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## Chapter 2: Overviews of Classical Transducers
In this chapter, we provide an overview of several physical transducers and sensors including analog signal processing circuits. The
descriptions that we provide are as follows : in section 2.1, thermocouple temperature
transducers; in
section 2.2, transducers using changes in electrical
resistance; in section 2.3, transducers using differential
transformers; in section 2.4, capacitive
transducers; in section 2.5, PZT transducers; in section 2.6, optical sensors using photo devices; in section 2.7, analog signal processing
circuits; and in section 2.8, application
examples for measurements.
Thermocouples
are widely used as temperature transducers. As shown in Fig.2.1, an output
signal is generated between the terminals of two dissimilar junction conductors
(wire-pairs) A and B, which were made by contacting and welding the two
conductors together, when the junction point of a
thermocouple has a temperature difference for a reference point. This
phenomenon is well known as the Seebeck- effect. Therefore, this
transducer is a temperature -to-EMF (electro-motive-force) converter which can produce an
output voltage without any additional power sources.
Various dissimilar metal combinations are utilized for this
transducer, and most frequently used combinations and their output
characteristics, i.e., the relationship between the output signals and temperature
based on difference from the ice point are shown in Fig.2.2. In this
figure, symbols Fe, CR, AL, Pt, Rh, W, CN, and Cu express an ion, a chromel,
an alumel, a platinum, a rhogium, a tungsten,
a constantan, and a copper, respectively. The output voltage-rate of an iron-
constantan, and an chromel- alumel themocouples are about
This figure was reprinted from Fig.13.20 in Ref. (1)
In
the extension of the output terminals as shown in Fig.2.3, a pair of copper twisted wires is used
for reducing noise induced in the extension wires. In this case, the thermal
EMF at junction points 2 and 3 have canceled each
other (See Fig.2.5). As a result, a thermal EMF at junction point-1 is obtained
from the output terminals of this sensor.
As
shown in Fig.2.4, the differential connections of thermocouples are used for
measuring the temperature difference between two points, i.e., one is the
measuring point (measurand), and the other is a reference point. In this case, the
output voltage of the
differential thermocouples is expressed as follows:
where .
This method is available for both surface contact and immersion
applications.
and ,(_{}_{}) express the output voltages of the junction points 1,2
and3,4,5,6, respectively.
(1)
(2)
The thermal EMF at junction points 3,4,5 and 6 have
the same values. Therefore,
(3)
From the results mentioned above, we can obtain the following result:
Figure
2.6 shows a balanced amplifier for an analog signal processing circuit using a shielded
twisted cable for the thermocouple transducer. In
this figure, (a) and (b) show a circuit configuration and its equivalent
circuit, respectively, where signals The use of a shielded twisted cable can reduce the interference
due to inductive and capacitive noise pickup. The details of this circuit are
described in section 2.7 of this chapter.
As well known, the resistance
where
A
resistivity of highly conductive solid metals or wires
increases with a change in temperature. The resistivity of a conductor
at the temperature
where
The resistance where Figure 2.7 shows an analog
signal processing circuit for these transducers. The output voltage of this circuit is
expressed as follows:
The
platinum, copper and tungsten wires were usually used as the conductors for
thermocouples. The ranges of
temperature difference are approximately from -180℃ to +630℃. 【Example 2.2】Find
the output voltage
Let’s analyze as follows using the Thčvenin theorem: (1)
We have to cut the two input lines of this amplifier and have to
open these input lines . As a result, the voltages
(2)
The resistance between A and B is expressed as (3)
Figure 2.8 shows an equivalent circuit of Fig.2.7,
which can be obtained by means of Thčvenin theorem. The following equations are
obtained from this figure:
The
output voltage of this amplifier is, then
expressed as follows
by means of theses equations:
Thermistors with resistances of NTC (negative temperature
coefficient) are ceramic semiconductors. The NTC thermistors change their
resistance exponentially with a change in temperature. These thermisters can,
then, be used as temperature transducers. The resistance
where 【Example 2.3】In a
thermistor temperature sensor , find a thermistor constant in
temperatures
From
Eq. (2.5), are expressed as
follows:_{}
From
these equations,
Thus, the relationship between the resistance and the temperature
is expressed as a non- linear characteristic. From Eq. (2.5), a small change in
the resistance R can be approximated as follows:
Forward-biased
semiconductor devices The Relationship between the voltage change
In
this circuit, the current
where
The following equation can be easily obtained from above equations:
where
From
Fig.2.9, the current is expressed as
Strain
gages are electromechanical transducers which convert
a change in strain into a change of electrical resistance. Strain gage transducers are used for measuring a force, a pressure,
and a flow. Strain gages are made of solid metals or semiconductors. Figure 2. 10 shows the square bar which
constitutes an electrical conductor. In this figure, one end of this bar is
fixed, and the other end is stretched with the force. The
average strain is defined as follows:
where The
sensitivity
where The values of
【Example 2.5】In the case
that the cross-section of conductor shown in Fig.2.10 has a circular one, the
parameters are given as: Find the change of resistance
We can, then obtain the following results from Eqs.(2.10) and(2.11).
When a tensile force acts on the conductor shown in Fig. 2.10, the
length and the cross-sectional area of the conductor will be _{}, respectively. Show the following relation:
where
The change of resistance
From the above equations, we can, then, obtain a following
relation:
Figure 2.11 shows a displacement transducer
using a
In
Fig.211, the output voltage of the LVDT is expressed as follows:
where
The output voltage The
linear rectifier circuit consists of small signal linear rectifier circuits and
a subtracting amplifier. Figure
2.13 shows a block-diagram of a small signal linear
rectifier circuit.
In this figure, the small signal linear rectifier circuit and a
subtracting amplifier are shown in Fig. 2.36 and Fig. 2.34, respectively.
Figure
2.14 shows a force sensor using the LVDT. The force is converted into the displacement
where
As well known, the capacitance
between electrodes, A and B shown in Fig.2.15 is expressed as follows,
where
A transducer using electrical capacitance,
can thus be expressed as a function of the area
Figure 2.16 shows a basic construction of a capacitive transducer using the gap distance
A
typical transducer of such a structure is a condenser
microphone.
Figure 2.17 shows a capacitance transducer using three electrodes,
where electrode 3 is moved to the right direction with a distance The capacitance
The
voltage
where
The value of maximum range of
the displacement is between
Figure
2.19 illustrates the fringe effect between electrode 1 and the left edge of
electrode 3. In this situation, the value of
For
minimizing the fringe effect, a guarded and shielded
box is used as shown in Fig.2.20, where an input voltage
From
these equations, the following result is obtained.
Figure
2.22 shows an example of an acceleration sensor device using a capacitive
sensor chip. The sensor chip in this figure is
made of an ASIC technology.
^{1), (2)}
PZT ceramics are mainly used as
piezoelectric materials. The root of the word “piezo” means pressure, and thus, piezoelectric material implies pressure electric
one. Chemical
components of PZT ceramics are
PZT that has elastic characteristics, convert
mechanical stress into electrical polarization and vice versa. Figure 2.23 (a) shows the relationship between the stress (force per unit
area)
The
relationship between the two is expressed as follows: where
The
relationship between the two is expressed as follows: where
where
where From
the relations mentioned above, the mechanical distortion
where
Figure 2.24 shows the
coordinate system for the PZT ceramics, and the numbering expressions. Where, subscriptions
1,2, and 3 express the x, y, and z- axes,
respectively. Table
5.1 shows these relations.
As an example described above, we show the stress-strain
relations as follows:
In Fig.2.23 (b), when the stress is zero( (1) strain (2) displacement
(1)
The electric polarization in the PZT is also caused by thermal
expansion. Such
an effect is called pyroelectricity. The pyroelectric coefficient
The
details of these applications are described in almost
all the sections throughout in chapter 3.
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