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AN2EApplication Note

Piezoelectric Accelerometers

Piezoelectric Principle

Metra Mess- und Frequenztechnik Radebeul Page 1

Meissner Str. 58 P.O. Box 01 01 13 Oct. 03

D-01445 Radebeul D-01435 Radebeul Internet: www.MMF.de

Phone +49-351-836 21 91 Fax +49-351-836 29 40  Email: Info@MMF.de

The active element of an accelerometer is a piezoelectric material. Figure 1 illustrates the piezoelectric effect with the

help of a compression disk. A compression disk looks like a capacitor with the piezoceramic material sandwiched be-

tween two electrodes. A force applied perpendicular to the disk causes a charge production and a voltage at the elec-trodes.

electrode areathicknessforcechargevoltage

piezo constants

AdFqu

d33, e33

piezo disk

q = d33 F

u = Fd33 d

e33 A

A F

q

u

F

d

Figure 1: Piezoelectric effect, basic calculations

The sensing element of a piezoelectric accelerometer consists of two major parts:

• Piezoceramic material

• Seismic mass

One side of the piezoelectric material is connected to a rigid post at the sensor base. The so-called seismic mass is

attached to the other side. When the accelerometer is subjected to vibration, a force is generated which acts on the pie-

zoelectric element (compare Figure 2). According to Newton’s Law this force is equal to the product of the acceleration

and the seismic mass. By the piezoelectric effect a charge output proportional to the applied force is generated. Since

the seismic mass is constant the charge output signal is proportional to the acceleration of the mass.

F = m a

charge sensitivity:

Bqa =qa

Bua =ua

voltage sensitivity:Acceleration a

m

Seismic mass

Piezoceramics

q

u

.

Figure 2: Principle of a piezoelectric accelerometer

Over a wide frequency range both sensor base and seismic mass have the same acceleration magnitude. Hence, the

sensor measures the acceleration of the test object.

The piezoelectric element is connected to the sensor socket via a pair of electrodes. Some accelerometers feature an

integrated electronic circuit which converts the high impedance charge output into a low impedance voltage signal (see

Application Note AN4E).

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AN2EApplication Note

Piezoelectric Accelerometers

Piezoelectric Principle

Metra Mess- und Frequenztechnik Radebeul Page 2

Meissner Str. 58 P.O. Box 01 01 13 Oct. 03

D-01445 Radebeul D-01435 Radebeul Internet: www.MMF.de

Phone +49-351-836 21 91 Fax +49-351-836 29 40  Email: Info@MMF.de

Within the useful operating frequency range the sensitivity is independent of frequency.

A piezoelectric accelerometer can be regarded as a mechanical low-pass with resonance peak. The seismic mass and the

piezoceramics (plus other “flexible” components) form a spring mass system. It shows the typical resonance behavior

and defines the upper frequency limit of an accelerometer. In order to achieve a wider operating frequency range the

resonance frequency should be increased. This is usually done by reducing the seismic mass. However, the lower the

seismic mass, the lower the sensitivity. Therefore, an accelerometer with high resonance frequency, for example a

shock accelerometer, will be less sensitive whereas a seismic accelerometer with high sensitivity has a low resonance

frequency.

Figure 3 shows a typical frequency response curve of an accelerometer when it is excited by a constant acceleration.

f0 fr0.5fr0.3fr

0.2fr ffL 2fL3fL

0.900.951.001.051.10

1.30

0.71

fLf

0

fr

lower frequency limitcalibration frequency

resonance frequency

Figure 3: Frequency response curve

Several useful frequency ranges can be derived from this curve:

•At approximately 1/5 the resonance frequency the response of the sensor is 1.05. This means that the measured error

compared to lower frequencies is 5 %.

•At approximately 1/3 the resonance frequency the error is 10 %. For this reason the “linear” frequency range should

be considered limited to 1/3 the resonance frequency.

•The 3 dB limit with approximately 30 % error is obtained at approximately one half times the resonance frequency.

The lower frequency limit mainly depends on the chosen preamplifier. Often it can be adjusted. With voltage amplifiers

the low frequency limit is a function of the RC time constant formed by accelerometer, cable, and amplifier input ca-

pacitance together with the amplifier input resistance (see Application Note AN6E).