mV at the frequency of 143 Hz for D1 and 149.3 mV at the frequency of 156 Hz for D2. Additionally, the functional area of T1, T2, D1, and D2 are 20.3 mm2, 20.6 mm2, 23.4 mm2 and 24.1 mm2, respectively. Thus, the torsional springs with a reduced functional area of the silicon layer

and lower frequency generate a higher output voltage.

frequency of 104 Hz, the output voltage reaches the maximum peak-to-peak value of 138.9 mV. For device T2, the maximum open-circuit peak-to-peak output voltage is 169 mV at the resonant frequency of 96 Hz. It is known that most of the ambient vibrations concentrate in the frequency band of 1–200 Hz, the resonant frequency around 100 Hz of the devices T1 and T2 may find applications in several industrial scenarios such as power transformers, transmission lines, and power inductors. In comparison, the open-circuit peak-to-peak output voltage of the EVEH devices presented in [20] is 208.3 mV at the frequency of 143 Hz for D1 and 149.3 mV at the frequency of 156 Hz for D2. Additionally, the functional area of T1, T2, D1, and D2 are 20.3 mm<sup>2</sup> , 20.6 mm<sup>2</sup> , 23.4 mm<sup>2</sup> and 24.1 mm<sup>2</sup> , respectively. Thus, the torsional springs with a reduced functional area of the silicon layer and lower frequency generate a higher output voltage. *Micromachines* **2021**, *12*, x FOR PEER REVIEW 9 of 13

**Figure 8.** The peak-to-peak open-circuit output voltage of the EVEH as a function of frequency: (**a**) T1 device; (**b**) T2 device. **Figure 8.** The peak-to-peak open-circuit output voltage of the EVEH as a function of frequency: (**a**) T1 device; (**b**) T2 device.

The presented energy harvester (T1 device) achieves 10 times higher maximum output voltage at 3.8 times lower resonant frequency, compared with a two-degree-of-freedom EVEH based on coils suspended by springs [24], and almost 188 times higher maximum output voltage at 1.2 times lower resonant frequency, compared with an EVEH based on magnet suspended by folded springs reported in 2014 [25]. Compared with the traditional planar coil used in MEMS or PCB technologies, the optimized performance of the EVEH device results from the stacked flexible coils, which greatly enhance the number of turns of the coils. The presented energy harvester (T1 device) achieves 10 times higher maximum output voltage at 3.8 times lower resonant frequency, compared with a two-degree-of-freedom EVEH based on coils suspended by springs [24], and almost 188 times higher maximum output voltage at 1.2 times lower resonant frequency, compared with an EVEH based on magnet suspended by folded springs reported in 2014 [25]. Compared with the traditional planar coil used in MEMS or PCB technologies, the optimized performance of the EVEH device results from the stacked flexible coils, which greatly enhance the number of turns of the coils.

#### *4.3. Impedance Matching 4.3. Impedance Matching*

Hz) for the D2 device.

To study the optimal closed-circuit behavior of the EVEH, matching resistors between 1 Ω and 1000 Ω were connected to the output of the energy harvester. Through the measured closed-circuit voltage, the output power of the EVEH can be described as To study the optimal closed-circuit behavior of the EVEH, matching resistors between 1 Ω and 1000 Ω were connected to the output of the energy harvester. Through the measured closed-circuit voltage, the output power of the EVEH can be described as

$$P = \frac{V\_{rms}^2}{R\_L} = \frac{V\_{pp}^2}{8R\_L} \tag{8}$$

where *Vrms* is the root-mean-square voltage over the matching resistor, *RL* is the resistance where *Vrms* is the root-mean-square voltage over the matching resistor, *R<sup>L</sup>* is the resistance of the matching resistor, and *Vpp* is the peak-to-peak voltage over the matching resistor.

*L L*

of the matching resistor, and *Vpp* is the peak-to-peak voltage over the matching resistor. Figure 9 shows the closed-circuit peak-to-peak output voltage and output power of the EVEH device as a function of the load resistance, under a sinusoidal excitation with an amplitude of ±0.5 g and frequency of 104 Hz for T1 device (96 Hz for T2 device). For both types of devices, the internal (coil) resistance of the EVEH under test is 128.7 Ω. With the increase in load resistance, the output voltage of the EVEH first increases sharply and then decreases gradually. For the T1 device, the maximum power measured is 4.6 μW at Figure 9 shows the closed-circuit peak-to-peak output voltage and output power of the EVEH device as a function of the load resistance, under a sinusoidal excitation with an amplitude of ±0.5 g and frequency of 104 Hz for T1 device (96 Hz for T2 device). For both types of devices, the internal (coil) resistance of the EVEH under test is 128.7 Ω. With the increase in load resistance, the output voltage of the EVEH first increases sharply and then decreases gradually. For the T1 device, the maximum power measured is 4.6 µW at

the load resistance of 128.7 Ω and the resonant frequency of 104 Hz. In comparison, the

designs of the proposed torsional EVEHs have lower frequencies than previous work in [20]; the maximum output power is 10.5 μW (143 Hz) for the D1 device and 5.4 μW (156

the load resistance of 128.7 Ω and the resonant frequency of 104 Hz. In comparison, the T2 device has a maximum power measured as 6.9 µW at the load resistance of 128.7 Ω and the resonant frequency of 96 Hz. Additionally, with the same coil resistance, both designs of the proposed torsional EVEHs have lower frequencies than previous work in [20]; the maximum output power is 10.5 µW (143 Hz) for the D1 device and 5.4 µW (156 Hz) for the D2 device. *Micromachines* **2021**, *12*, x FOR PEER REVIEW 10 of 13

**Figure 9.** The peak-to-peak output voltage and power of the EVEH as a function of load resistance: (**a**) T1 device; (**b**) T2 device. **Figure 9.** The peak-to-peak output voltage and power of the EVEH as a function of load resistance: (**a**) T1 device; (**b**) T2 device.

#### *4.4. Closed-Circuit Frequency-Domain Response of the EVEH Device 4.4. Closed-Circuit Frequency-Domain Response of the EVEH Device*

Figure 10 shows the closed-circuit peak-to-peak output voltage and output power of the EVEH device when connected to a load resistance of 128.7 Ω. The measurements were performed under sinusoidal excitation of ±0.5 g. For the T1 device, the maximum peak-topeak closed-circuit output voltage is 69.4 mV at 104 Hz (resonant frequency). For device T2, the maximum peak-to-peak closed-circuit output voltage of the EVEH is 84 mV at 96 Hz (resonant frequency). Due to the similar values of the coil and load resistance, the closed-circuit output voltage is approximately half of the open-circuit voltage in Figure 8. The maximum power device T1 and T2 are 4.6 μW at the frequency of 104 Hz and 6.9 μW at the frequency of 96 Hz, respectively. The performance of the EVEH device is improved, compared with recently reported work with similar technologies, in terms of output voltage, power, and resonant frequency (low resonant frequency is preferable for matching to the low-frequency ambient vibrations). For example, Zhang et al. reported an EVEH based on MEMS technology with an output power of 0.82 μW at the resonant frequency of 350 Hz under the acceleration of 4.5 g [26]. Tao et al. reported a MEMS electromagnetic vibration energy harvester with two degrees of freedom; the maximum amplitude of the output voltage in the study is 6.5 mV at the resonant frequency of 391 Hz [24]. The maximum closed-circuit output power of 4.6 μW (T1 device) is 4792 times higher than the maximum closed-circuit output power of 0.96 nW with an optimum load resistance of 12 kΩ at 0.12 g vibration reported in [24]. Since the volume of the EVEH device and external excitation vibration (*A0*) have a greater impact on device performance, to accurately describe it, the normalized power density (NPD) is given by Figure 10 shows the closed-circuit peak-to-peak output voltage and output power of the EVEH device when connected to a load resistance of 128.7 Ω. The measurements were performed under sinusoidal excitation of ±0.5 g. For the T1 device, the maximum peak-to-peak closed-circuit output voltage is 69.4 mV at 104 Hz (resonant frequency). For device T2, the maximum peak-to-peak closed-circuit output voltage of the EVEH is 84 mV at 96 Hz (resonant frequency). Due to the similar values of the coil and load resistance, the closed-circuit output voltage is approximately half of the open-circuit voltage in Figure 8. The maximum power device T1 and T2 are 4.6 µW at the frequency of 104 Hz and 6.9 µW at the frequency of 96 Hz, respectively. The performance of the EVEH device is improved, compared with recently reported work with similar technologies, in terms of output voltage, power, and resonant frequency (low resonant frequency is preferable for matching to the low-frequency ambient vibrations). For example, Zhang et al. reported an EVEH based on MEMS technology with an output power of 0.82 µW at the resonant frequency of 350 Hz under the acceleration of 4.5 g [26]. Tao et al. reported a MEMS electromagnetic vibration energy harvester with two degrees of freedom; the maximum amplitude of the output voltage in the study is 6.5 mV at the resonant frequency of 391 Hz [24]. The maximum closed-circuit output power of 4.6 µW (T1 device) is 4792 times higher than the maximum closed-circuit output power of 0.96 nW with an optimum load resistance of 12 kΩ at 0.12 g vibration reported in [24]. Since the volume of the EVEH device and external excitation vibration (*A*0) have a greater impact on device performance, to accurately describe it, the normalized power density (NPD) is given by

The calculated NPD values of the T1 device and T2 device are 17.04 (μW/cm3/g2) and 25.56 (μW/cm3/g2), respectively. Additionally, the NPD value is 38.89 (μW/cm3/g2) for D1 device and 20 (μW/cm3/g2) for D2 device [20]. Tao et al. reported a MEMS electromagnetic vibration energy harvester with two degrees of freedom in 2016 with the NPD value of up to 0.23 (μW/cm3/g2) at the resonant frequency of 391 Hz from 0.02 to 0.2 g [24]. Liu et al.

2014 with the NPD value of 0.62 × 10−2 (μW/cm3/g2) at the resonant frequency of 146.5 Hz and acceleration of 3 g [25]. Compared with the work reported in [24], the coil resistance

$$\text{NPD} = \frac{P}{\text{Volume} \cdot A\_0^2} \tag{9}$$

power of the proposed EVEH device can be further enhanced.

**Figure 10.** The peak-to-peak closed-circuit output voltage and power of the EVEH device as a function of frequency: (**a**) T1 device; (**b**) T2 device. **Figure 10.** The peak-to-peak closed-circuit output voltage and power of the EVEH device as a function of frequency: (**a**) T1 device; (**b**) T2 device.

*4.5. Acceleration Test*  The dependence of the EVEHs output on the acceleration level was studied, and the open-circuit and closed-circuit peak-to-peak output voltages of the EVEH device were measured as a function of acceleration, as shown in Figure 11. All data were obtained at EVEH's resonant frequency of 104 Hz, for the T1 device, and 96 Hz for the T2 device; the applied peak-to-peak acceleration increases from 1 g to 7 g (step length is 1 g). At acceleration higher than 7 g, the distance between coil and magnet must be increased to reduce the potential collision. The magnet–coil distance can be increased by simply changing the thickness of the spacers. At an acceleration of 7 g, the maximum peak-to-peak open-circuit output voltage is 185.2 mV and 222 mV for device T1 for T2, respectively. Compared with a previous work, also based on microfabricated springs, where the maximum peak-topeak open-circuit output voltage is 333.1 mV and 225.5 mV at 7 g [20], the output voltage– acceleration relationship in this work shows a similar trend but lower maximum voltage at higher acceleration levels. The output voltage in [20] increases almost linearly as the The calculated NPD values of the T1 device and T2 device are 17.04 (µW/cm3/g<sup>2</sup> ) and 25.56 (µW/cm3/g<sup>2</sup> ), respectively. Additionally, the NPD value is 38.89 (µW/cm3/g<sup>2</sup> ) for D1 device and 20 (µW/cm3/g<sup>2</sup> ) for D2 device [20]. Tao et al. reported a MEMS electromagnetic vibration energy harvester with two degrees of freedom in 2016 with the NPD value of up to 0.23 (µW/cm3/g<sup>2</sup> ) at the resonant frequency of 391 Hz from 0.02 to 0.2 g [24]. Liu et al. reported an in-plane approximated nonlinear MEMS electromagnetic energy harvester in 2014 with the NPD value of 0.62 <sup>×</sup> <sup>10</sup>−<sup>2</sup> (µW/cm3/g<sup>2</sup> ) at the resonant frequency of 146.5 Hz and acceleration of 3 g [25]. Compared with the work reported in [24], the coil resistance in this work is much smaller, so the increase in closed-circuit output power is much bigger than the square of the increase in open-circuit output voltage (see discussions about Figure 8). In addition, with the same footprint, the device T2 has increased its NPD by 50%, compared with T1, indicating the good potential of optimization for the torsional design of the EVEH device. For future optimization of the springs, coils, and magnets, the output power of the proposed EVEH device can be further enhanced.

in this work is much smaller, so the increase in closed-circuit output power is much bigger than the square of the increase in open-circuit output voltage (see discussions about Figure 8). In addition, with the same footprint, the device T2 has increased its NPD by 50%, compared with T1, indicating the good potential of optimization for the torsional design of the EVEH device. For future optimization of the springs, coils, and magnets, the output

#### acceleration increases, whereas the output voltage of devices shows a gradually decreas-*4.5. Acceleration Test*

ing rate of enhancement as the acceleration increases. The possible explanation for this phenomenon is that the shear strain induced in the single-beam torsional spring is much larger than the shear strain in the multibeam folded spring, at the same acceleration. Therefore, at elevated acceleration, nonlinearity in the torsional spring arises and limits the deflection angle of the magnet, which reduces the amplitude of enhancement of the output voltage. In addition, it is increasingly difficult for the magnet to maintain its movement perpendicular to the coil plane (z direction) as the vibration excitation acceleration increases, and there will be a tendency to twist in the x or y direction. The torsional vibration tendency will reduce the working efficiency of the device, thereby reducing the output voltage of the device. The closed-circuit output voltage shows a similar linear characteristic to the open-circuit output but with half of the amplitude of the open-circuit output. The dependence of the EVEHs output on the acceleration level was studied, and the open-circuit and closed-circuit peak-to-peak output voltages of the EVEH device were measured as a function of acceleration, as shown in Figure 11. All data were obtained at EVEH's resonant frequency of 104 Hz, for the T1 device, and 96 Hz for the T2 device; the applied peak-to-peak acceleration increases from 1 g to 7 g (step length is 1 g). At acceleration higher than 7 g, the distance between coil and magnet must be increased to reduce the potential collision. The magnet–coil distance can be increased by simply changing the thickness of the spacers. At an acceleration of 7 g, the maximum peak-to-peak open-circuit output voltage is 185.2 mV and 222 mV for device T1 for T2, respectively. Compared with a previous work, also based on microfabricated springs, where the maximum peak-to-peak open-circuit output voltage is 333.1 mV and 225.5 mV at 7 g [20], the output voltage–acceleration relationship in this work shows a similar trend but lower maximum voltage at higher acceleration levels. The output voltage in [20] increases almost linearly as the acceleration increases, whereas the output voltage of devices shows a gradually decreasing rate of enhancement as the acceleration increases. The possible explanation for this phenomenon is that the shear strain induced in the single-beam torsional spring is much larger than the shear strain in the multibeam folded spring, at the same acceleration. Therefore, at elevated acceleration, nonlinearity in the torsional spring arises and limits the deflection angle of the magnet, which reduces the amplitude of enhancement of the output voltage. In addition, it is increasingly difficult for the magnet to maintain its movement

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**Figure 11.** The peak-to-peak output voltage measured in the open circuit and closed circuit at different accelerations: (**a**) T1 device; (**b**) T2 device. **Figure 11.** The peak-to-peak output voltage measured in the open circuit and closed circuit at different accelerations: (**a**) T1 device; (**b**) T2 device.

#### **5. Conclusions 5. Conclusions**

In this work, an EVEH device was designed and fabricated based on hybrid PCB and MEMS technology. The proposed EVEH was composed of a stack of flexible coils and a disc permanent magnet mounted vertically. The assembled EVEH was excited by sinusoidal accelerations and its dynamic behavior was characterized. At a sinusoidal acceleration with a peak-to-peak value of 1 g (±0.5 g, ±4.9 m/s²), a maximum output peak-to-peak voltage of 169 mV and output power of 6.9 μW are realized at a resonant frequency of 96 Hz. At an elevated acceleration of 7 g (±3.5 g), a maximum output peak-to-peak voltage of 222 mV is realized. In the future, the bonding technologies between the stacked coils and silicon proof mass will be explored. In this work, an EVEH device was designed and fabricated based on hybrid PCB and MEMS technology. The proposed EVEH was composed of a stack of flexible coils and a disc permanent magnet mounted vertically. The assembled EVEH was excited by sinusoidal accelerations and its dynamic behavior was characterized. At a sinusoidal acceleration with a peak-to-peak value of 1 g (±0.5 g, <sup>±</sup>4.9 m/s<sup>2</sup> ), a maximum output peak-to-peak voltage of 169 mV and output power of 6.9 µW are realized at a resonant frequency of 96 Hz. At an elevated acceleration of 7 g (±3.5 g), a maximum output peak-to-peak voltage of 222 mV is realized. In the future, the bonding technologies between the stacked coils and silicon proof mass will be explored.

**Author Contributions:** Conceptualization, K.T. and Y.L.; methodology, X.W. and J.L.; formal analysis, D.Q.; investigation, X.W., J.L. and K.T.; data curation, C.Z.; writing—original draft preparation, X.W.; writing—review and editing, Y.L. All authors have read and agreed to the published version of the manuscript. **Author Contributions:** Conceptualization, K.T. and Y.L.; methodology, X.W. and J.L.; formal analysis, D.Q.; investigation, X.W., J.L. and K.T.; data curation, C.Z.; writing—original draft preparation, X.W.; writing—review and editing, Y.L. All authors have read and agreed to the published version of the manuscript.

**Funding**: This research received no external funding. **Funding:** This research received no external funding.

**Data Availability Statement:** The data presented in this study are available in [insert article or supplementary material here]. **Data Availability Statement:** The data presented in this study are available in [insert article or supplementary material here].

**Acknowledgments:** The authors would like to thank Junyuan Wang for fruitful discussions on modeling the EVEH devices. **Acknowledgments:** The authors would like to thank Junyuan Wang for fruitful discussions on modeling the EVEH devices.

**Conflicts of Interest:** The authors declare no conflict of interest. **Conflicts of Interest:** The authors declare no conflict of interest.

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