Piezoelectric Sensors

Direct piezoelectric material produces charge approximately proportional to applied force,

$$Q=dF,$$

where $d$ is an effective charge coefficient for the material, cut, and loading direction. Electrically the element resembles a charge source in parallel with capacitance and leakage resistance.

Why static force decays #

Sensor leakage, cable insulation, and amplifier input resistance provide a discharge path. The observed voltage therefore returns toward baseline after a step load. This is a physical high-pass behavior, not merely poor calibration. Piezoelectric sensors are excellent for vibration, impact, combustion pressure, and dynamic force; static load requires a different sensing principle.

Charge and voltage readout #

With a simple voltage amplifier, sensitivity depends on total capacitance:

$$V=\frac{Q}{C_{sensor}+C_{cable}+C_{input}}.$$

Cable motion and replacement therefore change gain and inject triboelectric charge. A charge amplifier instead holds the input near virtual ground and ideally gives $V_o=-Q/C_f$, making gain primarily set by feedback capacitance. Feedback resistance establishes the low-frequency cutoff and provides a DC return.

Mechanical installation #

Mount stiffness, preload, orientation, base strain, resonances, and cable restraint determine what acceleration or force reaches the crystal. Useful bandwidth must remain below strong mounted resonance unless the measurement explicitly models it.

Verification #

Check polarity, cable integrity and noise under flexing, settling after overload, low-frequency droop, cross-axis sensitivity, mounted resonance, and the complete mass/loading configuration. For vibration measurements, integrate acceleration only with controlled low-frequency filtering; otherwise small bias and drift become unbounded velocity or displacement error.