# Push–Pull Inverter Using Amplitude Control and Frequency Tracking for Piezoelectric Transducers

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Analysis

#### 2.1. Equivalent Circuit Model

#### 2.2. The Extraction of ${f}_{p}$

#### 2.3. Detection of Amplitude

## 3. Implementation of the Proposed Scheme

#### 3.1. Voltage Sensing Scheme in Push–Pull Topology

#### 3.2. Hardware Structure

#### 3.3. Control Structure

## 4. Experiment Results

#### 4.1. Experiment Setup

#### 4.2. Verification of Amplitude and Feedback Voltage

#### 4.3. Experimental Results in Glycerin and Chicken Tissue

#### 4.4. Experimental Results in Ultrasonic Motors

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Zeng, Y.; Wang, X.K.; Qin, X.P.; Hua, L.; Xu, M. Laser Ultrasonic inspection of a Wire plus Arc Additive Manufactured (WAAM) sample with artificial defects. Ultrasonics
**2021**, 110, 15. [Google Scholar] [CrossRef] - Perez-Sanchez, A.; Segura, J.A.; Rubio-Gonzalez, C.; Baldenegro-Perez, L.A.; Soto-Cajiga, J.A. Numerical design and analysis of a langevin power ultrasonic transducer for acoustic cavitation generation. Sens. Actuator A-Phys.
**2020**, 311, 112035. [Google Scholar] [CrossRef] - Yu, P.P.; Wang, L.; Jin, J.M.; Ye, Z.L.; Chen, D. A novel piezoelectric actuated underwater robotic finger. Smart Mater. Struct.
**2019**, 28, 105047. [Google Scholar] [CrossRef] - Cui, X.Y.; Yu, Y.H.; Liu, Q.J.; Liu, X.; Qing, X.L. Full-field monitoring of the resin flow front and dry spot with noninvasive and embedded piezoelectric sensor networks. Smart Mater. Struct.
**2023**, 32, 085021. [Google Scholar] [CrossRef] - He, S.F.; Tang, H.; Zhu, Z.Y.; Zhang, P.Y.; Xu, Y.; Chen, X. A Novel Flexure Piezomotor With Minimized Backward and Nonlinear Motion Effect. IEEE Trans. Ind. Electron.
**2022**, 69, 652–662. [Google Scholar] [CrossRef] - Wang, J.D.; Jiang, J.J.; Duan, F.J.; Zhang, F.M.; Liu, W.; Qu, X.H. A Novel Fast Resonance Frequency Tracking Method Based on the Admittance Circle for Ultrasonic Transducers. IEEE Trans. Ind. Electron.
**2020**, 67, 6864–6873. [Google Scholar] [CrossRef] - Gao, L.; Yang, S.L.; Meng, B.; Tong, G.X.; Fan, H.P.; Yang, G.S. Frequency matching optimization model of ultrasonic scalpel transducer based on neural network and reinforcement learning. Eng. Appl. Artif. Intell.
**2023**, 117, 105572. [Google Scholar] [CrossRef] - Quan, Q.Q.; Wang, T.Z.; Yu, H.Y.; Deng, Q.Y.; Tang, D.W.; Deng, Z.Q. An Ultrasonic Drilling System for Fast Drilling Speed With Uncertain Load. IEEE-ASME Trans. Mechatron.
**2023**, 28, 1477–1487. [Google Scholar] [CrossRef] - Zhao, C.S. Ultrasonic Motors: Technologies and Applications; Science Press Beijing: Beijing, China, 2011; pp. 1–494. [Google Scholar]
- Zhang, K.; Gao, G.F.; Zhao, C.Y.; Wang, Y.; Wang, Y.; Li, J.F. Review of the design of power ultrasonic generator for piezoelectric transducer. Ultrason. Sonochem.
**2023**, 96, 106438. [Google Scholar] [CrossRef] - Jiang, X.X.; Ng, W.T.; Chen, J. A Miniaturized Low-Intensity Ultrasound Device for Wearable Medical Therapeutic Applications. IEEE Trans. Biomed. Circuits Syst.
**2019**, 13, 1372–1382. [Google Scholar] [CrossRef] - Peng, H.; Sabate, J.; Wall, K.A.; Glaser, J.S. GaN-Based High-Frequency High-Energy Delivery Transformer Push-Pull Inverter for Ultrasound Pulsing Application. IEEE Trans. Power Electron.
**2018**, 33, 6794–6806. [Google Scholar] [CrossRef] - Kuang, Y.; Jin, Y.; Cochran, S.; Huang, Z. Resonance tracking and vibration stablilization for high power ultrasonic transducers. Ultrasonics
**2014**, 54, 187–194. [Google Scholar] [CrossRef] [PubMed] - Martin, R.W.; Vaezy, S.; Proctor, A.; Myntti, T.; Lee, J.B.J.; Crum, L.A. Water-cooled, high-intensity ultrasound surgical applicators with frequency tracking. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2003**, 50, 1305–1317. [Google Scholar] [CrossRef] [PubMed] - Ben-Yaakov, S.; Peretz, M.M. A self-adjusting sinusoidal power source suitable for driving capacitive loads. IEEE Trans. Power Electron.
**2006**, 21, 890–898. [Google Scholar] [CrossRef] - Pfeiffer, J.; Kuster, P.; Schulz, I.E.M.; Friebe, J.; Zacharias, P. Review of Flux Interaction of Differently Aligned Magnetic Fields in Inductors and Transformers. IEEE Access
**2021**, 9, 2357–2381. [Google Scholar] [CrossRef] - Viguier, C.; Nadal, C.; Rouchon, J.F. Feasibility investigation of a static force measurement with longitudinal piezoelectric resonant sensor. Solid State Phenom.
**2009**, 147–149, 876–881. [Google Scholar] [CrossRef] - Liu, C.; Xu, Z.; Xu, B.; Zhang, H.; Jin, L.; Sui, Q.; Shen, Z. Design and Research of Ultrasonic Motor Drive Based on LCLC Resonance Matching. In Proceedings of the 17th Annual Conference of China Electrotechnical Society, Beijing, China, 17–18 September 2022; Lecture Notes in Electrical Engineering (1013). Springer: Singapore, 2023; pp. 982–990. [Google Scholar]
- Fang, Z.W.; Yang, T.Y.; Zhu, Y.F.; Li, S.Y.; Yang, M. Velocity Control of Traveling-Wave Ultrasonic Motors Based on Stator Vibration Amplitude. Sensors
**2019**, 19, 5326. [Google Scholar] [CrossRef] [PubMed] - Van Dyke, K.S. The piezo-electric resonator and its equivalent network. Proc. Inst. Radio Eng.
**1928**, 16, 742–764. [Google Scholar] [CrossRef] - Liu, X.S.; Colli-Menchi, A.I.; Gilbert, J.; Friedrichs, D.A.; Malang, K.; Sanchez-Sinencio, E. An Automatic Resonance Tracking Scheme With Maximum Power Transfer for Piezoelectric Transducers. IEEE Trans. Ind. Electron.
**2015**, 62, 7136–7145. [Google Scholar] [CrossRef] - Yang, T.Y.; Zhu, Y.F.; Li, S.Y.; An, D.W.; Yang, M.; Cao, W.W. Dielectric loss and thermal effect in high power piezoelectric systems. Sens. Actuator A-Phys.
**2020**, 303, 111724. [Google Scholar] [CrossRef] - Di, S.S.; Fan, W.; Li, H.F. Parallel resonant frequency tracking based on the static capacitance online measuring for a piezoelectric transducer. Sens. Actuator A-Phys.
**2018**, 270, 18–24. [Google Scholar] [CrossRef] - Wang, T.Z.; Quan, Q.Q.; Tang, D.W.; Yang, Z.; Huang, J.C.A.; Guo, F.; Meng, L.Z.; Zhao, Z.J.; Deng, Z.Q. Effect of hyperthermal cryogenic environments on the performance of piezoelectric transducer. Appl. Therm. Eng.
**2021**, 193, 116725. [Google Scholar] [CrossRef] - Ebina, K.; Hasegawa, H.; Kanai, H. Investigation of frequency characteristics in cutting of soft tissue using prototype ultrasonic knives. Jpn. J. Appl. Phys. Part 1-Regul. Pap. Brief Commun. Rev. Pap.
**2007**, 46, 4793–4800. [Google Scholar] [CrossRef] - Yang, T.Y.; Zhu, Y.F.; Fang, Z.W.; Wu, H.Y.; Jiang, W.L.; Yang, M. A Driving and Control Scheme of High Power Piezoelectric Systems over a Wide Operating Range. Sensors
**2020**, 20, 4401. [Google Scholar] [CrossRef] - Gao, X.C.; Yang, M.; Zhu, Y.F.; Hu, Y.H. Two-Phase Stator Vibration Amplitude Compensation of Traveling-Wave Ultrasonic Motor. Actuators
**2022**, 11, 278. [Google Scholar] [CrossRef]

**Figure 2.**BVD equivalent circuit model of the piezoelectric transducer and the electrical parameters of the piezoelectric transducer (extracted by an impedance analyzer).

**Figure 4.**Phase difference–frequency characteristic curve of excitation current and partial voltage.

**Figure 5.**(

**a**) Voltage sensing bridge model in push–pull inverter and (

**b**) the waveforms of the proposed scheme.

**Figure 6.**Hardware architecture of the frequency tracking and amplitude control scheme based on the push–pull inverter.

**Figure 13.**(

**a**) Amplitude control process (in glycerol) and (

**b**) frequency tracking process (in glycerol).

**Figure 17.**Amplitude control under different loads: (

**a**) 0 Nm; (

**b**) 0.1 Nm; (

**c**) 0.2 Nm; and (

**d**) 0.3 Nm.

This Work | [21] | |
---|---|---|

Resonant Point | ${f}_{p}$ | ${f}_{s}$ |

Build-up Time | 3 ms | 10 ms |

Unloaded Frequency Variation | 50 Hz | 80 Hz |

Loaded Frequency Variation | 200 Hz | 250 Hz |

Inverter Topology | Push–Pull Inverter | Full bridge Inverter |

The Number of Used MOSFET Switching Tubes in the Inverter | Two | Four |

Inverter Complexity | Simple | Complex |

Controller Form | Discrete | Discrete |

Parameters | Values |
---|---|

Drive Frequency | 40–45 kHz |

Drive Voltage | 130 Vrms |

Rated Torque | 1.0 Nm |

Rated Output | 5.0 W |

Maximum Velocity | 150 rpm |

Proposed Scheme | [27] | |||
---|---|---|---|---|

Load (Nm) | Overshoot (%) | Velocity Fluctuation (rpm) | Overshoot (%) | Velocity Fluctuation (rpm) |

0 | 0.8 | 0.96 | 0.96 | 1.68 |

0.1 | 1.6 | 1.44 | 1.92 | 1.68 |

0.2 | 2.5 | 1.88 | 1.94 | 1.92 |

0.3 | 5.4 | 2.26 | 6.9 | 2.4 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hu, Y.; Yang, M.; Zhu, Y.; Wang, S.
Push–Pull Inverter Using Amplitude Control and Frequency Tracking for Piezoelectric Transducers. *Micromachines* **2023**, *14*, 2147.
https://doi.org/10.3390/mi14122147

**AMA Style**

Hu Y, Yang M, Zhu Y, Wang S.
Push–Pull Inverter Using Amplitude Control and Frequency Tracking for Piezoelectric Transducers. *Micromachines*. 2023; 14(12):2147.
https://doi.org/10.3390/mi14122147

**Chicago/Turabian Style**

Hu, Yinghua, Ming Yang, Yuanfei Zhu, and Shangting Wang.
2023. "Push–Pull Inverter Using Amplitude Control and Frequency Tracking for Piezoelectric Transducers" *Micromachines* 14, no. 12: 2147.
https://doi.org/10.3390/mi14122147