MMF utilizes for factory calibration a modern PC based calibration system. The calibration procedure is based on a transfer standard which is regularly sent to Physikalisch-Technische Bundesanstalt (PTB) for recalibration.
MMF sensors, with few exceptions, are supplied with an individual calibration chart (example in Figure 8). It shows all individually measured data like sensitivity, transverse sensitivity, insulation resistance, IEPE bias voltage and frequency response curve. Additionally, all available typical characteristics for the transducer are listed.
Figure 8: Calibration chart of Metra accelerometersThe following sections explain the parameters used in the individual calibration sheets.

A piezoelectric accelerometer with charge output can be regarded as either a charge source or a voltage source with very high impedance. Consequently, charge sensitivity or voltage sensitivity are used to describe the relationship between acceleration and output. In the individual characteristics sheet, MMF states the charge sensitivity at 80 Hz and room temperature in picocoulombs per g or perms -2 (1 g = 9.81 m/s²).
The sensitivity of accelerometers with IEPE output is stated as voltage sensitivity in millivolts per g or per ms-2.
The total accuracy of this calibration is 2 %, valid under the following conditions:
f = 80 Hz, T = 21 °C, a = 10 m/s², CCABLE = 150 pF, ICONST = 4 mA.
The stated accuracy should not be confused with the tolerance of nominal sensitivity which is specified for some accelerometers. Model KS80D, for instance, has ± 5 % nominal sensitivity tolerance. Standard tolerance window for sensitivity, if not otherwise stated, is ± 20 %. Hence the exact sensitivity of production accelerometers may vary from the nominal sensitivity within the specified tolerance range.
Charge sensitivity decreases slightly with increasing frequency. It drops about 2 % per decade. For precise measurements at frequencies differing very much from 80 Hz a recalibration in the desired frequency range should be performed.
Before leaving the factory each accelerometer undergoes a thorough artificial ageing process. Nevertheless, further natural ageing cannot be avoided completely. Typical are -3 % sensitivity loss within the first 3 years. For a high degree of accuracy, recalibration should be performed.

Frequency Response
Measurement of frequency response requires mechanical excitation of the transducer. Metra uses an especially-designed calibration shaker which is driven by a sine-wave generator swept over a frequency range from 20 or 80 Hz to 40 000 Hz. Acceleration is kept nearly constant at 3 m/s² over the entire frequency range by means of a feedback signal from a reference accelerometer. Most accelerometers are supplied with an individual frequency response curve. It shows the deviation of sensitivity in dB. For example, the upper 3 dB limit can be derived from this curve. The 3 dB limit is often used in scientific specifications. It marks the frequency where the measuring error becomes 30 %. It is usually at about 50 % of the resonance frequency (compare Figure 3). The 1 dB limit marks an error of approximately 10 %. It can be found in the range of 1/3 the resonance frequency. The mounted resonance frequency, which is the largest mechanical resonance, can be identified as well from this curve. Usually, there are sub-resonances present at lower frequencies.
MMF performs frequency response measurements under optimum operating conditions with the best possible contact between accelerometer and vibration source practical. In practice, mounting conditions will be less than ideal in many cases and often a lower resonance frequency will be obtained.
The lower frequency limit of IEPE accelerometers can be found in the linear frequency range given in the datasheet. It is stated for limits of 5 %, 10 % and 3 dB (see also page 5). For accelerometers with charge output, we do not state a lower frequency limit since it is mainly determined by the external electronics.

The frequency response of IEPE transducers can be altered by long cables.

Transverse Sensitivity
Transverse sensitivity is the ratio of the output caused by acceleration perpendicular to the main sensitivity axis divided by the basic sensitivity in the main direction. The measurement is made at 40 Hz sine excitation rotating the sensor around a vertical axis. A figure-eight curve is obtained for transversal sensitivity. Its maximum deflection is the stated value. Typical are <5 % for shear accelerometers and <10 % for compression and bender models.

Maximum Acceleration
Usually, the following limits are specified:â+ maximum acceleration for positive output directionâ- maximum acceleration for negative output direction
The maximum acceleration is given for frequencies within the operating frequency range and at room temperature. At higher temperatures, it may be lower.
For charge output accelerometers these limits are determined solely by the construction. If one of these limits is exceeded accidentally, for example, by dropping the sensor on the ground, the sensor will usually still function.
However, we recommend recalibrating the accelerometer after such incidents. Continuous vibration should not exceed 25 % of the stated limits to avoid wear. When the highest accuracy is required, acceleration should not be higher than 10 % of the limit.
If the accelerometer is equipped with built-in IEPE electronics, the limits â+ and â- are usually determined by the output voltage span of the amplifier.

The mechanical sensing elements of piezoelectric accelerometers have very low linearity errors. Within the stated measuring range the linearity error will be less than 1 % usually. 
Another issue is the linearity of IEPE transducers. The sensor electronics will contribute additional errors, particularly at higher output voltages. Typically the linearity error will be less than 1 % at within 70 % of the maximum output voltage.

Operating Temperature Range
The maximum operating temperature of a charge transducer is limited by the piezoelectric material. Above a specified temperature, called Curie point, the piezoelectric element will begin to depolarize causing a permanent loss in sensitivity. The specified maximum operating temperature is the limit at which the permanent change of sensitivity is 3 %. Other components may also limit the operating temperature, for example, adhesives, resins or built-in electronics. Typical temperature ranges are -35 to 150 °C and -10 to 80 °C. Accelerometers with built-in electronics are generally not suitable for temperatures above 120 °C.

Temperature Coefficients
Apart from permanent changes, some characteristics vary over the operating temperature range. Temperature coefficients are specified for charge sensitivity (TK(Bqa)) and inner capacitance (TK(Ci)). For sensors with built-in IEPE electronics, only the temperature coefficient of voltage sensitivity TK(Bua) is stated.
There is a simple way to reduce the temperature coefficient of charge mode accelerometers. Since the temperature coefficients of Bqa, Bua and Ci are different, the temperature behaviour can be compensated by a serial capacitor at charge amplification or a parallel capacitor in case of high impedance voltage amplification.
This can be a useful improvement in case of very changeable temperatures. Please consider, that the total sensitivity will become lower by this measure.

Temperature Transients
In addition to the temperature characteristics mentioned above, accelerometers exhibit a slowly varying output when subjected to temperature transients, caused by the so-called pyroelectric effect. This is specified by temperature transient sensitivity baT. Temperature transient errors have frequencies below 10 Hz. Where low-frequency measurements are made this effect must be considered. To avoid this problem, shear-type accelerometers should be chosen for low-frequency measurements. In practice, they are approximately 100 times less sensitive to temperature transients than compression sensors. 
Bendersystems are midway between the other two systems in terms of sensitivity to temperature transients. When compression sensors are used, the amplifier should be adjusted to a 3 or 10 Hz lower frequency limit.

Base Strain
When an accelerometer is mounted on a structure which is subjected to strain variations, an unwanted output may occur as a result of strain transmitted to the piezoelectric material. This effect can be described as base strain sensitivity bas. The stated values are determined by means of a bending beam oscillating at 8 or 15 Hz. Base strain output usually occurs at frequencies below 500 Hz. Shear type accelerometers have extremely low base strain sensitivity and should be chosen for strain-critical applications.

Magnetic Fields
Strong magnetic fields often occur around electric machines at 50 Hz and multiples. Magnetic field sensitivity baB has been measured at B=0.01 T and 50 Hz for some accelerometers. It is very low and can be ignored under normal conditions.
Generally, accelerometers with stainless steel cases provide better protection against magnetic fields than accelerometers with aluminium cases.
Stray signal pickup can be avoided by proper cable shielding. This is of particular importance for sensors with charge output.
Adequate isolation must be provided against ground loops. They can occur when a measuring system is grounded at several points, particularly when the distance between these grounding points is long. Ground loops can be avoided using accelerometers with insulated bases (for instance Models KS74C.10/100 and KS80D) or insulating mounting studs.

Sound Pressure
If an accelerometer is exposed to a very high noise level, a deformation of the sensor case may occur which can be measured as an output under extreme conditions. Acoustic noise sensitivity bap as stated for some models is measured at an SPL of 154 dB which is beyond the pain barrier of the human ear. Acoustic noise sensitivity should not be confused with the sensor response to pressure induced motion of the structure on which it is mounted.

Noise and Resolution
A piezoelectric sensing element can be regarded as a purely capacitive source. Therefore, the sensor itself is free of intrinsic noise. The only noise contribution is caused by the temperature motion of electrons in the built-in the IEPE charge converter. Consequently, a noise specification makes only sense for IEPE compatible sensors.
The intrinsic noise determines the resolution limit of the sensor. Signals below the noise level cannot be measured.
The signal-to-noise-ratio Sn is a measure of the error caused by noise. It is the logarithm of the ratio of the measured signal level (u) and the noise level (un).
The intrinsic noise of IEPE compatible accelerometers mainly depends on the frequency.
Below about 100 Hz it has the typical 1/f characteristics. Above 100 Hz the noise level is nearly independent of the frequency.
It is useful to state the noise of an accelerometer as equivalent acceleration level. For this purpose, the noise voltage (un) is divided by transducer sensitivity (Bua) yielding the equivalent noise acceleration (an).
While un only depends on the electronic circuit which is similar for all sensor types, the sensitivity of the piezoelectric sensing element will directly influence the equivalent noise acceleration. It can be seen that a transducer equipped with a very sensitive piezo system will provide the highest resolution.
The characteristics of most accelerometers show the wide-band noise (RMS) over the linear frequency range and noise densities at selected frequencies.
To obtain the RMS noise acceleration within a certain frequency range, choose the noise density of the lowest frequency within the considered range and multiply it by the square root of the difference between the upper and the lower frequency limit.
For the evaluation of the intrinsic noise of an entire measuring chain, the noise of all components including signal conditioners and other instruments has to be considered.
Accelerometer and instruments need to be selected carefully in terms of noise when lowest vibrations are to be detected. Examples are building vibration monitoring and the operation of vibration-sensitive equipment.

Generic Vibration Criteria Curves for Vibration-Sensitive Equipment
Environmental vibration is an important issue for facilities using sensitive tools and machines. Examples are photolithography in microelectronics, equipment for manufacturing nanoelectronic devices, scanning electron microscopes (SEM) or transmission electron microscopes (TEM) in biomedical and biopharmaceutical research. In some cases, acceptable limits have been specified by the manufacturer of the equipment but sometimes the limits are unknown. For this case “Generic Vibration Criteria” have been elaborated in the 1980’s, among others, by IEST.  
Generic Vibration Criteria (VC) are measured in three directions as third-octave band velocity RMS spectra. The curves are labelled VC-A through VC-G.

For comparison, the limit for perceptible vibration is between 100 and 200 µm/s.
Another method for the classification of vibration in buildings with sensitive equipment has been formulated by in ISO/TS 10811.
For the selection of a suitable sensor, it is most important to compare noise at the lower frequency end where the lowest acceleration components occur. As an example, the triaxial accelerometer KS823B has a noise density of 0.8 µg/sqrt(Hz) at a frequency of 1 Hz. Using the method described above for a frequency range from 1 to 10 Hz the noise density at the lower frequency is multiplied with the square root of the difference between the upper and the lower frequency limit. The approximate noise contribution of the sensor will be 2.4 µg or 24 µm/s². At 1 Hz this corresponds to a velocity of v = a/ω = 3.8 µm/s. Doing the same calculation for 10 to 80 Hz where the noise density is 0.2 mg/sqrt(Hz) at 10 Hz we get a noise value of 1.7 µg which corresponds to 2.7 µm/s at 10 Hz. Thus the KS823B can be used down to vibration criterion VC-D.
Even lower vibration can be detected with the accelerometer KB12VD with its noise density of 0.06 µg/sqrt(Hz) at 1 Hz. This sensor is suitable for measurements down to VC-F and Nano-EF under the assumption that the noise of the signal path is in the same range as the noise of the sensor.
MMF offers a PC based measuring solution for VC and Nano criteria.

Inner Capacitance
The inner capacitance is stated in the individual calibration sheet only for accelerometers with charge output. It can be relevant if the transducer is used with a high impedance voltage amplifier. The stated value includes the capacitance of the sensor cable which was used for calibration. This cable capacitance is stated separately in the calibration sheet. Its value has to be deducted from the sensor capacitance to obtain the actual inner capacitance.
Protection GradesThe IP protection grades to IEC 529 and DIN 40050 characterize the suitability of a product for given environmental conditions. The first digit of the IP number means the shielding from the insertion of objects and dust. The second digit marks the protection against humidity.

ATEX Certificates
For applications in explosive environments, Metra can supply for some of its products an ATEX certificate of typeII 3G EEx nA II T6which means:
II – equipment group: electrical equipment for all explosive environments, except mining
3 – equipment category: for zone 2 (explosive condition unlikely, if occur, only rarely for short time)
G – for gas-explosive endangered areas
EEx – per directive 94/9/EC (ATEX)
n – equipment cannot ignite an explosive atmosphere under normal operating conditions
A – no sparks
II – equipment group: electrical equipment for all explosive environments, except miningT6 – maximum surface temperature 85 °C

Vibration criteriaVibration level (RMS third-octave spectrum)ApplicationSize of structure
Perception threshold
100 µm/s (4 to 80 Hz)Threshold of human perception, for sensitive sleeping areas, opera halls, theaters, microscopes with 100× magnification30 µm
50 µm/s (4 to 80 Hz)Microscopes with 400× magnification8 µm
5 µm/s (1 to 80 Hz)Inspection instruments, high-quality laboratories, lithography equipment (including steppers)3 µm
12.5 µm/s (1 to 80 Hz)Microscopes with magnifications up to 1000×, good standard for most lithography and inspection equipment1 µm
6.25 µm/s (1 to 80 Hz)high-quality electron microscopes (REM, TEM), electron beam systems0.3 µm
3.1 µm/s (1 to 80 Hz)Compliance with this criterion is very difficult and may only be possible in a few cases, preferably on foundation slabs without an underlying cellar. Necessary for equipment of the highest precision.0.1 µm
1.6 µm/s (1 to 80 Hz)Extremely still research rooms, very difficult to achieve; only suitable for characterization and not as a design criterion.
0.8 µm/s (1 to 80 Hz)Extremely still research rooms, very difficult to achieve; only suitable for characterization and not as a design criterion.

Vibration Specialists Asia