Limitations

Limitations

Each piezoelectric material has a particular operating limit for temperature, voltage, and stress. The particular chemical composition of the material determines the limits. Operating a material outside of these limitations may cause partial or total depolarization of the material, and a diminishing or loss of piezoelectric properties.

Temperature Limitations

As the operating temperature increases, piezoelectric performance of a material decreases, until complete and permanent depolarization occurs at the material's Curie temperature.

The Curie point is the absolute maximum exposure temperature for any piezoelectric ceramic. Each ceramic has its own Curie point. When the ceramic element is heated above the Curie point, all piezoelectric properties are lost. In practice, the operating temperature must be substantially below the Curie point.

The material's temperature limitation decreases with greater continuous operation or exposure. At elevated temperatures, the ageing process accelerates, piezoelectric performance decreases and the maximum safe stress level is reduced.

Voltage Limitations

A piezoelectric ceramic can be depolarized by a strong electric field with polarity opposite to the original poling voltage.

The limit on the field strength is dependent on the type of material, the duration of the application, and the operating temperature. The typical operating limit is between 500V/mm and 1 000V/mm for continuous application.

It should be noted that alternating fields can have the same affect during the half cycle which is opposite to the poling direction.

Mechanical Stress Limitations

High mechanical stress can depolarize a piezoelectric ceramic. The limit on the applied stress is dependent on the type of ceramic material, and duration of the applied stress.

For dynamic stress (impact ignition) the limit is less severe; materials with higher energy output (high g constant) can be used.

For impact applications, the material behaves quasi statically (non-linear) for pulse durations of a few milliseconds or more. When the pulse duration approaches a microsecond, the piezoelectric effect becomes linear, due to the short application time compared to the relaxation time of the domains.

Power Limitations

The acoustic power handling capacity of a radiating transducer is limited by the following factors.
(1) Dynamic mechanical strength of the ceramic
(2) Reduction in efficiency due to dielectric losses
(3) Reduction in efficiency due to mechanical losses
(4) Depolarization of the ceramic due to electric field
(5) Depolarization of the ceramic due to temperature rise
(6) Instability resulting from the positive feedback between dielectric losses and internal heating (2 and 5)

In practice, power limitations are imposed by factors 2 and 5 and the feedback between them (6). depending on the composition of the ceramic. Factors 1, 3 and 4 may be neglected. Factor 1 may be reduced through mechanical bias in sonar, ultrasonic, and other similar applications. Factor 3 may be generally disregarded, since mechanical losses are negligible compared to dielectric losses. In the case of factor 4, the electric field necessary to cause sufficient depolarization will create extremely undesirable operating conditions with very high dielectric losses and resulting low efficiency.

A transducer may be efficiency-limited, temperature limited, or dynamic-strength limited. Dynamic strength is significant only when the transducer is not mechanically biased and the ceramic has a high QM A low frequency, low duty transducer is efficiency-limited. A high frequency continuous duty transducer is temperature-limited. Temperature limited transducers are dependent on the efficiency of the heat removal from the ceramic. Between these two extremes, the specific limitation is dependent on the mechanical design of the transducer. An absolute value on the power limitation of the ceramic cannot be determined without knowledge of its operating conditions.

The equations pertaining to the power handling capacities of the material may be readily derived from lumped equ ivalent circuits. It can be shown that the acoustic power density P per cubic metre is given by Formula 1.

where k Is equal to k33 for a stack of axially poled rings or plates or k31 for a radialy poled cylinder. E is the rms electric field, and f, is the resonance frequency.

It is assumed that the mechanical losses in the ceramic and the housing are negligible compared to dielectric losses. This tends to hold for materials with QM>100 The power per cubic metre dissipated in the ceramic by dielectric dissipation Pd is given by Formula 2.

Formula 2

where f is the operational frequency.

The efficiency of the transducer considering only the internal losses of the material is approximated by Formula 3.

Formula 3

With high values of Q_M power handling capacity of the material is limited at times by the dynamic tensile strength, even though a bias compressive stress as high as about 80 MPa is used with PZT-4D. In this case, the acoustic power is given by Formula 4.

Formula 4

where is the rms stress

These equations may be simplified for the specific case of a matched transducer. Matching is the term applied to the process of adjusting the acoustic load so that it corresponds to the image impedance of the transducer, which is treated as a bandpass filter. In this case, an inductor equal to:

is connected across the transducer. The impedance of the driving electric generator is set equal to the image impedance in order to maximize the transducer bandwidth, where the generator resistance, RG and the mechanical load impedance, RT are given by Formula 5; the bandwidth is given by Formula 6; and the acoustic power and efficiency are given by Formula 7.

Formula 5

Formula 6

where f1 and f2 are the lower and upper cut-off frequencies

Formula 7

Table 9 lists the relative power for PZT-4D and PZT-5A at resonance for the same acoustic load for a given volume of material, assuming that the material is limited by the dielectric losses with Tan ¦ = 0.04.

Relative Power for PZT-4D and PZT-5A