# Effect of the Matching Circuit on the Electromechanical Characteristics of Sandwiched Piezoelectric Transducers

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Analysis of a Sandwiched Piezoelectric Transducer with Series Matching Inductor

## 3. Effect of the Series Matching Inductor on the Electromechanical Characteristics of a Piezoelectric Transducers

#### 3.1. Effect of the Series Matching Inductor on the Frequency Response

#### 3.2. Dependency of the Electromechanical Parameters on the Series Matching Inductor

## 4. Experiments

_{r}, f

_{a}, K

_{effc}and f

_{mr}, f

_{ma}, K

_{meffc}are the theoretical and measured resonance/anti-resonance frequencies and effective electromechanical coupling coefficient.

## 5. Conclusions

- When a matching inductor is connected in series with a sandwiched piezoelectric transducer, the resonance frequency is decreased and the anti-resonance frequency is almost unchanged; the effective electromechanical coupling coefficient is increased.
- Without a series matching inductor, the electro-acoustical efficiency at resonance frequency is larger than that at anti-resonance frequency. When a series matching inductor is added, the electro-acoustical efficiency at resonance frequency is decreased and remains unchanged at anti-resonance frequency, and the electro-acoustical efficiency at resonance frequency is lower than at anti-resonance frequency.
- When the series matching inductor is increased, the electric quality factor corresponding to resonance frequency is decreased, while the electric quality factor corresponding to anti-resonance frequency is increased.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**A lumped electromechanical equivalent circuit and admittance circle diagram of a piezoelectric transducer at resonance.

**Figure 4.**Electro-mechanical equivalent circuit of a sandwiched piezoelectric transducer with a series matching inductor.

**Figure 8.**Theoretical relationship between the resonance/anti-resonance frequency and the series matching inductor.

**Figure 9.**Dependency of the effective electromechanical coupling coefficient on the series matching inductor.

**Figure 10.**Theoretical relationship between the electric quality factor and the series matching inductor.

**Figure 13.**Measured frequency response of the input electric impedance of a sandwich piezoelectric transducer. (

**A**) L = 0 (mH); (

**B**) L = 5 (mH).

**Table 1.**Experimental resonance/anti-resonance frequencies and effective electromechanical coupling coefficient of the piezoelectric transducers.

No. | L (mH) | f_{r} (Hz) | f_{a} (Hz) | f_{mr} (Hz) | f_{ma} (Hz) | K_{effc} | K_{meffc} |
---|---|---|---|---|---|---|---|

1 | 0 | 33805 | 39570 | 31212 | 33333 | 0.52 | 0.35 |

5 | 17823 | 39554 | 26607 | 33333 | 0.89 | 0.60 | |

10 | 12990 | 39539 | 20606 | 33333 | 0.94 | 0.79 | |

2 | 0 | 20585 | 28706 | 18182 | 20000 | 0.70 | 0.42 |

5 | 14699 | 28677 | 17727 | 20000 | 0.86 | 0.46 | |

10 | 11560 | 28650 | 16364 | 20000 | 0.91 | 0.57 |

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**MDPI and ACS Style**

Lin, S.; Xu, J.
Effect of the Matching Circuit on the Electromechanical Characteristics of Sandwiched Piezoelectric Transducers. *Sensors* **2017**, *17*, 329.
https://doi.org/10.3390/s17020329

**AMA Style**

Lin S, Xu J.
Effect of the Matching Circuit on the Electromechanical Characteristics of Sandwiched Piezoelectric Transducers. *Sensors*. 2017; 17(2):329.
https://doi.org/10.3390/s17020329

**Chicago/Turabian Style**

Lin, Shuyu, and Jie Xu.
2017. "Effect of the Matching Circuit on the Electromechanical Characteristics of Sandwiched Piezoelectric Transducers" *Sensors* 17, no. 2: 329.
https://doi.org/10.3390/s17020329