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Ceramic Engineering DISCUSSION
PZT datasheets list a charge constant d33 in pC/N and a voltage constant g33 in mV·m/N, and the selection guides say that actuators need a high d while sensors need a high g. Both describe the same piezoelectric effect, so I do not see why they are treated as separate figures of merit.
How are d and g related, and how do I use them to estimate the displacement of an actuator disc and the output voltage of a force sensor made from the same material?
They describe the two directions of the effect. d33 is strain per unit electric field, in m/V, which is numerically the same as charge per unit force, in C/N. g33 is electric field per unit stress, in V·m/N. The two are linked by the permittivity: g33 = d33 / ε, with ε = ε_r × ε_0.
That link is the reason they are not interchangeable. A material can reach a very high d by having a very high permittivity, and then its g is only ordinary. A soft PZT grade with d33 around 600 pC/N and ε_r of about 3400 has g33 near 20 mV·m/N, lower than a moderate grade with d33 of 400 pC/N and ε_r of 1800, which gives about 25 mV·m/N.
Actuator case: for a disc driven through its thickness, the free displacement is Δt = d33 × V. The thickness cancels out, because a thicker disc has a lower field for the same voltage. With d33 = 400 pm/V and 200 V, Δt = 80 nm. That is all a single disc gives, which is why actuators are built as multilayer stacks: 100 thin layers driven in parallel at the same voltage move 100 × 80 nm = 8 µm.
High d is wanted because it sets the displacement per volt directly. The field must stay within the limit for the material, especially in the direction opposite to the poling, and the temperature must stay well below the Curie point given on the datasheet, or the ceramic will depole.
Sensor case: the open-circuit voltage from a stress σ applied through the thickness t is V = g33 × σ × t. Take g33 = 25 mV·m/N, a 10 N force on a disc of 1 cm² area and 1 mm thickness. The stress is 10 / 10^-4 = 100 kPa, so V = 0.025 × 100,000 × 0.001 = 2.5 V.
The same answer comes from charge and capacitance. Q = d33 × F = 400 pC/N × 10 N = 4 nC, and the disc capacitance with ε_r = 1800 is C = ε × A / t = 1.6 nF, so V = Q / C = 2.5 V. A higher permittivity raises C and lowers the voltage for the same charge, which is exactly what a low g means.
Which constant matters for a sensor depends on the electronics. With a high-impedance voltage amplifier, the output follows g and is reduced by cable capacitance, which adds to C. With a charge amplifier, the output follows Q = d × F and is nearly independent of cable length, so for charge-mode sensors a high d is the useful figure after all.
Either way the sensor cannot hold a static reading. The charge leaks away through the insulation resistance of the ceramic and the amplifier input with a time constant R × C: with 1.6 nF and 10 GΩ that is 16 s. Piezo sensors are for dynamic force, pressure and vibration, not for weighing.
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