PIEZOELECTRIC EFFECT
The piezoelectric effect was discovered by Pierre and Jacques
Curie in 1880. It remained a mere curiosity until the 1940s. The
property of certain crystals to exhibit electrical charges under
mechanical loading was of no practical use until very high input
impedance amplifiers enabled engineers to amplify their signals.
In the 1950s, electrometer tubes of sufficient quality became
available and the piezoelectric effect was commercialized.
The charge amplifier principle was patented by W.P. Kistler in 1950 and gained practical significance in the 1960s. The introduction of MOSFET solid state circuitry and the development of highly insulating materials such as Teflon and Kapton greatly improved performance and propelled the use of piezoelectric sensors into virtually all areas of modern technology and industry.
Piezoelectric measuring systems are active electrical systems. That is, the crystals produce an electrical output only when they experience a change in load. For this reason, they cannot perform true static measurements. However, it is a misconception that piezoelectric instruments are suitable for only dynamic measurements. Quartz transducers, paired with adequate signal conditioners, offer excellent quasistatic measuring capability. There are countless examples of applications where quartz based transducers accurately and reliably measure quasistatic phenomena for minutes and even hours.
APPLICATIONS OF
PIEZOELECTRIC INSTRUMENTATION
Piezoelectric measuring devices are widely used today in the
laboratory, on the production floor and as original equipment.
They are used in almost every conceivable application requiring
accurate measurement and recording of dynamic changes in
mechanical variables such as pressure, force and acceleration.
The list of applications continues to grow and now includes:
The vast majority of Kistler transducers utilize quartz as the sensing element. As discussed in other sections of this web page, Kistler also manufactures transducers which utilize piezo-ceramic elements and micromachined silicon structures. However, the discussion in this section will be limited to quartz applications. Quartz piezoelectric transducers consist essentially of thin slabs or plates cut in a precise orientation to the crystal axes depending on the application. Most Kistler transducers incorporate a quartz element which is sensitive to either compressive or shear loads. The shear cut is used for patented multi-component force and acceleration measuring transducers. Other specialized cuts include the transverse cut for some pressure transducers and the patented polystable cut for high temperature pressure transducers. See Figures 1 and 2 below
.
Although the discussion which follows focuses on accelerometer applications, the response function for force and pressure transducers has essentially the same form. In fact, many force applications are closely related to acceleration. On the other hand pressure transducers are designed to minimize or eliminate (by direct compensation of the charge output) the vibration effect. Call Kistler directly for more information on this subject or refer to the inside back cover which lists available technical articles.
The finely lapped quartz elements are assembled either singly or in stacks and usually preloaded with a spring sleeve. The quartz package generates a charge signal (measured in picoCoulombs) which is directly proportional to the sustained force. Each transducer type uses a quartz configuration which is optimized and ultimately calibrated for its particular application (force, pressure, acceleration or strain). Refer to the appropriate section for important design aspects depending on application.
Quartz transducers exhibit remarkable properties which justify their large scale use in research, development, production and testing. They are extremely stable, rugged and compact. Of the large number of piezoelectric materials available today, quartz is employed preferentially in transducer designs because of the following excellent properties:
High and Low Impedance
Kistler supplies two types of piezoelectric transducers: high
and low impedance. High impedance units have a charge output
which requires a charge amplifier or external impedance converter
for charge-to-voltage conversion. Low impedance types use the
same piezoelectric sensing element as high impedance units and
also incorporate a miniaturized built-in charge-to-voltage
converter. Low impedance types require an external power supply
coupler to energize the electronics and decouple the subsequent
DC bias voltage from the output signal.
DYNAMIC BEHAVIOR OF
TRANSDUCERS
Piezoelectric transducers for measuring pressure, force and
acceleration may be regarded as under-damped, spring mass systems
with a single degree of freedom. They are modeled by the
classical second order differential equation whose solution is:
Where:
fn = undamped natural (resonant) frequency (Hz)
f =frequency at any given point of the curve (Hz)
ao = output acceleration
ab = mounting base or reference acceleration (f/fn = 1)
Q = factor of amplitude increase at resonance
Quartz transducers have a Q of approximately 10 to 40 and therefore the phase angle can be written as:
phase lag (deg) 
A typical frequency response curve is shown in Figure 3 shown, about a 5% amplitude rise can be expected at 9/40 of the resonant frequency. Low-pass (LP) filtering can be used to attenuate the effects of this. Many Kistler signal conditioners (charge amplifiers and couplers) have plug-in filters for this purpose.
Figure 3 -Typical
Frequency Response Curve
CHARGE AMPLIFIERS
Basically the charge amplifier consists of a high-gain inverting
voltage amplifier with a MOSFET or JFET at its input to achieve
high insulation resistance. A simplified model of the charge
amplifier is shown below in Figure 4.
Figure 4 - Simplified Charge
Amplifier Model
Ct =
transducer capacitance
Cc= cable capacitance
Cr = range (or feedback) capacitor
Rt = time constant resistor (or insulation of
range capacitor)
Ri = insulation resistance of input circuit
(cable and transducer)
q = charge generated by the transducer
Vo = output voltage
A = open loop Gain
The effects of Rt and Ri will be discussed below. Neglecting their effects, the resulting output voltage becomes:
For sufficiently high open loop gain, the cable and transducer capacitance can be neglected and the output voltage depends only on the input charge and the range capacitance.
In summary, the amplifier acts as a charge integrator which compensates the transducer's electrical charge with a charge of equal magnitude and opposite polarity and ultimately produces a voltage across the range capacitor. In effect, the purpose of the charge amplifier is to convert the high impedance charge input (q) into a usable output voltage
Time Constant and Drift
Two of the more important considerations in the practical use
of charge amplifiers are time constant and drift. The time
constant is defined as the discharge time of an AC coupled
circuit. In a period of time equivalent to one time constant, a
step input will decay to 37% of its original value.
Time Constant (TC) of a charge amplifier is determined by the product of the range capacitor (Cr and the time constant resistor (Rt):
TC = Rt Cr
Drift is defined as an undesirable change in output signal over time which is not a function of the measured variable. Drift in a charge amplifier can be caused by low insulation resistance at the input (Ri) or by leakage current of the input MOSFET or J-FET.
Drift and time constant simultaneously affect a charge amplifier's output. One or the other will be dominant. Either the charge amplifier output will drift towards saturation (power supply) at the drift rate OR it will decay towards zero at the time constant rate.
Many Kistler charge amplifiers have selectable time constants which are altered by changing the time constant resistor (Rt). Several of these charge amplifiers have a "Short", "Medium" or "Long" time constant selection switch. In the "Long" position, drift dominates any time constant effect. As long as the input insulation resistance (Rj) is maintained at greater than 1013 ohms, the charge amplifier (with MOSFET input) will drift at an approximate rate of 0.03 pC/s. Charge amplifiers with J-FET inputs are available for industrial applications but have an increased drift rate of about 0.3 pC/s.
In the "Short" and "Medium" positions, the time constant effect dominates normal leakage drift. The actual value can be determined by referring to the appropriate operation/instruction manual which is supplied with the unit. Kistler charge amplifiers without "Short", "Medium" or "Long" time constant selection, operate in the "Long" mode and drift at the rates listed above. Some of these units can be internally modified for shorter time constants to eliminate the effects of drift.
Frequency and Time Domain
Considerations
When considering the effects of time constant, the user must
think in terms of either frequency or time domain. The longer the
time constant, the better the low-end frequency response and the
longer the usable measuring time. When measuring vibration, time
constant has the same effect as a single-pole, high-pass (HP)
filter whose amplitude and phase are:
phase lead (deg) = arc tan 
For example, the output voltage has declined approximately 5% when f x (TC) equals 0.5 and the phase lead is 18 degrees.
When measuring events with wide (or multiple) pulse widths, the time constant should be at least 100 times longer than the total event duration. Otherwise, the DC component of the output signal will decay towards zero before the event is completed.
Other design features incorporated into Kistler charge amplifiers include range normalization for whole number output, low-pass filters for attenuating transducer resonant effects, electrical isolation for minimizing ground loops and digital/computer control of setup parameters.
LOW IMPEDANCE
PIEZOELECTRIC TRANSDUCERS
Piezoelectric transducers with miniature, built-in
charge-to-voltage converters are identified as low impedance
units throughout this catalog. These units utilize the same types
of piezoelectric sensing element(s) as their high impedance
counterparts. PIEZOTRON®, PICOTRON®,
PiezoBEAM® and K-SHEAR® are
all forms of Kistler low impedance transducers.
In 1966, Kistler developed the
first commercially available piezoelectric transducer with
internal circuitry. This internal circuit is a patented design
called the PIEZOTRON. This circuitry employs a miniature MOSFET
input stage followed by a bipolar transistor stage and operates
as a source follower (unity gain). A monolithic integrated
circuit is utilized which incorporates these circuit elements.
This circuit has very high input impedance (1014
) and low output impedance
(100) which allows the
charge generated by the quartz element to be converted into a
usable voltage. The PIEZOTRON design also has the great virtue of
requiring only a single lead for power-in and signal-out. Power
to the circuit is provided by a Coupler (Power Supply) which
supplies a source current (2-18mA) and energizing voltage
(20-30VDC). Connection is as shown in Figure 5. A Kistler
coupler and cable is all that is needed to operate a Kistler
transducer.
Figure 5 - PIEZOTRON Circuit & Coupler
q = charge generated by piezoelectric element
Vi = input signal at gate
V0 = output voltage (usually bias decoupled)
Cq = transducer capacitance
Cr = range capacitance
CG= MOSFET GATE capacitance
Rt = time constant resistor
The steady state output voltage is essentially the input voltage at the MOSFET Gate plus any offset bias adjustment. The voltage sensitivity of a PIEZOTRON unit can be approximated by:
The range capacitance (Cd and time constant resistor (Rt) are designed to provide a predetermined sensitivity (mV/g) and upper and lower usable frequency. The exact sensitivity is measured during calibration and its value is recorded on each unit's calibration certificate.
Since its invention, the PIEZOTRON design has been adapted by manufacturers worldwide and has become a widely used standard for design of transducers which measure acceleration, force and pressure The concept has become known by Many names besides PIEZOTRON such as low impedance or voltage mode. Also, a number of "brand names" have emerged by other manufacturers.
PICOTRON is a miniature accelerometer whose circuitry is very similar to the PIEZOTRON. PiezoBEAM incorporates a bimorph ceramic element and a miniature hybrid charge amplifier for the charge-to-voltage conversion. K-SHEAR is the newest member of the Kistler low impedance family and utilizes a shear quartz element together with the PIEZOTRON circuitry.
Time Constant
The time constant of a PIEZOTRON or PICOTRON transducer is:
TC = Rt (Cq + Cr + CG)
A PiezoBEAM's time constant is the product of its hybrid charge amplifier's range capacitor and time constant resistor.
Time constant effects in low impedance transducers and in charge amplifiers are the same. That is, both act as a single pole, high-pass filter as discussed previously.
LOW IMPEDANCE POWER
SUPPLY (COUPLER)
All of the low impedance types mentioned above
require similar excitation for their built-in electronics. A
single two-wire coaxial cable and a Kistler Power Supply Coupler
is all that is needed. Both the power into and the signal out
from the transducer are transmitted over this two-wire cable. The
coupler provides the constant current excitation required for
linear operation over a wide voltage range and also clecouples
the bias voltage from the output.
Time Constant
Bias decoupling methods can be categorized as AC or DC. DC
methods of bias decoupling will not effect a low impedance
transducer's time constant and therefore permit optimum low
frequency response. An offset voltage adjust is used to
"zero" the bias. AC decoupling methods, however, can
shorten the low impedance transducer's time constant and degrade
low frequency response. In low impedance systems, with AC bias
decoupling the system time constant can be approximated by taking
the product of the transducer and coupler time constants and
dividing by their sum. The resulting frequency response can be
computed as before.
Selection Matrix
Many other performance features are incorporated into
Kistler's line of power supply couplers. Included are versions
with multichannel inputs, 100X gain, plug-in filters and computer
control of set-up parameters.
Dual Mode Charge Amplifiers
Another method for powering low impedance transducers is to
use a Dual Mode Charge Amplifier (high/low impedance). Dual mode
units can be used as standard charge amplifiers with high
impedance transducers OR as couplers (with adjustable gain) for
low impedance units.
HIGH AND LOW IMPEDANCE SYSTEM COMPARISON
Similarities
Both systems utilize the same type of piezoelectric sensing
element(s) and therefore are AC coupled systems with limited low
frequency response or quasistatic measuring capability. Their
respective time constants determine the usable frequency range.
High Impedance Systems
Usually high impedance systems are more versatile than low
impedance. Time constant, gain, normalization and reset are all
controlled via an external charge amplifier. In addition, the
time constants are usually longer with high impedance systems
allowing easy short-term static calibration. Because they contain
no built-in electronics, they have a wider operating temperature
range.
Low Impedance Systems
Generally, low impedance systems are tailored to a particular
application. Since the low impedance transducer has an internally
fixed range and time constant, it may limit use to their intended
application. High impedance systems, with control of range and
time constant via an external charge amplifier, have no such
restriction.
However, for applications with well-defined measuring frequency and temperature ranges, low impedance (PIEZOTRON) systems offer a potentially lower cost (i.e. charge amplifier vs. coupler cost) alternative to high impedance systems. In addition, low impedance transducers can be used with general purpose cables in environments where high humidity/contamination could be detrimental to the high insulation resistance required for high impedance transducers. Also, longer cable lengths, between transducer and signal conditioner and compatibility with a wide range of signal display devices are further advantages of low impedance transducers.
EXTERNAL IMPEDANCE
CONVERTERS
An alternative method for processing charge from
high impedance transducers is to use an external impedance
converter. This method is often used to exploit the high
temperature range of high impedance transducers while
implementing the convenience and cost effectiveness of the
coupler.
External impedance converters incorporate the same circuitry s the PIEZOTRON. The equation for sensitivity and time constant can be found on above. The only difference is that the transducer cable capacitance must be added to the transducer capacitance (Cq)Refer to page 66 for additional information on Kistler's external impedance converters.
TRANSDUCER
QUALITY/CALIBRATION
Over the years, the Kistler name has become
synonymous with QUALITY. We at Kistler are dedicated to
continuous improvement in all areas: Design, Manufacturing,
Quality Control, Quality Assurance and Calibration.
All Kistler products are manufactured in conformance with the requirements of ISO 9001 and MIL-1-45208A. Kistler's calibration system complies with the requirements of MIL-STD-45662A. Calibrations performed at Kistler are traceable to the National Institute of Standards and Technology (NIST), or the Swiss Federal Office of Metrology. Kistler takes full advantage of the latest technology, performing computer controlled testing, calibration and data collection. Kistler products are used as primary standards for many of the world's leading test and national calibration laboratory facilities, including NIST.
KISTLER CALIBRATION TECHNIQUES
Pressure Transducers
Most piezoelectric pressure transducers have a time constant
which is long enough to permit quasistatic calibration. The
reference or standard transducer is typically a piezoelectric
transducer which is first calibrated against a Dead Weight
system. The reference and test transducers are simultaneously
pressurized in a hydraulic pump system and their outputs are
recorded on an XY-plotter. The sensitivity, linearity and
hysteresis are analyzed for each transducer.
For pressure transducers with a short time constant, a special dynamic pressure calibrator is used. During the assembly process, the sensing element is quasistatically calibrated as a charge device. During the final calibration, the dynamic calibration determines the actual sensitivity.
Force Transducers
The calibration of force transducers is very similar to
pressure transducers. The unit under test is calibrated against a
standard force ring whose calibration is traceable to NIST. A
hydraulic press is used to generate forces for this calibration.
Accelerometers
Kistler acceleration standards are periodically calibrated by
an independent third party providing NIST traceability. These
primary standards are used to calibrate a set of working
standards at Kistler. The working standards are configured to
accept direct mounting of the unit under test. This "Back to
Back" calibration technique minimizes errors. Calibration is
performed on a sinusoidal motion shaker.
GLOSSARY &
TECHNICAL REFERENCES
Kistler has placed a glossary and a list of technical articles on this web page.
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