# A Study on Parametric Amplification in a Piezoelectric MEMS Device

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. MEMS Device

#### 2.2. Measurement Scheme

## 3. Results

## 4. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**

**Top**: Optical image of typical devices with different supporting beam lengths. The device used has 1050 $\mathsf{\mu}$m length beams supporting an 800 $\mathsf{\mu}$m square plate.

**Bottom**: Coarse frequency sweep showing the two main modes. Displayed modeshapes were obtained from COMSOL simulations. Points “a” and “b” denote the location of the laser beam spot for the laser doppler vibrometer (LDV). The color code on the modeshapes indicates red for areas of maximum displacement and blue for no displacement.

**Figure 2.**Schematic diagram for measurement. A multi-frequency lock-in amplifier is used to generate the output signal to the micro-electro-mechanical systems (MEMS) and to detect the displacement and velocity signals from the LDV.

**Figure 3.**

**Top**: Effective quality-factor ${Q}_{eff}$ as a function of parametric excitation. The solid red line is a fit to Equation (3). The inset shows examples or resonance peaks at different voltages. The amplitude of the peaks was normalized by the fitted corresponding amplitude of each peak.

**Bottom**: Resonance peaks as the phase of the parametric signal was varied while the parametric excitation voltage was kept at 102 V. The inset shows the amplitude gain as a function of phase. The red line was fitted from Equation (2).

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**MDPI and ACS Style**

Gonzalez, M.; Lee, Y.
A Study on Parametric Amplification in a Piezoelectric MEMS Device. *Micromachines* **2019**, *10*, 19.
https://doi.org/10.3390/mi10010019

**AMA Style**

Gonzalez M, Lee Y.
A Study on Parametric Amplification in a Piezoelectric MEMS Device. *Micromachines*. 2019; 10(1):19.
https://doi.org/10.3390/mi10010019

**Chicago/Turabian Style**

Gonzalez, Miguel, and Yoonseok Lee.
2019. "A Study on Parametric Amplification in a Piezoelectric MEMS Device" *Micromachines* 10, no. 1: 19.
https://doi.org/10.3390/mi10010019