# Comparison of Four Electrical Interfacing Circuits in Frequency Up-Conversion Piezoelectric Energy Harvesting

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Model

#### 2.1. Device Configuration and Working Principle

#### 2.2. Modeling of the FUC Energy Harvesting System

#### 2.3. Voltage Model

#### 2.4. Energy Extraction Circuit

_{r}). The load resistance (R

_{load}) represents the equivalent input resistance of the following electronic module to be supplied. The diode is equivalent to an ideal diode, and the voltage drop V

_{D}and its loss are ignored. When V

_{P}> V

_{load}, the SEH circuit can transfer the energy generated by the piezoelectric element to the load end. The synchronous electrical charge extraction [28,44,45], as shown in Figure 1b, is an improvement of the standard circuit, which adds an inductance L, a switch S and a diode D between the rectifier bridge and the filter capacitor. In addition, a peak detection circuit is added to control the switch. The peak detection circuit is composed of an envelope detection circuit (1) and a comparator circuit (2). When the switch S is closed, L-C

_{0}circuit oscillation is established, and the charge accumulated in the clamped capacitor C

_{0}is transferred to the inductor L. After one quarter of the oscillation cycle, the energy stored on the inductor is transferred to the load once the switch is opened. The left side of the transformer is the primary-side coil, and the right side is the secondary-side coil. Parallel synchronized switch harvesting on inductor [46,47] is shown in Figure 1c. Compared with the standard circuit, an inductance, two electronic switches S and two identical peak detection circuits are added. The peak detection forces the corresponding switch to open when the output voltage of the piezoelectric element is the maximum value of the positive half cycle and to close when it is the minimum value of the negative half cycle. The peak circuit on the right is opposite to that on the left. When the mechanical displacement reaches the maximum and minimum values, the two switches S are closed alternately to establish L-C

_{0}circuit oscillation. After the switch is closed for half an oscillation period, the piezoelectric voltage is inverted. The optimized synchronous electrical charge extraction is shown in Figure 1d. The flyback transformer is used to replace the inductor. The transformer divides the circuit into two parts. The left part is similar to the parallel-switch circuit, in which the peak detection circuit and the electronic switch circuit are the same as the parallel-switch circuit. The left part of the transformer is the primary-side coil, and the right part is the secondary-side coil. The two switches are closed alternately in a vibration cycle. This switching strategy allows the voltage to be reversed twice in a vibration cycle. The power calculations of the four circuits are shown in Table 1.

## 3. Experimental Results

#### 3.1. Experimental Setup

#### 3.2. Experiments under Steady-State Conditions

_{I}and the diode connected to the primary-side coil become larger. In addition, the charge neutralization effect is increasingly obvious, and the capacitance value of the piezoelectric elements used is small, resulting in lower and lower efficiencies of the SP-OSECE circuit. The dissipation of SP-SECE is mainly caused by the full-bridge circuit and the circuit quality Q

_{I}, which have a relatively small growth range along with an increasing resistance. From the perspective of circuit structure, SP-SSHI has no secondary-side coils and diodes. Therefore, the energy dissipation of the SP-SSHI circuit is less than that of SP-SECE and SP-OSECE with a higher efficiency. In the steady state, in order to avoid the influence of electromechanical coupling and to focus on the circuits, the constant displacement case is considered first with the tip displacement of the high-frequency beam kept at 1 mm, while the resistance changes from 10 KΩ to 2 MΩ. The output power results are shown in Figure 5a. The SP-SSHI circuit is the best when it is above 100 KΩ, and the SP-OSECE circuit is the best when it is below 100 KΩ. Their general trends are basically the same, but there is a slight difference. From Figure 5a, it can be seen that the power of SP-OSECE with a large resistance at constant displacement decreases faster than that of the constant force. This is because more energy is extracted from the piezoelectric elements with a large resistance at constant displacement, but the dissipation is also large. As shown in Figure 5b, in the case of constant force, the coupling level decreases, and SP-OSECE becomes outstanding.

#### 3.3. Experiments under Frequency Up-Conversion Conditions

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Configuration of the FUC energy harvesting system. (

**a**) SEH circuit and wave of piezoelectric voltage (

**b**) SP-SECE circuit and waveforms of piezoelectric voltage (

**c**) SP-SSHI circuit and waveform s of piezoelectric voltage (

**d**) SP-OSECE circuit and waveforms of piezoelectric voltage (

**e**) Mechanical structure of FUC.

**Figure 3.**(

**a**) The mechanical part of the experimental system for steady-state conditions; (

**b**) the mechanical part of the experimental system for frequency up-conversion; (

**c**) interface circuit of experimental systems.

**Figure 4.**Efficiency of different loads under two piezoelectric plates at constant displacement of 1 mm (${k}^{2}{Q}_{m}=0.63$).

**Figure 5.**(

**a**) Power of different loads at constant displacement of 1 mm and constant force (${k}^{2}{Q}_{m}=0.63$); (

**b**) power of different loads at ${k}^{2}{Q}_{m}=0.63$ and$\text{}{k}^{2}{Q}_{m}=0.3072$.

**Figure 9.**Power under different electromechanical coupling coefficients. (

**a**) Coupling coefficient ${k}^{2}{Q}_{m}$ = 0.3072; (

**b**) coupling coefficient ${k}^{2}{Q}_{m}$ = 0.192; (

**c**) coupling coefficient ${k}^{2}{Q}_{m}$ = 0.1472; (

**d**) coupling coefficient ${k}^{2}{Q}_{m}$ = 0.1088.

Interface | Harvested Power |
---|---|

SEH | $P=\frac{\pi {k}^{2}{Q}_{m}}{{\left[\frac{\pi}{4}+\frac{{\zeta}_{R}}{{\left(1+{\zeta}_{R}\right)}^{2}}{k}^{2}{Q}_{m}\right]}^{2}}\frac{{\zeta}_{R}{}^{*}}{{\left(1+{\zeta}_{R}\right)}^{2}}$ |

SP-SSHI | $P=4{f}_{0}{C}_{0}{V}_{S}\left[{V}_{P}-{V}_{D}+{V}_{D}{e}^{-\pi /2{Q}_{I}}\right]-2{f}_{0}{C}_{0}{V}_{S}{}^{2}\left(1-{e}^{-\pi /2{Q}_{I}}\right)$ |

SP-SECE | $P=\frac{\pi {k}^{2}{Q}_{m}}{{\left[\frac{\pi}{4}+{k}^{2}{Q}_{m}\right]}^{2}}{e}^{-\pi /2{Q}_{I}}$ |

SP-OSECE | $P=\frac{\pi {k}^{2}{Q}_{m}}{{\left[\frac{\pi}{4}+X{k}^{2}{Q}_{m}\right]}^{2}}\frac{si{n}^{2}\left({\omega}_{I}{t}_{m}\right){e}^{\frac{-{\omega}_{I}{t}_{m}}{{Q}_{I}}}}{{\left[1+{\epsilon}_{c}+\mathrm{cos}\left({\omega}_{I}{t}_{m}\right){e}^{\frac{-{\omega}_{I}{t}_{m}}{2{Q}_{I}}}\right]}^{2}}\frac{{\left(2-2{\epsilon}_{v2}-{\epsilon}_{v2}{\epsilon}_{c}\right)}^{2}}{4}$ |

_{0}oscillating circuit, ${k}^{2}{Q}_{m}$ is the figure of merit of the electromechanical structure, ${\epsilon}_{v2}$ is voltage ratio and ${\omega}_{I}{t}_{m}=\mathrm{arctan}\left(-\frac{2}{\sqrt{{\zeta}_{R}}}\right)$+$\pi $, ${\epsilon}_{c}=\frac{{C}_{p}}{{C}_{0}}$.

Definition | Value | Definition | Value |
---|---|---|---|

Diode (D_{i}, D_{pi}) | BAQ135 | C_{r} | 100 uF |

Transformer | MSD1278T-105KL | R_{bi} | 3.3 kΩ |

BJT (S_{i}) | MMBTA05LT1G | R_{gi} | 1 MΩ |

R_{load} | Pin-type resistance (external connection) | R_{pi} | 100 kΩ |

Transistor (T_{pi}) | MMBTA56 | C_{pi} | 1 nf |

Inductance L_{1}, L_{2}, L_{3} (H) | 1 × 10^{−3} |

Parameter | Value |
---|---|

Clamped capacitance of the piezoelectric element C_{0} (F) | 20.68 × 10^{−9} |

Piezoelectric coefficient α (N/V) | 5.557 × 10^{−4} |

Open-circuit mechanical quality factor Q_{m} | 63.8 |

Squared electromechanical coupling coefficient k^{2} | 0.01 |

Open-circuit resonance frequency of HFB f_{1} (Hz) | 36.25 |

Stiffness of high-frequency beams (N/m) | 1450 |

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**MDPI and ACS Style**

Lu, H.; Chen, K.; Tang, H.; Liu, W.
Comparison of Four Electrical Interfacing Circuits in Frequency Up-Conversion Piezoelectric Energy Harvesting. *Micromachines* **2022**, *13*, 1596.
https://doi.org/10.3390/mi13101596

**AMA Style**

Lu H, Chen K, Tang H, Liu W.
Comparison of Four Electrical Interfacing Circuits in Frequency Up-Conversion Piezoelectric Energy Harvesting. *Micromachines*. 2022; 13(10):1596.
https://doi.org/10.3390/mi13101596

**Chicago/Turabian Style**

Lu, Han, Kairui Chen, Hao Tang, and Weiqun Liu.
2022. "Comparison of Four Electrical Interfacing Circuits in Frequency Up-Conversion Piezoelectric Energy Harvesting" *Micromachines* 13, no. 10: 1596.
https://doi.org/10.3390/mi13101596