CHAPTER 7: TRANSDUCERS
In general terms, the transduction process involves the transformation of one form of
energy into another form. This process consists of sensing with specificity the input energy from
the measurand by means of a "sensing element" and then transforming it into another form by a
"transduction element." The sensor-transduction element combination shown in figure below will
henceforth be referred to as the "transducer". Measurand relates to the quantity, property, or state
that the transducer seeks to translate into an electrical output.
Transducers may be classified as self-generating or externally powered. Self-generating
transducers develop their own voltage or current and in the process absorb all the energy needed
from the measurand. Externally powered transducers, as the name implies, must have power
supplied from an external source, though they may absorb some energy from the measurand.
I. TRANSDUCTION MECHANISMS
Capacitive
Inductive and electromagnetic Resistive
Resistive and thermoresistive
Piezoresistive effect
Hall effect
Lateral effect
Extrinsic, interferometric and evanesquenching cent effects in optical fiber
Magnetoresistive effect
Tunneling effect
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Peltier)
Thermoelectric effects (Seebeck and
Ionization effects
Photoelectric effect
Photoresistive effect
Photovoltaic effect
Acoustooptic effect
Fluorescence
and
fluorescence
Field effect
Doppler effect
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II. MEASURANDS
Displacement
Position
Velocity
Acceleration
Force and load
Strain
Rotation and encoding
Vibrations
Flow
Temperature
Pressure
Vacuum
Atomic and surface profiles
Gas concentration and pH
pH and partial pressure of O2 and CO2
in blood
Infrared radiation
Torque
Magnetic field
Acoustic fields
Medical imaging
Non-destructive testing
Audio fields and noise
Rotation and guidance
III. SELECTION OF TRANSDUCERS
When selecting a transducer, in addition to the question of cost, careful attention must be
given to the following
Sensitivity
Range
Physical properties
Loading effect and distortion
Frequency response
Electrical output format
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Output impedance
Power requirements
Noise
Error or accuracy
Calibration
Environment
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IV. CLASSIFICATION OF TRANSDUCERS
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Before discussing the transduction principles, we first examine several methods for
combining individual transduction principles into one single compound transducer. These
“composite methods” are employed to reduce or even totally eliminate certain restrictions
associated with individual transducers. A widespread method is to use 2 identical transducers in a
balanced configuration shown in Figure 3.1 below.
If the transducers have the same transfer characteristic, the output y of the balanced
configuration is:
y = f(x) – f(-x)
Here f(x) may be the non-linear transfer function that we intend to linearize. Let assume that
f(x) can be expressed with a Taylor expansion in the following form:
f(x)= a0+a1x+a2 x2+ a3x3+ a4x4+ a5x5 ….
Using the balance equation above, we find:
y = 2a1x + 2a3x3 + 2a5x5 + …
Evidently, the constant (or offset) a0 and the even terms a2x2, a4x4, … disappear when
balancing the two transducers. If the non-linearity of f(x) does not contains any uneven terms, we
will obtain a perfectly linear system. The systems then referred to as a “difference configuration”.
However, usually balancing will only improve the linearity of the system over a limited range of the
input quantity x. Such system is called a “differential configuration”. The balanced configuration is
not sensitive to external disturbances, since it inherently makes use of parallel compensation. The
configuration is immune to additive disturbances when the transducers T and T’ have the same
sensitivity to these disturbances. In order to be immune to multiplicative disturbances, the
transducers T and T’ must have disturbance coefficients with the same magnitude, but opposite
signs.
A second commonly used configuration is the feedback configuration of 2 transducers T1
and T2 in Figure 3.2 below. The purpose of the system is to convert an input signal x into an
electrical output signal y. We could use a single transducer T1 for this. Assume T1 is unsuitable to
be used directly, due to an unacceptably large non-linearity and has too large a sensitivity to
disturbances. If we have a second transducer, capable of the reverse conversion (conversion of y to
x) and this conversion is linear and not susceptible to disturbances, then when we combine both
transducers T1 and T2 (with an amplifier to increase the loop gain) in the feedback configuration,
we can realize a compound transducer for conversion of measurement signal from x into y, with the
same characteristics as the employed reverse transducer. The necessary conditions for achieving this
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are a large gain and a quasi-static dynamic behavior for T1, T2 and A. In practice, though, the
dynamic behavior of especially T1 and T2 is often of a higher order and, therefore, the situation
may not be as ideal as described above.
Finally, the reliability of the transducers is often a problem. Sometimes this can be solved by
using several transducers which all measure the same quantity. This “redundant configuration”
greatly improves the reliability of the system at, of course, an increased cost.
V. MECHANOELECTRIC TRANSDUCERS
These transducers measure mechanical quantities.
1. Displacement transducers
Displacement transducers can measure either linear displacement (translation) or angular
displacement (rotation). They can also be classified according to the principle of transduction on
which they are based. We can distinguish between, for instance, resistive, capacitive, inductive and
optical translation or rotation transducers. These mechanical transducers are also referred to as
gauges or sensors.
a. Resistive displacement transducers
The potentiometric transducer is a popular type of displacement transducer. For measuring
translation it is, in fact, no more than a sliding potentiometer. For measuring rotation, a rotating
potentiometer can be used. Usually the potentiometers are wire-wound to achieve a better accuracy,
temperature coefficient, etc. However, a limitation of wire-wound displacement transducers is their
finite resolution. The maximal resolution R = x/Ax is equal to the number of turns on the
potentiometer body. Metal film potentiometers do not have this limitation. A disadvantage of all
transducers of the potentiometric type is that mechanical wear and chemical corrosion can change
the transfer characteristic over the lifetime of the transducer.
Another type of resistive displacement sensor makes use of the fact that the electrical
resistance of a conductor depends on the dimensions of the conductor. The resistance R is a function
of the cross sectional area of the conductor, its length l and its resistivity ρ.
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R=R(A,l,ρ)
If the conductor is mechanically strained or compressed, the parameters A, l, and ρ, and as a
consequence R, will change. This enables one to measure very small displacements. Figure 3.4a
shows a piece of wire (stain gauge) which is elongated a distance ∆l by applied tensile stresses.
Figure 3.4(b) shows the meanders of a metal foil strain gauge are made extra wide when they turn,
in order to reduce the sensitivity of the strain gauge to strain perpendicular to the main axis of
operation. If, besides the magnitude of the strain, we also wish to measure the direction of the strain,
a combination of strain gauges is used, arranged in a certain geometric pattern, for instance 3 strain
gauges oriented at 120 degrees angles with respect to one another. This arrangement is known as a
strain gauge rosette.
b. Capacitive displacement sensors
b. Capacitive displacement transducers
Capacitance C is a function of distance d between the electrodes of a structure, the surface
area A of the electrodes and the permittivity ε of the dielectric.
C=C(d,A,εε)
Therefore the capacitance can be changed when the three variables are changing. Figure 3.6
shows the displacements sensors using the detection of capacitance and the applicable capacitances
for each displacement. It is shows that the variable distance transducer has a non-linear
characteristics and can be linearized by using it in a balanced configuration.
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The force F(x) causes the movement of sensor with a constant voltage across the capacitor is
given by:
c. Inductive displacement sensors
It is not only possible to vary the self-inductance of a single coil as a function of the
displacement to be measured, it is possible to vary the mutual inductance between two coils as a
function of the displacement. An obvious way of varying the inductance of a coil is to vary the
effective number of turns, Figure 3.8(a), and vary the magnetic resistance (reluctance) of the yoke
by means of an air gap of variable width, Figure 3.8(b).
The displacement of the second transducer, based on variable reluctance, is incorporated in a
bridge network to obtain a linear transfer characteristic.
d. Optical displacement sensors
Displacement can also be detected optically, by means of an encoding strip (translation) or a
rotary encoder (rotation). Figure 3.10(a) shows an optical displacement sensor which utilizes an
encoder strip consisting of rows of alternating transparent and opaque bars. The position of the strip
is converted directly to a digital signal with a narrow beam of light and a number of light sensors.
The digital code is determined by the position of the transparent and opaque bars on the strip.
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2. Velocity transducers
There are two transducers used to measure velocity: translational and angular transducers.
The measure of velocity is often converted to a frequency measurement. The conversion is
performed by a strip or disc on which a large number of marks (detection elements) have been put
at equal distances x. The velocity can be calculated from v=∆xn/t = ∆xf, in which n is the number
of detection element which passes the detector in t seconds and f is the frequency of output signal.
The detection can be performed optically, mechanically, inductively or capacitively.
a. Measurement of velocity by differentiation or integration:
For linear velocity v(t)
v( t ) =
dx( t )
dt
where x(t) is the linear displacement
d (t)
dt
where θ(t) is the rotation angle.
For angular velocity ω(t):
(t ) =
From these two equations, it is evident that we can obtain a signal, for the velocity of an
object, by calculating the derivative of the output signal of a displacement sensor. It is simple to
design an electronic circuit for differentiating an electrical signal.
Another possibility for obtaining the velocity is by integrating of the linear acceleration a(t)
t
v( t ) = a (t )dt + v(0)
0
or of an angular acceleration α(t):
(t) =
t
(t )dt + (0)
0
The integration can be performed by a relative simple analogue electronic circuit. It should be
noted that the differentiator and integrator circuits having a disadvantage of increasing or decreasing
very slowly, even when the input is zero, due to leakage or drop.
b. Inductive velocity transducers:
In this kind of transducers, the velocity of the measurement object is made to give rise to a
change of magnetic flux Φ, which induces an electrical potential in a conductor. The induced voltage
of Figure 3.11(a) in turn i of the coil of this inductive velocity pick up is given by:
Vi = −
d i
dt
For a total of n turns, the coil terminal voltage is:
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Vi = −
n d
i
i = n dt
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Since ΦI=ΦI(x), in which x is the position of the magnet with respect to the center of the coil, and
x=x(t), we find:
n d
n
i dx = − v d i = vk( x )
i = n dt dt
i =1 dx
Vi = −
Thus, the output voltage V is proportional to the velocity v of the magnet for a given value
of x. The sensitivity of the transducer is equal to k. Unfortunately, since k=k(x), the transducer is
non-linear. Therefore, again this type of transducer is often used in a balanced configuration. Since
the magnet is moving here the velocity sensor is referred to as a magneto-dynamic transducer.
3. Acceleration transducers
Transducers for measuring acceleration rely on the measurement of the force F required to
give a known mass (the seismic mass m) the same acceleration, a, as the measurement object. From
the force and the mass, the acceleration is determined: a=F/m. The extra mass has to be kept to a
minimum, especially when the measurement object is highly elastic or has a low mass (extra mass
influences the measure acceleration).
VI. THERMO-ELECTRIC TRANSDUCERS
1. Resistive temperature sensors
a. Metal:
The electrical resistance of any material depends to a certain extend on the temperature and
can be used to convert a temperature measurement into a measurement of resistance. Depending on
the material used, we can distinguish two kinds of thermometers: metal thermometers and
semiconductor thermometers.
The resistive of pure metals can be written in the form of power series:
R (T) = R (T0 )[1 + (T − T0 ) + (T − T0 ) 2 + (T − T0 ) 2 + ....]
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in which R(T) is the resistance of the sensor at temperature T and R(T0) is the resistance at certain
reference temperature T0. If the temperature range is not too large, the first 2 terms of the
expansion will suffice, the sensor is approximately linear. The most frequently used metals are
platinum and nickel. The measurement range of a platinum sensor runs from 70K to 1000K and
nickel from 200K to 500K. At T0=273K:
αPt=3.85 x 10-3 K-1
αNt =6.17 x 10-3 K-1
βPt=-5.83 x 10-7 K-2
γPt=-3.14 x 10-12 K-3
b. Semiconductors:
In both intrinsic and extrinsic semiconductors, this effect is overshadowed by a much
stronger effect: the number of free charge carriers depends on the absolute temperature. The higher
the temperature, the larger the number of electrons which cross the band gap from the valence band
into the conduction band (intrinsic) or the larger the number of activated donor and acceptor atoms
(extrinsic). The number of free charge carriers increases according to:
n=n0e-Eg/2kT
in which Eg is the energy required for the crossing the band gap and k is Boltzmann’s constant
(1.3804 x 10-23 J/K). Thus the resistance of a semiconductor will decrease as the temperature
increases, the semiconductor has a Negative Temperature Coefficients (NTC-resistor).
The resistance of a semiconductor can be expressed as:
R(T)=AeB/T
The coefficients A and B also depend on the temperature and therefore a more accurate expression
is given by:
R (T) = R (T0 )e B(1 / T −1 / T0 )
Obviously, a semiconductor sensor is highly non-linear. The temperature coefficient is
given by:
( T) =
1 dR (T)
B
=−
R (T) dT
T2
In practice, the value of the coefficient B lies between 2700K and 5400K at a temperature
of 300K. Thus, at 300K, the temperature coefficient ranges from –3 x 10-2 K-1 to –6 x 10-2 K-1. At
300K, a semiconductor sensor is an order of magnitude more sensitive than a metal sensor. Such a
semiconductor temperature-sensing resistor is often referred to as thermistor. More improvement in
the making of thermistors yields better linear characteristic.
2. IC temperature sensors
An alternative temperature sensor can be found in the bipolar transistor. Such a sensor
makes use of the fundamental band gap voltage of silicon, which depends in the temperature. Two
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bipolar transistors located close together, on the same IC, are biased to different collector current.
If the ratio of the (collector) current densities (the transistors may have different areas) is equal to r,
the difference between the base-emitter voltages of the two transistors is equal to (kT/q)ln(r). This
base-emitter voltage difference is a linear measure of absolute temperature. Addition electronic
circuits amplify this voltage to provide a practical output value. Typical IC sensor specifications
are: range -55oC to 150oC, non-linearity over the entire range of approximately 0.3K, sensitivity
10mV/K or 1uA.K, instability over 1000hr of operation ±0.08K, dissipation 1.5mW to 3mW.
3. Thermal couples
When two different metals are brought into atomic contact with each other, an electrical
potential difference is generated. This so-called junction potential depends only on the nature of
the two metals and on the absolute temperature. The surface area of the junction has no influence.
For many combinations of metals the junction potential difference is approximately linearly
proportional to the absolute temperature of the junction, provided that the temperature range is
not too large. When two junctions are connected in series, as illustrated in Fig. 3.16(a), a net
thermo voltage V will result if the two junctions are at different temperatures. This configuration
is called a thermocouple. Several characteristics of thermocouples have been plotted in Fig.
3.16(b).
The thermovoltage is a measure of the temperature difference between the two junctions.
The output voltage of a thermocouple can be written more accurately as a power series of the
temperature difference T-To, with To a certain calibration temperature than it can if it is assumed to
be proportional to temperature: i.e.
As n increases, this expression will describe the behavior of a given thermocouple more and
more accurately. Every thermocouple (so every combination of two metals) is characterized by its
own series of temperature independent coefficients ai (i = 1, ..., n). An inaccuracy of ±l% requires
roughly eight coefficients (n=8) for most materials. The coefficient a1 is referred to as the Seebeck
coefficient. Fig. 3.16(c) shows how this coefficient would depend on the temperature if a
thermocouple were to be described by only one single coefficient, a1.
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If we are dealing with a large temperature range, we must use more than one coefficient
for reasons of accuracy. There are four physical effects that contribute to the output voltage of the
thermocouple.
-Seebeck effect.
This is the desired effect which is measured when no current is allowed to flow through the
thermocouple. It arises from the temperature dependence of the junction potential
difference. This junction potential difference originates from the difference in Fermi levels
of two dissimilar metals. The higher the temperature, the larger the number of electrons
with a higher energy level than the Fermi level. This causes the junction potential
difference to become temperature dependent.
-Peltier effect.
When a current flows through a junction of two dissimilar metals, the temperature of the
junction will change. Depending on the direction of the current, the junction will become
either warmer or cooler than ambient. This effect is caused by the fact that with every
electrical conduction process there is also transportation of heat. In a metal, thermal
conduction as well as electrical conduction are caused by free electrons. The Peltier effect is
undesirable in a thermocouple since it gives rise to a temperature error.
-Thomson effect.
If a current is flowing through a uniform metal conductor in the direction in which there is a
negative temperature gradient, thermoelectric heat will be generated. If the direction of the
current is reversed, heat will be extracted from the conductor. This reversible effect also
originates from the fact the electrical conduction process in a metal is accompanied by the
transfer of heat and, inversely, heat conduction is accompanied by electrical conduction.
This effect also gives rise to errors.
-Joule heat.
With the last two effects, we assumed that no heat was generated by the dissipation of
electrical energy in the electrical resistance of the metals. If the total resistance is R, then,
per second, I2R joules is dissipated. The thermocouple will therefore heat itself up. Thus, the
clear conclusion is that no current may flow through the thermocouple when one is
interested in accurate temperature measurements; the measurement circuit must have a high
input impedance.
An additional source of measurement errors is moisture. Moisture can create a galvanic
element with both metals, which generates a galvanic cell voltage many times larger than that of
the thermocouple. Therefore, thermocouples are often supplied in a waterproof case.
If we wish to measure the absolute temperature as opposed to a temperature difference by
means of a thermocouple, we must hold one of the junctions at a fixed known reference
temperature. This can be achieved by controlling the temperature of one of the junctions with a
thermostat. It is also possible to compensate the temperature of the reference junction, as indicated
in Fig. 3.17. The temperature of the reference junction is measured here by a resistance sensor
R(T), which is connected to a bridge network. The output voltage of the bridge is connected in
series with the thermocouple such that it compensates for the temperature of the reference junction.
Of course, the temperature sensitivity of the reference junction must oppose that of the
bridge network. The temperature measured by the active junction AB is usually located some
distance away from the rest of the circuitry. The metal of the thermocouple junction is usually too
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expensive to use for long interconnections and, therefore, two wires A'B' of a cheaper metal are
used for the interconnections. Provided that these two wires A' and B' have the same thermoelectric
characteristics as the two wires A and B of the measurement junction, no error will be introduced. It
can be seen that when two (other) metal conductors are connected in series with the two junctions
of the thermocouple, as in Fig. 3.17, the new junctions will not contribute a net potential
difference, as long as the new junctions are kept at the same temperature (isothermal). The extra
junction potentials will cancel each other. Temperature differences between these new junctions
will cause measurement errors. If the cable which connects the two junctions of the thermocouple
has the same thermoelectric characteristics it is referred to as compensation cable.
4. Radiation thermometers
A radiation thermometer absorbs a fraction of the infrared radiation emitted by the
measurement object. A radiation thermometer for high temperatures is usually called a pyrometer.
The radiation is usually focused on the actual thermal detector by means of a concave mirror (as
illustrated in Fig. 3.18(a)). If the temperature of the measurement object is lower than that of the
detector, it will supply heat energy to the object, causing the detector to cool. The use of lenses is
avoided, especially for low temperatures, since lenses which easily transmit heat radiation
(diathermanous infra-red lenses) are very expensive.
Other pyrometers are based on quantum detectors. This principle of operation relies on the
electrons of the material being excited by infrared radiation. This can only occur when the quantum
energy E of the radiation quanta is equal to or larger than a certain threshold energy Eo. This
threshold energy corresponds to the transition of electrons to a higher energy state.
With:
hc
E 0 = hf 0 =
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0
This threshold energy is related to infrared radiation above a certain minimal frequency fo
or below a certain maximal wavelength λ0 Fig. 3.18(b) shows the spectral sensitivity of this kind of
quantum detector.
Photodiodes are used as quantum detectors for near infrared radiation; photoresistors are
used in the far infrared region. Quantum detectors respond quickly, but only measure radiation in a
limited band of wavelengths. Pyrometers are used for measuring extremely high temperatures
(T>1000K) when no other means are available. They are also used for measuring objects with a
high thermal resistance, such as plastics, rock, etc.
Besides the described methods for converting a temperature into an electrical signal, there
are many more. One is the (quartz) crystal thermometer which is based on the temperature
dependence of the resonance frequency of a piezoelectric crystal. The crystal is used to determine
the frequency of an oscillator accurately. This frequency can be determined by the enumeration
method, resulting in a small inaccuracy of only 0.01K and a very high resolution of 104 in the range
from -80°C to 250°C. These excellent specifications are realized by cutting the quartz crystal very
accurately with respect to the crystal orientation axes. This is done in such a way that the
temperature sensitivity of the resonance frequency is maximal and as stable as possible. A
calibration curve of temperature versus frequency is recorded and built into the instrument
(PROM) to increase the accuracy even further.
VII. MAGNETOELECTRIC TRANSDUCERS
The induction of a magnetic field can be measured with transducers referred to as
magnetometers or magnetic field sensors. The magnetic induction B is expressed in teslas (T).
Sometimes, it is also referred to as the magnetic flux density. A unit which is consistent with this
terminology is the weber per square meter with, of course,
1T = 1Wb/m2.
Sometimes a rotating coil (with area A, n turns and angular frequency ω) is used for
measuring the induction B of a static magnetic field. Assuming the coil is so small that the induction
is constant across the surface area of the coil and Bn is the component of B perpendicular to the axis
of rotation, the flux Φ through the coil is equal to Φ = BnA sin θ(t), where (θ) is the instantaneous
angle between the coil and Bn. With θ(t) =ωt, the induced ac voltage is given by:
V = −n
d
= −nBn cos( t )
dt
We can determine Bn from this expression. Induction sensors always require a changing
flux. The change in magnetic flux can obviously also arise from an alternating magnetic field in a
static coil.
Another type of magnetometer is based on the influence of a magnetic field on the electrical
resistance of a material. As early as 1856 W. Thomson (Lord Kelvin) discovered that if one
exposes a current conducting body to a magnetic field the electrical resistance changes. This effect,
called the magnetoresistive effect, was only used much later for realizing transducers. It was not
until the American physicist E. F. Hall had discovered the so called Hall effect that an explanation
for this phenomenon could be given.
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The Hall effect is a result of the Lorentz force, exerted on charge carriers in solids. When a
platelet of conducting material is positioned in a magnetic field (as sketched in Fig. 3.19), the
charge carriers will be deflected in a direction perpendicular to the direction of motion of these
charge carriers and perpendicular to the induction vector B of the magnetic field. The Lorentz force
acting on a charge q with velocity v is equal to:
Fl=q(vB)
As the charge carriers are deflected, a transverse charge gradient will build up, resulting in
an electrical field E across the plate. This field will subject the charge carriers to an opposing force
Fe which is given by:
Fe=qE
At a certain point, equilibrium is reached between the Lorentz force and the force produced by the
electrical field, so Fe = Fl and therefore:
E=vB
Assuming the charge carriers all have approximately the same velocity v, the current
density J is equal to nqv, with n the concentration of charge carriers. If, in addition, we assume that
B is perpendicular to v, as in Fig. 3.19, then E = JB/nq. The factor 1/nq is called the Hall
coefficient and usually denoted by RH. With I=bdJ and V =Eb we find:
V=
1 IB
IB
= RH
nq d
d
For semiconductor materials, in which the majority charge carriers are holes (p-type
semiconductors), q is positive and the output voltage of the Hall plate will have the polarity
indicated in Fig. 3.19. If the majority charge carriers are electrons (n-type semiconductors) the
polarity will be opposite. The Hall coefficient is large for semiconductors, since the concentration n
of charge carriers is much smaller in semiconductors than in metals.
Obviously, a Hall plate can measure static magnetic fields, without any moving or rotating
parts. A Hall plate is also suitable for high-frequency measurements; it has a wide frequency range
(up to several GHz). Furthermore, the disturbance to the magnetic field, caused by the Hall plate is
very small. In addition to measuring magnetic fields directly, Hall plates are often used for
measuring large DC currents and in current probes for oscilloscopes.
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VIII. TRANSDUCER SELECTION
The selection of a transducer begins with the specifications of the physical quantity to be
measured. The user must ascertain the required accuracy of the measurement, the duration of the
test, and may need to consider cyclic behavior or other factors. In addition, consideration needs to
be given to the environment in which the transducer is placed. Finally, the calibration procedure
should be considered. Each of these categories is discussed as part of the selection criteria for
transducers. The general selection criteria listed in this section should be considered representative;
additional factors may be necessary for specific transducers.
MEASUREMENT REQUIREMENTS
The measurement requirements for a transducer are as follows
Range:
The range is the set of values a transducer is designed to measure. The minimum and
maximum values of the transducer'
s range are called the endpoints. Some transducers can be
adjusted to cover a different range by attenuating the measurand -for example, a sensitive radiation
transducer can be used if the measured quantity is attenuated using radiation-absorbing filters. It is
not always possible to find a single transducer to cover the entire range of measurand values; in
these cases transducers with overlapping ranges must be selected
Input threshold
The input threshold is the smallest detectable value of the measured quantity starting near
the zero value of the variable. For an input to be discerned, it must be possible to assign a unique
number to the input. The selection of a transducer requires that it respond in a discernible manner to
the threshold.
Dynamic behavior
The dynamic behavior of a transducer specifies how the transducer can respond to a
changing input. No transducer could follow an instantaneous change. (For that matter, no
measurand can change instantaneously!) The transducer'
s dynamic performance is usually specified
as a frequency response or response time, depending on the type of transducer. The response time is
the time required to reach a specified percentage (typically 90% to 99%) of the final value for a
given change of the input. The response time is measured in much the same way as the time
constant for an RC or RL circuit. (Recall that the time constant is the time required for the output to
reach 63% of its final value.)
Accuracy and resolution
Accuracy is the difference between the measured and accepted value. The accuracy
requirements for a particular measurement can greatly affect the total cost of the measurement
system. In addition, certain transducers, such as strain gages and pressure transducers, have a
fatigue life that can change the accuracy, depending on the duration and cyclic behavior of the
measurand. In some cases, the accuracy isn'
t as important as the ability to detect a small change
(resolution), as when quantities are being compared. For example, in underground-tank testing, the
interface between the liquid and air can be located by observing the small temperature difference
between the air and liquid. In other cases, consistency is the most important criterion. Other
accuracy errors include nonlinearities due to a zero shift or drift due to aging, which can affect the
long-term repeatability of measurements
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Repeatability and hysteresis errors
Repeatability is the maximum difference between consecutive measurements of the same
quantity when the measured point is approached each time from the same direction for full-range
traverses. It is usually expressed as a percentage difference of the full-scale output. Hysteresis error
is the maximum difference between consecutive measurements for the same quantity when the
measured point is approached each time from a different direction for full-range traverses. An
example is when backlash in gearing causes the readings of a dial to be different, depending on
whether the gearing was turned in one direction or the other.
OPERATIONAL AND ENVIRONMENTAL CONSIDERATIONS
The operational and environmental considerations for a transducer are as follows
Natural hazards
The transducer, wiring, and connectors must all be able to withstand the effects of exposure
to the required environment. Natural hazards include the effects of dust and dirt, high or low
temperatures, water (including salt water), and humid conditions. Wire insulation is available that is
resistant to these effects as well as solvents, acids, bases, and so forth. In contrast, the transducer
should not present a hazard to the environment in which it is placed-including causing electrical
problems such as explosion hazard or shock hazard.
Human-caused hazards
Human-caused hazards include high-radiation environments, corrosive or dangerous
chemicals, immersion, abrasion, vibration, and explosive environments, to name a few. The
electrical signal from the transducer may be interfered with if the signal cables are routed in an
electrically noisy environment, another possible hazard for proper operation, particularly with
transducers that have a low output signal.
Power requirements
Power requirements depend on the type of transducer. Passive transducers, such as
photocells, convert some of the incident source energy into electrical energy. Others require a
source of excitation, which can be a dc or ac source. If the transducer is being operated in a remote
or noisy environment, the power leads become a source of potential problems.
Signal-conditioning requirements
If the transducer produces a very small signal or it is located at a remote location or in a noisy
environment, amplification or other signal conditioning may be required at the transducer. The
transducer output may need to be converted into a compatible format for the remainder of the
instrumentation system.
Physical requirements
In some installations, the space available may be limited or the measurand may be over a
limited region. If the quantity to be measured is concentrated, such as in the case of a collimated
light source, the physical size of the transducer can affect the output.
Loading effects
Loading effects cause the measurand to be disturbed in some manner by the presence of the
transducer. All measurements in some way modify the quantity to be measured. For example, a
rotating-vane flowmeter extracts a small amount of the energy from the fluid to turn the vane and
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thus changes the flow from its undisturbed value. Loading can also occur in the electrical-measuring
circuit. Electrical loading can occur when a transducer with an equivalent high Thevenin resistance
is connected to an amplifier with a finite input impedance. In this case the transducer signal is
reduced by the connection to the amplifier. Many transducers have a very high equivalent Thevenin
resistance (pH electrodes, for example), so it is important to be aware of the need for compatible
amplifiers.
Human factors
Human factors that need to be considered in the selection of a transducer are the operating
skill of the persons installing and using the transducer, the ease of installation, the cost of the
transducer, and the required maintenance.
CALIBRATION REQUIREMENTS
Our final consideration for selecting a transducer is the calibration requirements. The
calibration interval and type of calibration necessary need to be considered. The calibration interval
is determined by the operating life of the transducer and other factors such as long-term sensitivity
shift, zero shift, and the accuracy requirements of the application. The calibration interval,
complexity, and need to refer to calibration data can affect the total cost of the transducer.
The ideal calibration will precisely predict the response of the transducer in the application
setting. This prediction may be difficult, particularly when there are large differences between the
calibration process and the application such as different loading, dynamic response, or
environmental conditions. Calibration methods vary widely, depending on the transducer, but
should be made in a manner that is traceable to NIST. The errors associated with the standard
should be much smaller than the transducer that is being calibrated. The calibration can consist of
comparing the transducer to a known reference instrument or a physical standard (such as a known
mass for a load cell) or using a physical reference (such as the triple point of water for a temperature
transducer).
Frequently, the physical parameter is varied and the response of the transducer is observed
and compared to a known reference. Generally, the specific calibration points should extend over
the full range of the measurand to avoid the need for extrapolation. For example, a pressure
transducer should be subjected to the same range of pressures in the calibration process that it will
be subjected to in its intended application to reveal any nonlinearities or other problems. The data
should be taken in both an increasing and decreasing direction to reveal any hysteresis present. Data
taken during calibration is called a calibration record. A line connecting the data points is called a
calibration curve for the particular transducer. If the calibration of the transducer is not done under
the same conditions as the operating conditions, systematic error can result whenever the transducer
is used. For example, a radiation transducer that is calibrated with a radio- active source that has a
different spectrum than the spectrum that is to be monitored will lead to flawed data if the
difference is not accounted for.
A calibration performed in a manner that gives the transducer time for the output to settle to a
fixed value is called a static calibration. Transducers used in dynamic measurements can be tested
for their response with a dynamic calibration. A dynamic calibration is often a comparison of the
transducer that is being calibrated with a known reference transducer that is faster. Another dynamic
test is called a step-function response test. In it, the transducer is subjected to a rapid change in the
input measurand, typically from 10% to 90% of the transducer'
s range. For example, a temperature
transducer is very quickly moved to a much warmer or colder environment and its response is
observed. The time required for the output to settle to the new temperature is a measure of the
transducer'
s response time.
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IX. BRIDGE MEASUREMENT
Many transducers - such as strain gages, resistance temperature devices, and certain
displacement transducers-use resistive transduction principles. Typically, these transducers produce
a very small resistance change in response to the measurand. A circuit that can detect these very
small changes is the Wheatstone bridge. Because of their great sensitivity and other advantages,
bridge circuits are widely used for transducer measurements.
A bridge circuit that consists of four resistance arms with a source of energy (called the
excitation) and a detector is shown in Figure 13-4. This circuit is shown with two pairs of leads to
the power supply, a common method of ensuring that the voltage at the bridge is stable. Current to
the bridge flows on the excitation leads. Any variation in the voltage due to IR drop in the excitation
leads is detected by the sense leads and is used to regulate the supply. Notice that the sense leads
carry almost no current, so they have almost no IR drop.
Figure 13-4
The balance condition can be detected with great sensitivity using an instrumentation
amplifier (IA) connected across the differential output, as shown in Figure 13-5. For general
application, the circuit shown is good choice (CMRR is typically greater than or equal to 110 dB).
The IA is selected for low-drift, high- common-mode rejection and gain stability.
Figure 13-5
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When a Wheatstone bridge is used to detect the change in resistance of a single resistive
transducer, the transducer is placed in one arm of the bridge, and the output of the bridge is
observed. Frequently, more than one active transducer is used in a bridge to increase the sensitivity
of the measurement. It is not always necessary to balance the bridge to determine the unknown
resistance; instead, the magnitude of the off-balance condition can be used as an indicator of the
resistance or to detect a change in resistance. The output change is not a linear function of the
resistance change (it is approximately linear when Rl » Runknown), but this non-linearity has some
advantages in certain measurements. It is possible to construct bridges that tend to linearize the
output of nonlinear transducers such as thermistors. Transducer manufacturers have developed a
number of techniques for increasing the linearity, sensitivity, and stability of bridge circuits. These
include specialized amplifiers, changing the excitation source, and matching the thermal or other
characteristic of the transducer with the bridge resistors. For example, strain gages respond to more
than just strain; they also respond to temperature changes. To cancel the temperature effects, a
"dummy" gage can be placed in the same environment but not subjected to the strain of the
measuring strain gage. The dummy gage is placed on the same side of the bridge as the measuring
gage. Temperature effects change the resistance of both gages in a like manner, causing no change
in the output.
Many resistive transducers produce only a tiny change in resistance for a given input
change. For sensitive measurements, the detecting instrument must have good common-mode
rejection (CMR) because each side of the bridge includes a common-mode signal from the
excitation supply. When the detecting instrument is located some distance from the transducer, an
even more serious common-mode problem can occur when ground current causes a common-mode
source to appear between the bridge ground and the instrument ground. Notice that the output
(signal leads) of the bridge in Figures 13-4 and 13-5 are not connected to circuit ground, a condition
referred to as a floating output.
When a voltmeter is connected as a detecting instrument to the bridge outputs, the voltmeter
signal connections should be isolated from circuit ground; however, there is always some high
impedance to ground (Figure 13-6(a)).
Assume that the impedance to ground is different between the high and low inputs (the usual
case). Current from the common-mode ground source finds a path through the voltmeter'
s leads and
generates a differential voltage due to the impedance difference in the return paths. This means that
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a common-mode signal has been converted into a differential-mode signal, and the meter will
respond to this potential. One possible solution is shown in Figure 13-6(b). The excitation supply is
floating-in other words, its reference is isolated from the circuit ground by using an isolation
transformer or a battery. This method can provide CMRRs greater than 160 dB. The left side of the
bridge is connected to circuit ground and the right side of the bridge is connected to a single-ended,
non-inverting op-amp.
Another solution is to use a guarded voltmeter. The guard connection is made so that it shunts
common-mode current away from the meter'
s inputs. One of the best ways to do this is to connect
the guard lead to a low-impedance point that is at the same potential as the low side of the meter.
This is done by adding a low-impedance divider to the bridge, as illustrated in Figure 13-6(c). Most
of the common-mode current will flow through the low-impedance path provided by the voltage
divider. There are other variations of sensing circuits that are designed to optimize dc offset, voltage
or temperature drift, non-linearity, noise performance, or other characteristic.
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