Properties of Piezoelectric Materials

Piezoelectric transducer elements are normally based on poly crystalline ceramics, such as barium titanate, lead zirconate, lead titanate, and lead metaniolbate (or what are generally known as ferroelectric substances), artificially polarized. This enables the piezoelectric properties to be controlled in the manufacturing process.

Manufacture starts with proportioning and mixing component ceramic powders, followed by high-temperature calcination. The now chemically combined ingredients are then re-powdered, mixed with binder, and formed into pellets. These are then fired in a kiln to produce the final rough ceramic elements. These are then lapped and cleaned, and electrodes are plated on them. They are then followed by a high-voltage field under completely controlled conditions.

PIEZOELECTRIC PARAMETERS

The piezoelectric constant, symbol d_ij is a measure of the basic sensitivity of a piezoelectric material and is defined as the change generated (g) per unit of applied force (F):

d_ij = g / F

Other important parameters are:

- Frequency constant—or a monitor relating the dimension of a given piezoelectric element to its natural frequency (usually quoted as K in inches).

- Dielectric constant—or a measure of the internal capacity and designated E.

- Elastic modules—or a measure of stiffness.

- Volume resistivity—or capacity to hold a charge.

- Curie point—or temperature at which the material markedly loses its piezoelectric characteristics. Note: Up to the Curie point the piezoelectric constant increases with increasing temperature.

- Open-circuit voltage—or voltage sensitivity of the piezoelectric element, defined as the open-circuit voltage generated from unit of applied force. This is related directly to both the piezoelectric constant and dielectric constant:

open-circuit voltage =d_ij/E

EQUIVALENT CIRCUITS

The equivalent circuit for a piezoelectric transducer is shown in ill. 6-1. The internal resistance R will be very high (normally in excess of 20,000 M also the effect of the inductance L is in significant at the natural frequency of the material, so both R and L can be ignored. Effectively, therefore, the piezoelectric transducer behaves as a capacitor C producing a charge across its plates proportional to the load force on the element.

ill. 6-1. A piezoelectric transducer is equivalent to this combination of capacitance (C inductance (L), and resistance (R).

The open-circuit voltage (E) out of the transistor is then equal to this charge divided by the transducer component:

E = q/Cp

In a working device the output is connected to a load ( e.g., amplifier circuit). The load is thus the input resistance of the amplifier. Some capacitance (C) will also be added from the wiring when the working voltage generator equivalent circuit is as shown in ill. 6-2:

output voltage = q / (Cp + C)

where q is the sensitivity determined by original calibration of the transducer alone.

This relationship also provides a means of adjusting the sensitivity of a piezoelectric transducer to any required level (below its original calibrated sensitivity) by calculating an exact value of capacity to be added: that is,

C = Q / E - Cp

Or, in more complete form,

C = Ecal / E (Cp + Ccal) - Cp

where the subscript “cal” refers to calibrated values for the transducer.

ill. 6-2. In practice, the piezoelectric transducer behaves as a combination of internal capacitance (Cr) and parallel-wiring capacitance (C).

CHARGE SENSITIVITY

Capacity added in shunt with the transducer will have no effect on its charge sensitivity. However, capacity added in series will reduce the charge output. Thus, in the circuit shown in ill. 6-3, Cs is a series capacitor acting with a swamp effect. C1 represents any parallel capacitance ahead of Cs and C2 any parallel capacitance beyond Cs. Neither C1 nor C2 will have any effect on charge sensitivity, but the charge appearing at the input to the amplifier will be

Q1 = Q (Cs/(Cp + C1 + Cs))

where Q is the basic transducer charge sensitivity.

ill. 6-3. Series capacitance affects the behavior of a transducer (see below for discussion).

FREQUENCY RESPONSE

When a changing load is applied to a piezoelectric material ( e.g., when a piezoelectric transducer is being used as an accelerometer), it becomes a self-generating source of variable electrical signals. The significant parameter in this case is the product fRC:

where f is the frequency of (changing) load in Hz

R is the input impedance of the amplifier in ohms

C is the total capacitance in farads of the transistor plus additional shunt capacity (if any).

At values of fRC less than 1.0, transducer response falls off sharply (See ill. 6-4). This can be a significant factor when using a piezoelectric transducer for low-frequency measurement.

Example: Suppose the frequency to be measured is 2 Hz. The total capacitance of the transducer and cables (Cp + C) is 500 pF, and the input impedance of the amplifier 100 M-Ohm. In this case

fRC = 2 x 500 x 10^-12 x 100 x 10^6 = 0.10

Note that a method of improving the relative response of a piezoelectric transducer at low frequencies is to increase the value of RC in the circuit by using additional shunt capacitance and /or larger cables. However, any gain in this respect will produce a loss of sensitivity.

At higher frequencies a different problem arises. With in creasing frequency the relative response tends to rise above 100 per cent. In order to maintain a linear (true 100-percent) response it’s necessary to limit the frequency to be received to about one-fifth of the resonant frequency of the transducer. For higher frequency, correction factors are involved.

LINEARITY

Linearity of response (above fRC = 1.0) can also be affected by physical effects resulting from the environment in which they are used. Such effects are normally observable well before the transducer itself suffers physical damage.

ill. 6-4. Relative response of a piezoelectric transducer. The response is similar to that of a highpass filter with cutoff frequency f such that fRC = 1.0.

CROSS-AXIS SENSITIVITY

Because of its polarization, a piezoelectric transducer has maximum response along an input axis. Sensitivity to force exerted at an angle 0 to this axis is reduced in proportion to the cosine of that angle—that is, by Q cos φ.

However, a more general expression for cross-axis sensitivity, related to the angle at θ which the load axis deviates from the polarized axis is

Qt / Qxx = = (tan θ cos φ) x 100

This is given as a percentage, representing the loss of sensitivity or misalignment of applied force from the design axis, and is usually less than 5 percent.

USE IN MAGNETIC FIELDS

Magnetic fields or RF fields normally have no effect on the performance of piezoelectric transducers. At very low frequencies, however, the presence of rotating magnetic fields can cause spurious readings. In such cases magnetic shielding of the transducer, and also similar shielding of the amplifier, may be necessary.

SIGNAL TREATMENT

Piezoelectric transducers may be operational in either the voltage-sensory or charge-sensory modes. In the voltage-generating mode the following voltage amplifier may be a simple cathode follower with unity gain, or it may provide any degree of gain required. System sensitivity is reduced with added series capacitance, such as long cables.

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Fundamentals of Transducers (all articles)