Piezoelectric principle

The active element of an accelerometer is a piezoelectric material. The following picture illustrates the piezoelectric effect with the help of a compression disk. A compression disk looks like a capacitor with the piezoceramic material sandwiched between two electrodes. A force applied perpendicular to the disk causes a charge production and a voltage at the electrodes.

q = d₃₃·F
u = d₃₃/e₃₃·d/A·F
F = m·a
Transfer factors for acceleration a
a = q_a/B_qa = u_a/B_ua

A Electrode area
d Thickness
F Force
q Charge
u Voltage
d₃₃, e₃₃ Piezo constants

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 piezoelectric element. 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 (see following picture).

The piezoelectric element is connected to the sensor socket by a pair of electrodes. Many accelerometers are also equipped with an integrated an intergrated electronic circuit acc. to IEPE standard so that the high impedance charge output of the piezo ceramic is converted into a low impedance voltage signal.

Transfer behaviour

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 correctly. 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 will be less sensitive whereas a seismic accelerometer with high sensitivity has a low resonance frequency.

The following picture shows a typical frequency response curve of an accelerometer when it is excited by a constant acceleration.

: 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.

These values are typical values and may vary depending on the accelerometer type.
The lower frequency limit mainly depends on the chosen preamplifier. Often it can be adjusted. With voltage amplifiers the lower frequency limit is a function of the RC time constant formed by accelerometer, cable, and amplifier input capacitance together with the amplifier input resistance.

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