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Two common amplifier circuits used for piezoelectric sensors are voltage amplifiers and charge amplifiers (pictured respectively). Charge Amplifier Circuit Voltage Amplifier Circuit

With the charge amplifier, the sensor is shorted but this is not the case with a voltage amplifier. Does this effect the physical properties of the sensor?

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Yes it does effect the stiffness and thus also the resonant frequency of the sensor.

Liu, et al. in [1] show that for an closed circuit stiffness of \$Y_\text{open}\$, the short circuit stiffness \$Y_\text{closed}\$ is given by $$Y_\text{short} = (1-k^2)Y_\text{short}$$ where \$k\$ is the electromechanical coupling factor. From this they compute the relationship of resonant frequencies:

$$\frac{f_\text{open}}{f_\text{closed}} = \sqrt{\frac{1}{1-k^2}}$$

As \$k\$ gets closer to \$1\$, the voltage amplifier can have significantly more usable bandwidth than the charge mode configuration.

\$k\$ values quoted in ceramic suppliers' specifications typically are theoretical maximum values. At low input frequencies, a typical piezoelectric ceramic can convert 30 - 75% of the energy delivered to it in one form into the other form, depending on the formulation of the ceramic and the directions of the forces involved.

Piezoelectric Constants from American Piezo

[1] Liu, Weiqun & Feng, Zhihua & Liu, R & Zhang, J. (2008). The influence of preamplifiers on the piezoelectric sensor's dynamic property. The Review of scientific instruments. 78. 125107. 10.1063/1.2825404.

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