UNIT 11 Ghosh_EMI_Chap_05 Transducers.pdf

CHAPTER 5
Transducers
Electrical quantities, such as current, voltage, etc. themselves produce electrical signals.
Hence their measurements involve proper conditioning of the signals and displaying them in
convenient ways. Transducers are seldom necessary in such measurements. Sometimes called
sensors1 or detectors, transducers more often than not constitute the first stage of an
instrumentation set up for the measurement of non-electrical quantities.
A transducer is a device which receives energy in one form or state and transfers it to a
convenient form or state. So, transduction is just not conversion of energy from one form to
another, although sometimes it may be so. For example, a diaphragm will produce a
displacement on the application of pressure. Now, pressure and displacement are both
manifestations of mechanical energy, though from the measurement point of view the
displacement is more convenient. So, a diaphragm is a pressure transducer although it does
not convert energy from one form to another. Again, a junction of dissimilar
metals-thermocouple-produces an electrical output with the change of temperature. Here,
it is a case of conversion of heat energy to an electrical one, the latter being preferred from
the standpoint of convenience of measurement. A thermocouple is, therefore, a temperature
transducer.
The transducer, or the responding device can be mechanical, electrical, optical, acoustic,
magnetic, thermal, nuclear, chemical or any of their combinations. But, of course, devices
with electrical output are preferred for the following reasons:
1. The signal can be conditioned, i.e. modified, amplified, modulated, etc. as desired.
2. A remote operation as well as multiple readout is possible.
3. Devices, such as op-amps are available to ensure a minimal loading of the system.
4. Observer-independent data acquisition and minute control of the process with the help
of microprocessors, or for that matter computers, are possible.
5.1 Classification of Transducers
Transducers can broadly be divided into the following categories:
1. Active and passive transducers
2. Analogue2 and digital transducers
3. Primary and secondary transducers
4. Direct and inverse transducers
1 Some authors prefer to reserve this word for passive transducers only.
2 We will use the British spelling instead of the American spelling Analog.
113

114 Introduction to Measurements and Instrumentation
Active and Passive Transducers
Active transducers are self-generating devices, their functioning being based on conversion of
energy from one form to another. And since they generate energy themselves, no external
source of energy is necessary to excite them. For example, the thermocouple is an active
transducer. Depending on their principles of operation, active transducers can be
1. Thermoelectric
2. Piezoelectric
3. Photovoltaic
4. Electromagnetic
5. Galvanic
Table 5.1 gives a rough idea of the use of different kinds of active transducers in the
measurement of representative non-electrical properties.
Property used
Thermoelectricity generation
Piezoelectricity generation
Photoelectricity generation
Electricity generation by
moving a coil in a magnetic
field
Table 5.1 Active transducers
Device
Thermocouple
Thermopile
Thermocouple gauge
Piezoelectric transducer
Photodiode in combination
with a diaphragm
Electromagnetic pick-up
Application in the
measurement of
Temperature
Radiation pyrometry or
temperature of distant objects
Low pressure
Pressure
Pressure
Flow
Passive transducers, on the other hand, do not generate any energy. They need be excited
by the application of electrical energy from outside. The extracted energy from the measurand
produces a change in their electrical state which can be measured. For example, a photoresistor
can be excited by an emf from a cell and the voltage against the photoresistor can be measured.
When exposed to a light of certain intensity (measurand) its resistance changes, thus changing
the voltage across it.
Depending on their principles of operation, passive transducers can be
1. Resistive
2. Inductive
3. Capacitive
4. Magnetoresistive
5. Photoconductive
6. Thermoresistive
7. Elastoresistive
8. Hall effect-based.

Transducers 115
Table 5.2 gives a rough idea of the use of different kinds of passive transducers in the
measurement of representative non-electrical properties.
Table 5.2 Passive transducers
Property used
Resistance variation
Inductance variation
Capacitance variation
Device
Potentiometer
Strain gauge
Pirani gauge
Hot-wire anemometer
Platinum resistance
thermometer
Thermistor
Photoconductive cell or
light-dependent-resistor
(LDR) in combination with
a diaphragm
Linear variable differential
transformer (LVDT)
Synchro
Eddy-current gauge
Capacitor gauge
Dielectric gauge
Application in the measurement of
Displacement
Small displacement useful in
the measurement of strain,
pressure, force, torque
Low pressure
Flow
Temperature
Temperature
Pressure
Displacement
Angular displacement
Displacement
Displacement, pressure
Liquid level, thickness
(which are basically
displacements)
The lists are not exhaustive but representative. As discussed earlier, we are dealing with
electrical transducers only because of their adaptability to instrumentation.
Analogue and Digital Transducers
An analogue transducer, such as a CdS cell3 might be wired into a circuit in a way that it will
have an output that ranges from 0 volt to 5 volt. The value is continuous between 0 and 5
volt. An analogue signal is one that can assume any value in a range. It works like a tuner on
an older radio. We could turn it up or down in a continuous motion. We could fine tune it by
turning the knob ever so slightly. Transducers that we have discussed so far generate analogue
outputs.
But digital transducers generate output in the discrete form. This means that there is a
range of values that the sensor can output, but the values increase in steps. Discrete signals
typically have a stair step appearance when they are graphed on chart. Consider a modern
television set tuner. It allows us to change channels in steps. Or, consider a push button
switch. This is one of the simplest forms of sensors. It has two discrete values. Either it is
3 Cadmium Sulphide cells measure light intensity.

ON, or it is OFF. Other discrete transducers might provide us with a binary value. Digital
displacement encoders4 belong to this category.
Primary and Secondary Transducers
A transducer is said to be a primary transducer when the applied signal is directly sensed
by it. A transducer producing output in the electrical format may be the first element in an
instrumentation system. Generally, such sensing elements are called primary transducers .
Sometimes, as for example in pressure measurement, a mechanical sensor senses the input
and then another device converts the output of that sensor to an electrical format. There, the
latter sensors are called secondary transducers.
Direct and Inverse Transducer
A direct transducer is a device which receives energy in one form or state and transfers it to an
electrical signal. The sensing device can be mechanical, optical, acoustic, magnetic, thermal,
nuclear, chemical or any of their combinations.
Inverse transducer is the transducer which converts electrical quantity into a non-electrical
quantity. A current carrying coil moving in a magnetic field may be called an inverse transducer
because the current carried by it is converted to a force which causes translational or rotational
displacement. Many data indicating and recording devices are practically inverse transducers.
For example, an analogue ammeter or voltmeter converts current to the mechanical rotation
of a pointer, or a speaker in a public address system converts voltage to vibration of air which
produces sound.
5.2 A Few Phenomena
Now we will consider a few not so well-known phenomena based on which transducers are
constructed. They are:
1. Magnetic effects
2. Piezoelectricity
3. Piezoresistivity
4. Surface acoustic wave
5. Optical effects
Magnetic Effects
All the magnetic effects that are of importance for production of transducers are given in
Table 5.3.
Of these effects, magnetoelastic effects-namely, Joule effect, Villari effect, Wiedemann
effect and Matteucci effect-and Hall effect are finding more and more use in so-called smart
sensors. So we discuss these effects in a little more detail here.
4 See Section 6.6 at page 216.

Effect
Faraday effect
Joule effect
(Magnetostriction)
l:!..E effect
Matteucci effect
Thomson effect
Wiedemann effect
Villari effect
Hall effect
Skin effect
Josephson effect
Transducers 117
Table 5.3 Magnetic effects used in transducers
Year of
discovery
1831
1842
1846
1847
1856
1858
1865
1879
1903
1962
What it is
Generation of electricity in a
coil with the change in the
ambient magnetic field
Change in shape of a ferro-
magnetic body with magnetis-
ation
Change in Young's modulus
with magnetisation
Torsion of a ferromagnetic rod
in a longitudinal field changes
magnetisation
Application
Reluctance based transducers
In combination with piezo-
electric elements for magneto-
meters and potentiometers
Acoustic delay line components
for magnetic field measurement
Magnetoelastic sensors
Change in resistance with Magnetoresistive sensors
magnetic field
A torsion is produced in a
current carrying ferromagnetic
rod when subjected to a
longitudinal field
Torque and force measurement
Displacement measurement
Level measurement
Effect on magnetisation by Magnetoelastic sensors
tensile or compressive stress
A current carrying crystal Magnetogalvanic sensors
produces a transverse voltage
when subjected to a magnetic
field vertical to its surface
Displacement of current from Distance and proximity sensors
the interior of material to
surface layer due to eddy
currents
Quantum tunnelling between SQUID magnetometers
two superconducting materials
with an extremely thin
separating layer
Magnetoelastic effects
Various aspects of the coupling between the magnetisation of the ferromagnetic materials and
their elasticity can be employed to sense parameters of interest. Several effects which have
application for sensing are
Direct effect
Joule effect
Wiedemann effect
We discuss these effects briefly here.
Inverse effect
Villari effect
Matteucci effect

Joule5 effect. The Joule effect, the first of the magnetoelastic effects discovered in 1842, is
a change in length due to an applied magnetic field. A transverse change in length and the
associated volumetric change are also observed.
The change in the shape of a material due to a change in its magnetisation is also called
Magnetostriction.
The mechanism of magnetostriction at an atomic level is relatively a complex subject but
on a macroscopic level may be segregated into two distinct processes:
1. The first process is dominated by the migration of domain walls within the material in
response to external magnetic fields.
2. The second is the rotation of the domains.
These two mechanisms allow the material to change the domain orientation which in turn
causes a dimensional change. Since the deformation is isochoric6 there is an opposite
dimensional change in the orthogonal direction. Although there may be many mechanisms to
the reorientation of the domains, the basic idea, represented in Fig. 5.1, remains that the
rotation and movement of magnetic domains cause a physical length change in the material.
H=O
Fractional change= MIL
I
I
I
I
____..:AL:+---
' I
I
I
I
GGGGGGGG
GGGGGGGG
H
Fig. 5.1 Alignment of magnetic domains in a material due to a magnetic field H that causes a change in
its length t::..L {magnetostriction).
We hear a humming sound emitted from a transformer or a fluorescent tube choke. This
is caused by magnetostriction. 50 Hz ac generates magnetic fields in transformers causing the
core to change the maximum length twice per cycle thus producing the familiar and sometimes
annoying 100 Hz (or higher harmonics) hum.
Villari7 effect. The Joule effect has an important inverse effect known as the Villari effect.
A stress induced in the material causes a change in the magnetisation. This change in
magnetisation can be sensed, and once calibrated, used to measure the applied stress or force.
The Villari reversal is the change in sign of the magnetostriction coefficient as it happens
in iron (crystal, 100 axis) from positive to negative when exposed to magnetic fields of
approximately 40,000 A-turn/m (500 oersted).
5 James Prescott Joule (1818-1889) was an English physicist.
6 An isochoric process, aka a constant-volume process, or an isovolumetric process, is a thermodynamic
process during which the volume of the closed system undergoing such a process remains constant.
7 Named after an Italian physicist E Villari (1836-1904).

Transducers 119
The Joule effect and the Villari effect are both utilised in producing magnetostrictive
displacement sensors (see Section 6.5) and level sensors (see Section 12.1).
Wiedemann8 effect. A wire made of a magnetostrictive material exhibits an important
characteristic known as the Wiedemann effect (Fig. 5.2). When an axial magnetic field is
applied to a magnetostrictive wire, and a current is passed through the wire, a twisting
occurs at the location of the axial magnetic field. The twisting is caused by the interaction of
the axial magnetic field, usually from a permanent magnet, with the magnetic field along the
magnetostrictive wire, which is present due to the current in the wire.
-I
t t t t t t t t t t t t t t t t t
t t t t t t t t t t t t t t t t t
/
Ferromagnetic tube
""'
tt tt t ''''1111 tt tt t-+-+-
T tt tt t,,~, 11.11tt tt t
/ ' /
Fig. 5.2 Twisting of a current carrying ferromagnetic tube when subjected to an axial field of a bar
magnet.
Matteucci9 effect. When a wire made of a magnetostrictive material or a magnetised wire is
twisted, its magnetisation (i.e. magnetic permeability) changes. The change in magnetisation
can be measured and related to the external torque that twisted it. This inverse of the
Wiedemann effect, known as the Matteucci effect, is used for magnetoelastic torque sensors.
Magnetostriction coefficient. The magnetostriction coefficient A is defined as the fractional
change in length as the magnetisation increases from zero to its saturation value. Thus,
A - 6..LI
L saturated B
where, L is the original length of the material and 6..L is the change in length.
If the material expands, the magnetostriction is considered positive and if it contracts, it
is negative. While an iron bar shows positive magnetostriction, a nickel bar shows negative
magnetostriction.
Thus, the coefficient A may be positive or negative and is usually on the order of 10- 5 .
The coefficients A of common ferromagnetic materials are given in Table 5.4.
8 Gustav Heinrich Wiedemann (1826- 1899) was a German physicist. He was also a litterateur.
9 Carlo Matteucci (1811- 1868) was an Italian physicist and neurophysiologist who was a pioneer in the study
of bioelectricity.

Table 5.4 Magnetostriction coefficients for different materials
Material
Iron
Nickel
Cobalt
Terfenol-D
(TbxDY1-xFey)
Crystal axis
100
111
Polycrystalline
100
111
Polycrystalline
Polycrystalline
Polycrystalline
Magnetostriction coeficient
>. (x 10-5 )
+Ll to +2.0
-1.3 to -2.0
-0.8
-5.0 to -5.2
-2.7
-2.5 to -4.7
-5.0 to -6.0
2000
It is seen from Table 5.4 that cobalt exhibits the largest room temperature magnetostriction
of a pure element at 60 microstrain. Among alloys, the highest known magnetostriction is
exhibited by Terfenol-D10 . It exhibits about 2000 microstrains in a field of 2 kOe (160 kA-
turn/m) at room temperature and is the most commonly used engineering magnetostrictive
material.
In the case of a single stress a applied on a single magnetic domain, the magnetic strain
energy density Eu can be expressed as:
where, As is the magnetostrictive coefficient at saturation
() is the angle between the saturation magnetisation and the stress direction
For As and a > 0 (like in iron under tension), Eu is minimum for () = 0 i.e., when
the tension is aligned with the saturation magnetisation. Consequently, the magnetisation is
increased by tension.
This elastic strain energy associated with the deformation, leads to dissipation of energy
in transformer cores in the form of sound.
Applications. The existence of both direct and reciprocal Joule and Wiedemann effects leads
to two modes of operation for magnetostrictive transducers:
1. Transferring magnetic energy to mechanical energy
2. Transferring mechanical energy to magnetic energy
The first mode is used to design
1. Actuators for generating motion and/or force
2. Sensors for detecting states of magnetic field
10 Ter for terbium, Fe for iron, NOL for Naval Ordnance Laboratory (USA), and D for dysprosium.

Transducers 121
The second mode is used to design
1. Sensors for detecting motion and/or force
2. Devices for inducing change in the magnetic state of a material
3. Passive damping devices, which dissipate mechanical energy as magnetically and/or
electrically induced thermal losses
As with many other transducer technologies such as electromagnetic (moving coils) and
piezoelectricity, a magnetostrictive transducer has the ability to both actuate and sense
simultaneously. Applications such as the telephone, scanning sonar and others make use of
this dual mode. For example, a Terfenol-D sonar transducer can be used as either a
transmitter or a receiver or both at the same time. Another potential use of dual mode
operation is in active vibration and acoustic control. One transducer can be used to sense
deleterious structural vibrations and provide the actuation force to suppress them.
It is also utilised to produce ultrasonic vibrations either as a sound source or as ultrasonic
waves in liquids which can act as a cleansing agent in ultrasonic cleaning devices.
Hall effect
When a current-carrying conductor is placed into a magnetic field B, a voltage VH is generated
perpendicular to both the current I and the field. This phenomenon is known as the Hall effect.
Written mathematically,
VH <XI x B
The phenomenon originates from the action of the Lorentz11 force on the moving charge
carriers in the conductor.
If e is the electronic charge
v is the velocity of carriers
E is the electric field
then the Lorentz force F experienced by charge carriers due to the combined electric and
magnetic fields is given by
F = e(E +v x B) (5.1)
The second factor on the RHS of Eq. (5.1) is responsible for the generation of Hall voltage.
Figure 5.3 illustrates the basic principle of the Hall effect. It shows a thin sheet of
semiconducting material (Hall element) through which a current is passed. The output
connections are perpendicular to the direction of current.
The current consists of the movement of many small charge carriers- typically electrons,
holes, ions or all three. When no magnetic field is present [Fig. 5.3(a)], the charges follow
approximately straight paths between collisions with impurities, phonons12 , etc. As a result,
the current distribution through the material is uniform and no potential difference is seen
across the output. However, when a perpendicular magnetic field is applied, moving charges
experience a Lorentz force. As a result, their paths between collisions are curved as shown
in Fig. 5.3(b). So, the moving charges accumulate on one face of the material. This leaves
11 Named after the Dutch physicist Hendrik Antoon Lorentz (1853-1928) who first formulated it. He was
awarded the Nobel Prize in physics in 1902.
12 Quantised lattice vibrations.

fx
V=O {_
(a)
B (b)
Fig. 5.3 Hall voltage generation principle: (a) no magnetic field and (b) magnetic field present.
equal and opposite charges exposed on the other face, where there is a scarcity of mobile
charges. The result is an asymmetric distribution of charge density across the Hall element
that is perpendicular to both the current path and the applied magnetic field. The separation
of charge establishes an electric field that impedes the migration of further charge so that
a steady electrical potential difference builds up for as long as the charge is fl.owing. This
potential difference or voltage is the Hall13 voltage (VH).
Hall effect in metals. For a simple metal, where only electrons are the charge carriers, the
Hall voltage is given by
IB
VH = - - (5.2)
nedz
where n is the charge carrier density and dz is the thickness of the Hall element. The Hall
coefficient is defined as
Ey
RH = J B (5.3)
x
where Jx is the current density in the x-direction of the carrier electrons and Ey is the generated
Hall electric field. Now,
(5.4)
where dy and dz are dimensions of the Hall element in y and z directions respectively.
Therefore, we have from Eqs. (5.2), (5.3) and (5.4)
R VHdz 1
H = IB = - ne (5.5)
13 Named after its discoverer Edwin Herbert Hall (1855- 1938), an American Physicist.

Transducers 123
But then, Hall coefficients for metals are too low to serve any useful purpose. A few
representative values are given in Table 5.5.
Table 5.5 Hall coefficients at room temperature for metals
Metal
Gold
Copper
Aluminium
Magnesium
Tin
Hall coefficient (m3 /Ct
-0.72
-0.55
-0.30
-0.94
-0.04
a Source: American Institute of Physics Handbook, New York (1985).
Therefore although discovered in 1879, the Hall effect found its first applications with
the advent of semiconducting materials in the 1950s. The Hall voltage in semiconductors is
appreciable.
Hall effect in semiconductors. In a semiconductor, there are both negative and positive charge
carriers namely, electrons and holes. Let us consider a semiconducting Hall element.
If n is the concentration of electrons
p is the concentration of holes
µe is the drift mobility of electrons
µh is the drift mobility of holes
E is the electrostatic field
then,
the drift velocity of electrons Ve = µeE
the drift velocity of holes vh = µhE
Now, the net electrostatic force F acting on a single electron is given by
F=eE
With the help of Eqs. (5.6) and (5.7), we get
Ve= µe F
e
}
(5.6)
(5.7)
(5.8)
We note that since both holes and electrons are present in the sample, both charges experience
a Lorentz force in the same direction because they will be drifting in opposite directions as
shown in Fig. 5.4.
Thus, both electrons and holes tend to accumulate near the bottom surface though the
magnitudes of Lorentz forces will be different because drift mobilities, and hence drift velocities,
will be different for electrons and holes. In equilibrium, there will be no current flowing in

B
rl y= o
B
8 8
- + - + - - + - + -
l x + ,e, l x
'~ll E, t-•m
eEy evexB evhxB
+ - + - + + - + - +
8
1 8
B B
v
I
I
Fig. 5.4 Schematic of drift velocities and forces experienced by holes E& and electrons e in an ambipolar
Hall element. The magnetic field B is out from the plane of the paper.
the y-direction as we have an open output circuit. Let us assume that more holes accumulate
near the bottom surface so that an electric field Ey builds up thereby. Since there exists no
current in the y-direction, we have
(5.9)
where Vhy and Vey indicate drift velocities of holes and electrons in the y-direction respectively.
Eq. (5.9) yields
PVhy = -nVey
We note that the electrons and holes experience the following Lorentz forces:
F ey = - eEy - eVexB
Fhy = eEy - evhxB
}
(5.10)
(5.11)
where Vex and Vhx indicate drift velocities of electrons and holes in the x-direction respectively.
Now, from Eq. (5.8), we can write
}
Combining Eqs. (5.11) and (5.12), we get
€Vey
- - = eEy + eVexB
µe
evhy
- - = eEy - evhxB
µh
(5.12)
} (5.13)

Transducers
Substituting Vex= µeEx and Vhx = µhEx, we get from Eq. (5.13)
Vey
- = Ey +µeExB
µe
Vey = µeEy +µ;ExB
Vhy
- = Ey-µhExB
µh
Vhy = µhEy - µ~ExB
Substituting for Vey and Vhy from Eqs. (5.14) and (5.15) in Eq. (5.10), we obtain
p µhEy - p µ~ExB = -nµeEy - nµ;ExB
Ey(P µh + nµe) = BEx(P µ~ - nµ;)
E _ Ey P µh +nµe
x - B pµ~ - nµ~
125
(5.14)
(5.15)
(5.16)
Now, let us consider the current flow in the x-direction. Here the total current density is finite
and is given by the following equation:
(5.17)
Substituting the value of Ex from Eq. (5.16) in Eq. (5.17), we get after a little algebraic
manipulation
So, from the definition of Hall coefficient [Eq. (5.3)] we get for ambipolar semiconductors
p-nb2
e(p +nb)2
where b = µe/µh. The following conclusions can be drawn from Eq. (5.18):
(5.18)
1. RH depends on both the drift mobility ratio and the concentrations of holes and electrons
2. RH is positive for p > nb2
3. RH is negative for p < nb2
4. Equation (5.5) for metals is obtained by substituting p = 0
Let us now work out an example to see what is the value of the Hall coefficient of a
semiconductor.
Example 5.1
The following are the data for the intrinsic Si: n = p = ni
µh = 450 cm2v-1s-1 , and µe = 1350 cm2v-1s-1 . Calculate RH.
Solution
From the given data we have
n = p = 1.5 x 1016 m- 3
b = µe = 1350 cm2v-1s-1
µh 450 cm2v-1s-1
=3

Therefore,
RH = ( 1.5 x 1016) - (1.5 x 1016) (3)2 m3/C
(1.6 x 10-19) [(1.5 x 1016) + (1.5 x 1016)(3)2]
= -208.3 m3 /C
Thus, it is evident that the Hall coefficient of a semiconductor is orders of magnitude higher
than that for typical metals. This is why all Hall devices use a semiconductor rather than a
metal element.
Basic Hall Effect Sensor. Hall effect sensors convert a magnetic field to a useful electrical
signal. When physical quantities, like position, speed, temperature, etc. other than a magnetic
field are sensed, the magnetic system converts this physical quantity to a magnetic field which,
in turn, can be sensed by Hall effect sensors. The block diagram in Fig. 5.5 illustrates this
concept.
Sensing device
.----------------------------------------------.I
Physical ---;--•~l__M_a_g_n_e_t_ _J-~~~~~~=====:1l__H_a_n_s_e_n_so_r_;-..----• Electrical
quantity . : . signal
I
Magnetic flux
-----------------------------------------------
Fig. 5.5 Basic Hall effect sensor.
Many physical parameters can be measured by inducing the motion of a magnet. For
example, both temperature and pressure can be sensed through the expansion and contraction
of a bellows to which a magnet is attached. We will discuss them in detail in appropriate
chapters.
Elimination of piezoresistivity. Silicon, the basic semiconductor which is used to construct Hall
elements, exhibits piezoresistivity 14 . This interferes with the Hall sensing. It is necessary to
minimise this effect in a Hall sensor. This is accomplished by using multiple Hall elements and
orienting them on the IC to minimise the effect of stress. Figure 5.6 shows two Hall elements
located in close proximity on an IC. They are positioned in this manner so that they may
both experience the same packaging stress. The first Hall element has its excitation applied
along the vertical axis and the second along the horizontal axis. Summing the two outputs
eliminates the signal due to stress. Micro-switch Hall ICs use two or four elements.
Signal conditioning. The Hall element, which is the basic magnetic field sensor, requires
signal conditioning to make the output usable for most applications. The signal conditioning
electronics comprises
1. An amplifier stage
2. A temperature compensator
3. A voltage regulator when operating from an unregulated supply
14See Section 5.2 at page 150.

Transducers
+
Hall
element
- - - - - - _.,.
Fig. 5.6 Orientation of Hall elements.
+
'
T -
Figure 5.7 illustrates the signal conditioning of a basic Hall effect sensor.
+ Voltage
regulator
Fig. 5.7 Schematic diagram of a basic Hall effect sensor.
127
We know that the Hall voltage is zero when no magnetic field is present. However, if voltage
at each output terminal is measured with respect to ground, a non-zero voltage will appear.
This is the common mode voltage, and is the same at each output terminal. Obviously the
potential difference is zero. The amplifier shown in Fig. 5.7 is thus a differential amplifier
which amplifies only the potential difference, i.e. the Hall voltage.
The generated Hall voltage is on the order of 30 microvolts when subjected to a magnetic
field of one gauss. This low-level output requires an amplifier with low noise, high input
impedance and moderate gain. An op-amp differential amplifier with these characteristics
can be readily integrated with the Hall element. Temperature compensation is also easily
integrated (not shown in the diagram).
We know that the Hall voltage is a function of the input current. The purpose of the
voltage regulator in Fig. 5.7 is to hold this current constant so that the output of the sensor
only reflects the intensity of the magnetic field. Since the regulated power supply is available
in many places, some Hall effect sensors do not include an internal regulator.
Zero elevation. According to the orientation of the sensed magnetic field, the output of the
amplifier may be driven either positive or negative, thus requiring both plus and minus power
supplies. To obviate the requirement for two power supplies, a fixed offset or bias is introduced
into the differential amplifier. The bias value appears on the output when no magnetic field
is present and is referred to as a null voltage. When a positive magnetic field is sensed, the
output increases above the null voltage. Conversely, when a negative magnetic field is sensed,

the output decreases below the null voltage, but remains positive. This is akin to the zero
elevation used in pressure measurement15 .
To further increase the interface flexibility of the device, an open emitter, open collector,
or push-pull transistor is added to the output of the differential amplifier. Analogue output
sensors are commercially available in ranges of 4.5 to 10.5 V, 4.5 to 12 V, or 6.6 to 12.6 V de.
They typically require a regulated supply voltage to operate accurately.
Transfer characteristic of a Hall sensor. The transfer characteristic of a device relates its
output to its input. It can be expressed in the form of either an equation or a graph.
For analogue output Hall effect sensors, the transfer characteristic expresses the relationship
between the magnetic field (gauss) input and the voltage output. For a typical analogue output
sensor, it is illustrated in Fig. 5.8.
-640
Output (V) 10
-320 0.0
-2.5
- 5.0
320
Vs= 10 V
V5 =8 V
V:,=5V
640
Applied magnetic
field (gauss)
Fig. 5.8 Transfer characteristics of a typical Hall device.
For -640 < B (gauss) < 640, the transfer characteristic equation for this particular sensor
is given by
Vout (volt) = 6.25 X 10- 4 V8 B + 0.5V8 (5.19)
where, B is the magnetic field strength and V8 , the supply voltage.
The transfer characteristic of a Hall sensor is specified by the following properties:
1. Sensitivity
2. Null offset
3. Span
Sensitivity. By definition, the sensitivity is the ratio of the change in output resulting from a
given change in input. In this case, it is
S = I~:;t I = 6.25 x 10- 4 vs volt/gauss) [ From Eq. (5.19)]

Transducers 129
Here, we have considered the Hall sensor as a whole comprising the Hall element and the
electronics.
Another term, cross or secondary sensitivity is often mentioned. That indicates the
sensitivity of the Hall element with respect to the variation of parameters like temperature or
pressure.
Null offset. The null offset is the output from a sensor with no magnetic field excitation.
Therefore, substituting B = 0 in Eq. (5.19), we get
Null offset = 0.5V8
The imperfection in the fabrication process of the sensor may give rise to the null offset.
Span. The span, defined as the difference between the maximum output and the minimum
output, is
Span= Vautl B - Voutl · B
max min
for a given supply voltage V8 •
Magnetoresistance
The magnetoresistance effect is closely associated with Hall effect transducers.
Suppose, in Fig. 5.3 if dy of the Hall element is made much shorter than dx, the Hall voltage
can be almost short-circuited. As a consequence, the charge carriers move at the Hall angle
to the x-direction. The increase in path length for the carriers causes an increase in resistance
of the device. This increase in resistance of the Hall element owing to the application of a
magnetic field is known as the geometrical magnetoresistance effect.
A magnetic field applied to a current-carrying conductor causes deviation of some charge
carriers from their path. So, when a Hall voltage grows, there is a current decrease, which
results in an increased electric resistance. In most conductors this magnetoresistive effect is
of a second order when compared to the Hall effect. But in anisotropic materials, such as
ferromagnetics, their resistance depends on their state of magnetisation. Then the effect of
an external applied magnetic field is more pronounced and the resistance varies from 2 to
5%. The relation between change in resistance and the magnetic field intensity is not linear
but quadratic; however, it is possible to linearise it by using biasing methods. If we ignore
this need for linearisation and their thermal dependence, magnetoresistors offer the following
advantages as compared to other magnetic sensors:
1. A magnetoresistor is a zero order system while inductive sensors are first order systems
because their response depends on the time derivative of the magnetic flux density.
2. Hall effect sensors also are zero order systems. But magnetoresistors show increased
sensitivity, temperature range, and frequency passband (from de to several megahertz)
compared with 25 kHz for Hall effect sensors.
Construction. Magnetoresistors are usually manufactured from permalloy, which is an alloy
of approximately 20% iron and 80% nickel. Also Ni-Fe-Co and Ni-Fe-Mo alloys have been
tried.
Application. Depending upon the principle, the applications can be divided into two groups
as shown in Table 5.6.

Table 5.6 Applications of magnetoresistive effect
Principle
Direct measurement of magnetic fields
Measuring magnetic field variationa
Application
Magnetic audio recording
Reading machines for credit cards,
magnetically coded price tags
Measurement of linear and angular
displacement
Proximity switches
Position measurement
Angular velocity of ferrous gear wheels
a To accomplish this, it must be either a metallic object or an object with a metallic coating or an
identifier placed in a constant magnetic field, or the moving element to be detected must incorpo-
rate a permanent magnet.
Piezoelectricity
Certain materials, especially the crystalline ones, produce an emf when deformed by an
application of pressure along the specific axes. The phenomenon is known as piezo-
electricity16 or piezoelectric effect and is widely used for the construction of many
transducers that involve the measurement of dynamic pressure.
Origin of piezoelectricity
In most crystals, the unit cell (the basic repeating unit) is symmetrical; in piezoelectric crystals,
it is not. Normally, piezoelectric crystals are electrically neutral- the atoms inside them may
not be symmetrically arranged, but their electrical charges, are perfectly balanced. A quartz
(Si02 ) tetrahedron is shown in Fig. 5.9. When a pressure is applied to the tetrahedron (or
a macroscopic crystal element) a displacement of the positive ion charge towards the centre
of the negative ion charges occurs. Hence, the outer faces of such a piezoelectric element get
charged under this pressure.
Fig. 5.9 Piezoelectricity generation in quartz. Arrows indicate the direction of application of pressure.
16 Pronounced as pie'zo or pea'zo (Webster's Universal Collegiate Dictionary, 1997). The prefix is a Greek
word meaning squeeze.

Transducers 131
Conversely, when an electric field is applied to a piezoelectric crystal, a mechanical strain
is produced in it. This is sometimes called the inverse piezoelectric effect. If an alternating
field is applied to such a crystal, the strain also varies periodically-but generally there is a
phase lag between the applied field and the resulting strain, depending on the frequency of
the applied field. At the natural frequency of vibration of the crystal, called the resonance
frequency, the two are exactly in phase. This effect is utilised to construct resonant transducers
and also to stabilise frequency in electronic clocks.
Piezoelectric materials
Generally, piezoelectric materials are classified into the following four categories:
Category
Naturally occurring single crystals
Man-made crystals
Man-made polycrystalline ceramic materials
Man-made polymers
Examples
Quartz
Tourmaline
Topaz
Cane Sugar
Rochelle salt (potassium sodium tartrate
tetrahydrate, KNaC4H40s, 4H20)
Gallium Orthophosphate (GaP04)
Langasite (La3GasSi014)-
both quartz analogous crystals
Barium Titanate (BaTi03)
Lead Zirconate Titanate (Pb[ZrxTh-x]03
where 0 < x < 1)-more commonly known as
PZT
Lead Titanate (PbTi03)
Potassium Niobate (KNb03)
Lithium Niobate (LiNb03)
Lithium Tantalate (LiTa03)
Sodium Tungstate (NaW03)
PolyVinyliDene Fluoride (PVDF)
PZT is the most common piezoelectric ceramic in use today. Among the naturally occurring
crystals, quartz is inexpensive. Tourmaline, a naturally occurring semi-precious form of quartz,
has sub-microsecond response time and, therefore, very useful in the measurement of rapid
transients.
PVDF exhibits piezoelectricity several times greater than quartz. Unlike ceramics, where
the crystal structure of the material creates the piezoelectric effect, in polymers the intertwined
long-chain molecules attract and repel each other when an electric field is applied.
The so-called natural crystals are already polarised and the piezoelectric element is usually
a cut from the crystal in the direction of any of the electrical axes (called X-axes) or mechanical
axes (called Y-axes)[Fig. 5.lO(a)]. Figures 5.lO(b) and (c) show how an X-cut piece of the
hexagonal quartz crystal can be obtained.
Synthetic polycrystalline ceramic materials have to be baked under a strong de electric
field to provide polarisation. Thus, they have the advantage of being moulded into any shape
or size.

132
y
y
Introduction to Measurements and Instrumentation
y
(a)
Cleavage lines
.4 qjpio~
(b) (c)
Fig. 5.10 Quartz crystal: (a) X and Y axes, (b) and (c) X-cutting
Curie temperature. The Curie temperature Tc is the temperature at which the piezoelectric
material changes to a non-piezoelectric form. Before polarisation or above Curie
temperature17 , PZT crystallites have symmetric cubic unit cells [Fig. 5.ll(a)]. Below the
Curie temperature, the lattice structure becomes deformed and asymmetric. The unit cells
then exhibit spontaneous polarisation [Fig. 5.ll(b)], i.e. the individual PZT crystallites
become piezoelectric.
+
r
(a) (b)
002- • Pb e ZrTi
Fig. 5.11 PZT unit cell : (a) Perovskite-type PZT unit cell in the symmetric cubic state above the Curie
temperature, and (b) tetragonally distorted unit cell below the Curie temperature.
Domains. Groups of unit cells with the same orientation of polarisation are akin to Weiss
domains of ferromagnetism. The random distribution of the domain orientations in the
ceramic material manifests no macroscopic piezoelectric behaviour [Fig. 5.12(a)]. Due to the
ferroelectric18 nature of the material, it is possible to force permanent alignment of the
different domains using a strong electric field. This process is called poling [Fig. 5.12(b)].
Some PZT ceramics must be poled at an elevated temperature to acquire a remnant
17 Named after brothers Pierre and Jacques Curie of France who discovered piezoelectricity in 1880.
18 Dielectrics which show hysteresis effect for applied field and polarisation are called ferroelectrics. A
ferroelectric is spontaneously polarised, i.e. it is polarised in the absence of an electric field . Since the dielectric
behaviour of these materials is in many respects analogous to the magnetic behaviour of ferromagnetic materials,
they are called ferroelectric solids.

Transducers 133
polarisation. The ceramic then exhibits piezoelectric properties [Fig. 5.12(c)]. It will also
change dimensions when an electric potential is applied (inverse piezoelectricity).
"" ++++
:: J_
"' ++++
- J
,/ ~
++++
-
(a) (b) (c)
Fig. 5.12 Electric dipoles in domains: (a} unpoled ferroelectric ceramic, (b} during poling and (c} after
poling (piezoelectric ceramic}.
Modes of utilising piezoelectricity
In piezoelectric sensors, many modes of stressing the piezoelectric material can be used.
Acting as precision springs, the different element configurations shown in Fig. 5.13 offer
various advantages and disadvantages as detailed in Table 5.7.
I+ +I
1+ +1
I + + I
+ +++++++
+++++ + ++
Compression Flexure Shear
Fig. 5.13 Different modes of stressing the piezoelectric material. The white represents the piezoelectric
crystals, while the arrows indicate how the material is stressed . Compression and shear modes
typically have a seismic mass, which is represented by the grey colour.
Table 5.7 Advantages and disadvantages of different configurations
Configuration Advantages
Compression High rigidity, making it useful for
implementation in high frequency
pressure and force sensors
Flexure Simplicity of design
Shear Offers a well balanced blend of wide
frequency range, low off-axis
sensitivity, low sensitivity to base
strain and low sensitivity to thermal
inputs
Disadvantages
Somewhat sensitive to thermal
transients
Narrow frequency range and low
overshock survivability
Rather complicated design

Piezoelectric coefficients
Because of the anisotropic nature of piezoelectric ceramics, piezoelectric effects are dependent
on direction. To identify directions, the axes 1, 2, and 3 are introduced, corresponding to
X, Yand Z of the classical right-handed orthogonal axis set. The axes 4, 5 and 6 identify
rotations (shear)- 23, 31, 12. Figure 5.14 illustrates them.
3
i::
.g 6
ell
"'
·;::::
z
ell
0 5
0...
x y 2
4
Fig. 5.14 Orthogonal system describing the properties of a poled piezoelectric ceramic. Axis 3 is the
poling direction .
The direction of polarisation (axis 3) is established during manufacturing process by a
strong de field applied between two electrodes. For linear actuators19 which involve translation,
the piezo properties along the poling axis, along which the largest deflection generally takes
place, are the most important.
Piezoelectric materials are characterised by d, g, h, e coefficients as well as a coupling
parameter k. We will discuss them after we talk about the notations used in defining them.
Apart from the piezoelectric coefficients, piezoelectricity is also affected by
1. Electric properties like permittivity and pyroelectricity20
2. Elastic property like the Young's modulus
3. Thermal property like the Curie temperature
Notations. Piezoelectric constants are generally expressed with double subscripts. The
subscripts link electrical and mechanical quantities. The first subscript indicates the
direction of the stimulus while the second, the direction of the reaction of the system.
For example, d33 applies when the electric field is along the polarisation axis (direction 3)
and the strain (deflection) is along the same axis. d31 applies if the electric field is in the same
direction as before, but the deflection of interest is that along axis 1 (perpendicular to the
polarisation axis).
In addition, piezoceramic material constants may be written with a superscript which
specifies either a mechanical or electrical boundary condition. The superscripts are T, E, D
and S are explained in Table 5.8.
19 See at page 146.
20 Pyroelectric materials are those which produce electric charge as they undergo a temperature change.
Piezoelectric materials are also pyroelectric. When their temperature is increased, they develop a voltage that
has the same orientation as the polarisation voltage. When their temperature is decreased, they develop a
voltage having an orientation opposite to the polarisation voltage. This creates a depolarising field with the
potential to degrade the state of polarisation of the part.

Transducers 135
Table 5.8 Significance of superscripts used to specify piezoelectric material constants
Superscript Implication Meaning
T Stress = constant Mechanically free
E Electric field = 0 Short circuited
D Charge displacement (i.e. current) = 0 Open circuit
S Strain = constant Mechanically clamped
Note: 1. We use here S for strain and T for stress rather than the conventional symbols c
and a only to avoid confusion with the permittivity symbol c.
2. In a dielectric material the presence of an electric field E causes the bound charges
in the material (atomic nuclei and their electrons) to slightly separate, inducing a
local electric dipole moment. The electric displacement field D is defined as
D =c0E+P
where co is the vacuum permittivity (also called permittivity of free space), and P
is the (macroscopic) density of the permanent and induced electric dipole moments
in the material, called the polarisation density.
3. In a linear, homogeneous, isotropic dielectric with instantaneous response to changes
in the electric field, P depends linearly on the electric field, giving rise to the relation
P = XcoE
where the constant of proportionality x is called the electric susceptibility of the
material. Thus
D = c0 (1 +x)E = cE
where c (= cocr) is the permittivity and cr (= 1 +X) is the relative permittivity of
the material.
4. In linear, homogeneous, isotropic media c is a constant. However, in linear
anisotropic media it is a matrix.
Now, let us define the different coefficients we have talked about.
d coefficient. The piezoelectric charge coefficient (aka charge constant), dij, is defined as
follows:
Direct effect
d·. = Charge density developed in i-direction I C/N
•J Applied stress in j-direction E=O
[from C/m:]
N/m
(5.20)
Inverse effect
d·. = Developed strain in j-direction I m/V
•J Applied electric field in i-direction T=const.
(5.21)
Note: The directions i and j are inverted in the inverse effect-the j-direction is in the
numerator in this case.

Equations (5.20) and (5.21) may be written in the following form:
d·· = ({)Di)E = (asj)T
' 3 8Ti 8Ei
Because for the inverse piezoelectric effect, the strain induced in a piezoelectric material by
an applied electric field is the product of the value for the electric field and the value for dij, it is
an important indicator of a material's suitability for strain-dependent (actuator) applications.
The larger the value of dij, the larger the mechanical displacement which is usually sought in
motional transducer devices.
g coefficient. The piezoelectric voltage coefficient (aka voltage constant or voltage sensitivity),
gij, is defined as
Direct effect
.. = _Developed electric field in i-direction I Vm/N
g,J Applied stress in j-direction D=D
[from V/~]
N/m
(5.22)
Inverse effect
.. _ Strain developed in j-direction I m2 /C
g,J - Applied charge density in i-direction T=constant
[from m/~]
C/m
(5.23)
Combining Eqs. (5.22) and (5.23), we can write
(asj )r
8Di
(5.24)
Because the strength of the induced electric field produced by a piezoelectric material in
response to an applied physical stress is the product of the value for the applied stress and the
value for gij, high gij constants favour large voltage output, and therefore, are sought after
for sensor applications.
h coefficient. The third coefficient hij is defined as
It can be interpreted as negative of the voltage gradient per unit strain when the displacement
is constant for the direct effect, or negative of the stress gradient per unit charge displacement
when the strain is constant for the inverse effect.
e coefficient. The fourth coefficient eij is defined as

Transducers 137
Coupling factor. The electromechanical coupling factor, k, is an indicator of the effectiveness
with which a piezoelectric material converts electrical energy into mechanical energy, or vice
versa. It is defined as
For an electrically stressed component
k~. = Mechanical energy stored
•J Electrical energy applied
For a mechanically stressed component
k~. = Electrical energy stored
•J Mechanical energy applied
Obviously, k (0 ::; k < 1) is a dimensionless quantity. It can be associated with the vibratory
modes of certain simple transducer shapes. The first subscript to k denotes the direction
along which the electrodes are applied and the second denotes the direction along which the
mechanical energy is applied/stored.
A high k usually is desirable for efficient energy conversion, but k does not account for
dielectric losses or mechanical losses, nor for recovery of unconverted energy. The accurate
measure of efficiency is the ratio of converted, usable energy delivered by the piezoelectric
element to the total energy taken up by the element. By this measure, piezoelectric ceramic
elements in well designed systems can exhibit efficiencies that exceed 90%.
Useful relations
Piezoelectricity is a combined effect of the electric and elastic behaviour of the material.
Electric behaviour. The electrical condition of an unstressed medium placed under the
influence of an electric field is defined by two quantities: the field strength, E and the
dielectric displacement, D. Their relationship is expressed as:
D=eE
where e is the permittivity of the medium.
Elastic behaviour. The elastic behaviour is of the same medium at zero electric field strength
is defined by two mechanical quantities: the applied stress, T and the strain, S. These two
quantities are related by the well known Hooke's law
S =sT
where s denotes the compliance of the medium. The compliance is the inverse of the Young's
modulus. Piezoelectricity involves the interaction between these two behaviours of the medium.
To a good approximation, this interaction can be described by eight linear equations which
relate the different electrical and mechanical variables. Three of them are as follows:
where dt indicates the transpose of d.
D = dT+eTE
S = sET+dtE
E=-gT+D/eT
(5.25)
(5.26)
(5.27)

The reason for writing the quantities in bold letters is that they are not scalar quantities.
In fact, E, D are vectors (tensors of rank 1)
T, S are tensors of rank 2, but converted to 6-dimensional vectors
s is a 6 x 6 symmetric matrix
e is a 3 x 3 symmetric matrix
d, g are 3 x 6 piezoelectric matrices
When written in their matrix forms, these equations relate the properties to the
crystallographic directions. For ceramics and other crystals, the piezoelectric constants are
anisotropic. For example, Eq. (5.25) can be written explicitly as follows:
di3 d14 d15
d23 d24 d25
d33 d34 d35
T1
T2 T
~: + [:t~
T5 €31
T5
(5.28)
Here T1 , T2 , T3 denote longitudinal stress in 1, 2 and 3 directions while T4 , n, T6 indicate
shear stress along 23, 31, 12 directions as defined earlier.
Although Eq. (5.28) looks formidable, it simplifies a lot when the symmetry considerations
of the crystal structures are invoked. For example, for the poled piezoelectric ceramic PZT,
which possesses tetragonal symmetry, it simplifies to the following:
~]
Relation between d and g constants. Utilising Eqs. (5.25) and (5.27) we can establish the
relation between d and g as follows:
D = dT+eTE
= dT +eT (-gT + :; )
= dT-eTgT +D
d=eTg
Alternatively, we know from Eq. (5.20) that d33 denotes the ratio of charge per unit area
perpendicular to the 3-direction to the stress applied in the 3-direction when the electrodes
are open circuited. Therefore, d33 is given by the following expression:
(5.29)

Transducers 139
where A is the area stressed by a force F3 , C is the capacitance between the electrodes of
the piezoelectric and V:i is the voltage generated. Now, the capacitance of the piezoelectric of
thickness t and plate area A can be written as
where co = 8.85 x 10-12 F/m.
C = cocrA
t
Substituting the value of C from Eq. (5.30) in Eq. (5.29), we get
d _ cocrAV:i V:i/t
33 - F3t = cocr F3/A
[from Eq. (5.22)]
Other useful relations are:
d= esE
e = e8 h = dYE
g= hsD
h=gYD
Table 5.9 gives the useful data of a few piezoelectric materials.
Material
Quartz
Tourmaline
Rochelle salt
Lithium sulphate
Ammonium
dihydrogen
phosphate
PZT
Barium titanate
Table 5.9
d
(C/N)
x 10-12
2.3
1.9
550
13.5
48
356
150
Useful data of piezoelectric materials
er
4.5
6.6
350
10.3
15.3
1750
1412
Young's modulus
(N/m)
x109
80
160
19
46
19.3
59
86
Max. Temp.
(aC)
550
1000
45
75
125
285
100
(5.30)
Humidity
range
(%)
0-100
0-100
40-70
0-95
0-94
Of all piezoelectric transducer materials, quartz is the most suitable for many applications.
It has a lower temperature sensitivity and a higher resistivity, thus giving an inherently long
time-constant which permits static calibration. Further, it exhibits good linearity with very
low hysteresis over a wide range of pressure. Piezoelectric ceramics, though possessing higher
sensitivity and wider adaptability in the form of shapes and sizes, have a poor temperature
characteristic. Rochelle salt is hygroscopic and can be used only up to 45°C, while quartz
devices can work between -200°C and 550°C.

With the advent of microelectronics and field effect transistors (FET), the piezoelectric
transducer design has undergone a considerable change. Nowadays isolation amplifier and
signal conditioning circuitry are packaged with the transducer. These integrated circuit
piezoelectric transducers, called smart sensors21 operate over a simple 2-wire cable and are
commercially available for all kinds of measurements where piezoelectricity helps.
Circuit analysis
The piezoelectric material is an insulator. Therefore to apply voltage to it or to extract
voltage from it, metal electrodes have to be plated on the selected faces of the material. This
configuration gives it the shape of a capacitor.
The piezoelectric transducer is also a charge generator. The charge is generated whenever
it is stressed but it slowly dissipates through the piezoelectric material when left alone. So, the
circuit constitutes a voltage source, a capacitor and a leakage resistor. The leakage resistance
is very high, generally around 1011 n. Since the leakage resistance is high, the corresponding
time constant will be considerable so as to make the decay a slow process. To measure such
voltage, one needs to connect it to an op-amp with either a resistor in the feedback path
(voltage amplifier configuration, see page 143) or a capacitor in the feedback path (charge
amplifier configuration, mentioned later in this chapter, see page 144).
The connecting cables introduce some stray capacitance to the circuit. As a result, the
equivalent circuit looks like Fig. 5.15(a) where the subscript p refers to the piezoelectric
transducer.
Sensor
L _____________ I
(a) (b)
Fig. 5.15 (a) Equivalent circuit of a piezoelectric transducer installation and (b) its reduced form .
Cc indicates cable capacitance, and Ca, Ra indicate amplifier capacitance and resistance
respectively.
The circuit of Fig. 5.15(a) can be replaced by that of Fig. 5.15(b) where Req = Rp II Ra and
Ceq =Gp+ Cc+ Ca. This equivalent circuit is similar to the one for a capacitive displacement
transducer (see Section 6.2 at page 198) where Eb is replaced by a current generator.
In the Laplace transformed form, the input-output relation can be written as
(5.31)
where T(= ReqCeq) is the time constant.

Transducers 141
Now, the input voltage ei, generated by the piezoelectric transducer, can be written as
Q dF
ei=-=-
Ceq Ceq
(5.32)
where Fis the applied force. Combining Eqs. (5.31) and (5.32), we get
d ST
(5.33)
Ceq ST+ 1
We know, F ='TJX where 'T/ is the force constant and xis the displacement. Incorporating this
in Eq. (5.33), we get
where K = ~'T/ is the gain.
eq
E0 (s) _ d'TJ ST _ K ST
X(s) - Ceq . ST+ 1 - ST+ 1
(5.34)
Impulse response For a unit impulse input, X(s) = 1. Therefore, the impulse response can
be worked out from Eq. (5.34) as follows
ST [ 1 ]
E0 (s)=K-- =K 1- - -
sT+l sT+l
= K [l - ~. s + ~1/T)]
ea(t) = K [8(t) - exp(~t/T)] (5.35)
It is interesting to observe from Eq. (5.35) that for an input of 8(t), the output generates two
factors-a 8(t) which dies out in a short time e (e---+ 0) and another negative quantity that is
slowly driven to a zero value.
To visualise what happens within time e, let us consider it as a step function of amplitude
l/e and duration e. The Laplace transform of the input is then 1/(es). So, the response is as
follows:
ST 1
E0 (s) = K · - - · -
sT+ 1 es
K 1
e 1 + (1/T)
K
e0 (t) = - exp(-t/T)
€
(5.36)
(5.37)
Plots of Eqs. (5.37) and (5.35) for several values of Tare shown in Figs. 5.16(a) and (b).
It is clear from Fig. 5.16 that for a linear response, a large time constant is desirable. Now,
the time constant can be increased by increasing either R or C. The latter can be increased,
by adding a capacitor in parallel to the transducer, at the expense of the gain K which varies
inversely with Ceq. Thus, a higher C reduces the sensitivity. Therefore, the connection of an
R in series before feeding the transducer output to an amplifier is a better choice.

142
KIE
0
Introduction to Measurements and Instrumentation
Time
(a)
Time
E t--+-+-+-+-+--+--+--+--+----<
-Klr
(b)
Fig. 5.16 Impulse response of piezoelectric transducer: (a) initial response for duration Es [input assumed
a step function of short duration] and (b) final response.
Frequency response In the frequency domain, the input-output relation can be written as
eo(Jw) = Req ei(Jw) = JWReqCeq ei(Jw)
Req + (1/JwCeq) JWReqCeq + 1
JWT
---ei(Jw)
JWT+ 1
(5.38)
Thus e0 (Jw) = K JWT =K 1 L.¢
x(Jw) JWT + 1 ,/1 + (1/wr)2
(5.39)
where
7r - 1
rp = - - tan wT
2
(5.40)
The frequency response is shown in Fig. 5.17. Equations (5.39) and (5.40) , and Fig. 5.17 help
us conclude that
I:IK --------------------------------- (rfd) 1.6
l.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 2 4 6 8 LO 0 2 4 6 8 LO
(a) (b)
Fig. 5.17 Frequency response of a piezoelectric transducer: (a) amplitude and (b) phase.

Transducers 143
1. For WT = 0, e0 = 0. That means, for a static pressure, the transducer produces no steady
voltage.
2. For WT---+ oo, e0 /x = K , </> = 0°. That means, the response is independent of frequency,
but dependent on Ceq at high frequencies. This property makes piezoelectric trans-
ducers suitable for hi-fidelity low power sound reproduction speakers. There, the inverse
piezoelectric effect is utilised.
Signal conditioning
Two circuits are used for signal conditioning, namely
1. Voltage mode amplifier circuit
2. Charge mode amplifier circuit
Voltage mode amplifier. The voltage mode amplification is used when the amplifier is pretty
close to the sensor.
The circuit and its frequency response are shown in Fig. 5.18. Here, the output depends
on the amount of capacitance seen by the sensor.
Vccf2
Sensor
------------------------,
I
'
-------------------------
(a)
Gain
-----------~~~~~~~~~~~~~~
1
fL = _2_JZ(_R_p_
ll R-b-)(_C_p_
ll-Cc
-)
(b)
1 Frequency
fH = 21'RtCJ
Fig. 5.18 Voltage mode amplifier: {a} Circuit and {b} frequency response. Output voltage, V0
Qp [l+ Rt]+ Vee .
GP+ Cc R 9 2
The capacitance of the interface cable, Cc, will affect the output voltage. If the cable is
moved or replaced, variations in Cc may cause problems. The resistor Rb provides a de bias
path for the amplifier input stage. The choice of R 1 and c1 sets the upper cutoff frequency.
The lower cutoff frequency is calculated from the relation:

1
fL = 27r(Rp II Rb)(Cp II Cc)
Rb should be high and the interface cable length low. The biasing will put the output voltage
at Vcc/2 with no input. The output is given by
where Qp is the charge developed on the piezoelectric
Gp is the capacitance of the piezoelectric
Cc is the capacitance of the connecting cable
Rt is the feedback resistor
Ct is the feedback capacitor
R9 is the regulating resistor
It is obvious from Eq. (5.41) that V0 will swing above and below the de bias Vcc/2.
(5.41)
Charge mode amplifier. The charge mode amplification is resorted to when the amplifier is
remote to the sensor.
The charge mode amplifier circuit and its frequency response are shown in Fig. 5.19.
Sensor
R;
r-------------------------
'
~------------------------~
(a) Vcc/2
Gain
Frequency
(b)
Fig. 5.19 Charge mode amplifier: {a) Circuit and {b) frequency response.
The amplifier will balance the charge injected into the negative input by charging the
feedback capacitor Ct . The resistor Rt does two functions, namely

Transducers 145
1. It bleeds the charge off the capacitor Ct at a low rate to prevent the amplifier from
drifting into saturation.
2. It also provides a de bias path for the negative input.
The values of Rt and Ct set the lower cutoff frequency of the amplifier given by
1
h=---
27rRtCt
The amplifier action maintains a 0 V across its input terminals so that the stray capacitance
of the connecting cable poses no problem. The resistor Ri provides ESD22 protection as well
as it combines with the capacitors Gp and Cc to set the higher cutoff frequency given by
1
fH=--~--~
27rRi(Cp +Cc)
The output is given by
V = _ Qp +Vee
o Ct 2
Thus, for no input the biasing puts the output voltage at Vcc/2. Which means, the output
will swing around this de level.
Example 5.2
Determine the pressure sensitivity of a quartz piezoelectric transducer of thickness 2.5 mm.
Voltage sensitivity of quartz is 50x 10-3 Vm/N.
Solution
Given g = E0 /tp = 50 x 10-3 Vm/N and t = 2.5 mm = 2.5 x 10-3 m. Therefore, pressure
sensitivity = E0 /p =gt= 125 mV/kPa.
Example 5.3
A quartz piezoelectric transducer has the following specifications: area = 1 cm2 , thickness =
1 mm, Young's modulus = 9x 1010 Pa, charge sensitivity = 2 pC/N, relative permittivity =
5 and resistivity = 1014 fl-cm. A 20 pF capacitor and a 100 Mn resistor are connected in
parallel across the electrodes of the piezoelectric transducer. If a force F = 0.02sin(103 t) N is
applied, calculate
(a) the peak-to-peak voltage generated across the electrodes
(b) the maximum change in crystal thickness
Solution
Given:
Area of the piezoelectric transducer, A= 1 cm0 = 10-4 m0
Thickness, t = 1 mm = 10-3 m
Young's modulus, Y = 9 x 1010 Pa
Charge sensitivity, d = 0 pC/N = 0 x 10-10 C/N
Relative permittivity, C:r = 5, therefore, c: = C:oC:r = 4.405 x 10-11 F/m
Resistivity, p = 1014 fl-cm = 1010 0-m
Parallel resistance, R = 100 Mn = 108 n
Parallel capacitance, C = 00 pF = 00 x 10-1°F
22 ElectroStatic Discharge.

Therefore,
Resistance of the piezoelectric transducer, RP = pA/t = 1011 n
Capacitance of the piezoelectric transducer, Gp = eA/t = 4.425 x 10-12 F
Equivalent resistance, Req = Rp II R ~ 108 n
Equivalent capacitance, Geq = Gp +G = 24.425 x 10-12 F
Time constant, T = ReqGeq = 24.425 x 10-4 s
The applied force is sinusoidal with an amplitude of 0.02 N, i.e. with a peak-to-peak value,
(F)p-p = 0.04 N and its angular frequency, w = 103 rad.
(a) Therefore, from Eq. (5.40), we get
d 1
(eo)p-p = Geq Jl + (1/wr)2 (F)p-p
2 x 10-12 1
-----~ x x 0.04 v
24.425 x 10-12 J1+1/(103 x 24.425 x 10-4 ) 2
~ 2.8mV
( ) . , _ longitudinal stress _ F/A
b Smee, Youngs modulus, Y - 1 "t d" 1 t . - " / , we have,
ong1 u ma s ram LJ.t t
(~ ) _ (F)p-pt
t p-p - AY
0.04 x 10-3
= m
10-4 x 9 x 1010
~ 4.4 x 10-12 m = 4.4 pm
Piezoelectric actuator
An actuator is a mechanical device for moving or controlling a mechanism or system. It is
operated by a source of energy, usually in the form of an electric current.
In instrumentation, actuators are a subdivision of transducers. They are devices which
transform an input signal (mainly an electrical signal) into motion. Specific examples include:
electrical motors, pneumatic actuators, hydraulic actuators, linear actuators etc. Piezoelectric
actuators are also used because piezoelectrics deform linearly with an applied electric field.
Commonly used stack actuators achieve a relative displacement of up to 0.2%.
Displacement of piezoceramic actuators is primarily a function of the applied electric field
strength E, the length L of the actuator, the forces applied to it and the properties of the
piezoelectric material used. The material properties can be described by the piezoelectric
charge constant dij. We know that this constant describes the relationship between the
applied electric field and the mechanical strain produced.
The change in length, ~L, of an unloaded single-layer piezo actuator can be estimated by
the following equation:
where Sis the strain =~L/L.

Transducers 147
Because strains are so small, piezoelectric actuators are mainly used in speakers or precision
micro-positioning applications where small, precise motion is needed. However, deflection
amplification methods make piezoelectrics possible actuators in other applications including
micro-robotics.
Unimorph. One method of amplification is using the unimorph design shown in Fig. 5.20.
When a voltage is applied across the ceramic and metal plate, the unimorph bends. It bends
in the other direction if the voltage is reversed.
Piezoelectric
Metal
7s
Deforms when voltage
is applied
Fig. 5.20 Schematic diagram of unimorph.
This device relies on the d31 piezoelectric constant. This relates the change in strain induced
perpendicular to the electric field. The value of d31 is typically half of d33value. However, a
motion of 0.875 inch can be produced by a unimorph of approximately one inch in diameter
and 0.02 inch thick. This design is typically found in loudspeakers.
Bimorph. The bimorph uses two piezoelectric plates that amplify the deflection as shown in
Fig. 5.21. Since piezoelectricity appears only on the surface, it is easy to understand why two
layers, instead of a thicker piezoelectric plate, is used for this purpose.
A piezo bimorph operates like a bimetallic strip in a thermostat. When the ceramic is
energised, the substrate is deflected with a motion proportional to the applied voltage.
Bimorph actuators providing motion up to 1000 µm are available and greater travel range is
possible.
E Piezoelectric 2
-----
Piezoelectric l
Fig. 5.21 Schematic diagram of bimorph.
Two basic versions are available:
1. Two electrode bimorph, i.e. serial bimorph [Fig. 5.22(a)]
2. Three electrode bimorph, i.e. parallel bimorph [Fig. 5.22(b)]
Serial bimorph operates with the two ceramic plates in the same direction of polarisation.
To avoid depolarisation in the middle, the maximum electric field is limited to a few hundred
volts per millimetre. Serial bimorph benders are widely used as force sensors because of halved
capacity and higher output voltage.

+
(a) (b)
Fig. 5.22 Bimorphs: (a} serial and (b} parallel.
Parallel bimorph produces twice the capacitance as that of a series connection and in a sender-
type transducer admits the full excitation voltage across each plate.
In either case the device relies on the d31 piezoelectric constant and that the strain is
proportional to the square of the applied voltage.
Multimorph. Instead of two plates, monolithic, multi-layer type piezo benders, known as
multimorphs, are available too. Similar to multilayer stack actuators, they run on a low
operating voltage (60 to 100 V).
Bender type actuators provide large motion in a small package at the expense of stiffness,
force and speed.
Advantages and disadvantages
From its discovery by the Curies in 1880, it took about 70 years before the piezoelectric effect
was used for industrial sensing applications. Since then, its utilisation has experienced a
constant growth and can nowadays be regarded as a mature technology with an outstanding
inherent reliability. It has been successfully used in various critical applications like in medical,
aerospace and nuclear instrumentation.
Advantages. The high modulus of elasticity of many piezoelectric materials is comparable
to that of many metals and the maximum stress that they can withstand can be as high as
105 x 106 N/m2 . Even though piezoelectric sensors are electromechanical systems that react
on compression, the sensing elements show almost zero deformation. The piezoelectric sensors
are
1. Rugged
2. Have an extremely high natural frequency
3. An excellent linearity over a wide amplitude range
4. Insensitive to electromagnetic fields and radiation, enabling measurements under harsh
conditions
5. Materials like gallium phosphate or tourmaline have an extreme stability over
temperature enabling sensors to have a working range of 1000°C
Table 5.10 gives an idea about the relative standing of piezoelectric transducers vis-a-vis the
strain sensitivity of other transducers.

Transducers 149
Table 5.10 Comparison of sensitivity of sensing principles
Principle Sensitivity (V/µm) Resolution (µm) Dynamic range (dB)
Piezoelectric 5.0 0.00001 160
Piezoresistive 0.0001 0.0001 128
Inductive 0.001 0.0005 126
Capacitive 0.005 0.0001 117
Disadvantages. In comparison to the advantages of piezoelectric transducers, disadvantages
are only a few, namely
1. The major disadvantage is that they cannot be used for true static measurements. A
static force will generate a fixed amount of charge on the piezoelectric material. Working
with conventional electronics, not perfect insulating materials, and reduction in internal
sensor resistance will result in a constant loss of charge, thus yielding an inaccurate
signal.
2. Elevated temperatures cause an additional drop in internal resistance. Therefore, at
higher temperatures, only piezoelectric materials can be used that maintain a high
internal resistance.
Applications
The piezo materials are available in a variety of shapes and sizes such as discs, plates, bars,
rings, rods, tubes, etc. Some of their typical applications as transducers are as follows:
1. Vibration and shock measurement
2. Accelerometers
3. Ultrasound flow meters
4. Dynamic force and pressure measurement
5. NDT (non-destructive testing) transducers23
Other applications include
1. Stable oscillation frequency generators
2. High voltage generators tor gas lighters
3. Fuses for explosives
4. Nebulisers
5. SONAR
6. Deepwater hydrophones24
7. Actuators/translators
8. Ultrasonic cleaners, welders
23 Ultrasound waves are passed through a material and received at different speeds relative to the density
and elastic properties of the material, producing data that can be utilised to create a cross-sectional image.
24Device for converting sound waves into electrical signals, similar in operation to a microphone but used
primarily for detecting sound waves from an underwater source, such as a submarine.

We would like to mention in this context that many creatures make an interesting use of
piezoelectricity. Bones are piezolelectric materials and they act as force sensors. Once loaded,
bones produce charges proportional to the resulting internal strain. Those charges stimulate
and drive the development of new bone material. This leads to the strengthening of structures
where the internal displacements are the greatest. Thus, with time weaker structures increase
their strength and stability as material is laid down proportional to the forces affecting the
bone.
Piezoresistivity
The piezoresistive effect is the change of electric resistivity of the material caused by an
applied mechanical stress. Many materials change their resistance when stressed, but the
piezoresistive effect is the most pronounced in semiconductors. Semiconductor piezoresistive
sensing elements, or piezoresistors, are typically used as pressure and force sensors, where the
applied mechanical load is converted into a proportional electric signal.
Origin ofpiezoresistivity
It is apparent that piezoresistivity has nothing to do with piezoelectricity, though some
piezoresistors are piezoelectric as well for reasons different altogether.
When a semiconducting material is stressed, the interatomic spacings within the material
change. This eventually changes the bandgaps in each atom making it easier (or harder
depending on the material and strain) for electrons to be raised into the conduction band. A
higher or lower electron population in the conduction band results in a change in resistivity of
the semiconductor.
We know that the resistance R of a conductor is given by
l
R=p-
A
where p is the resistivity of the material of the conductor
l is the length of the conductor
A is the area of cross-section of the conductor.
For metals, p is more or less a constant at a given temperature because their conduction bands
are already sufficiently populated with electrons. But the conduction bands of semiconductors
are not so populated normally and as already discussed, at a given temperature p varies for
semiconductors when they are stressed. For them the piezoresistivity Pu is defined by
where dp is the change in resistivity
p is the original resistivity
c is the strain
dp/p
Pu= - -
c
Now, when a semiconductor is strained, its length and area of cross-section will eventually
change with a consequent change in its resistance. But its piezoresistive change can be several

Transducers 151
orders of magnitudes larger than the geometrical effect. This effect is conspicuous in materials
like germanium, polycrystalline silicon, amorphous silicon, silicon carbide, and single crystal
silicon.
Piezoresistors
Piezoresistors are fabricated using a wide variety of piezoresistive materials. The simplest form
of silicon piezoresistors are diffused resistors. They consist of a simple two contact diffused n
or p-well within a p or n-substrate. The typical square resistances of these devices are in the
range of several hundred ohms. This necessitates additional p+ or n+ diffusions to facilitate
ohmic contacts to the device (Fig. 5.23).
Electrode Electrode
A Insulation
A
z
lix
ln+contactj
n-well
ln+contactj
p-substrate
Fig. 5.23 Schematic cross-section of an elementary silicon n-well piezoresistor.
For typical stress values in the order of mPa, the piezoresistivity can be written as
dp/p
Pa = - - = 7rY
c
where 7r is the piezoresistive coefficient and Y is the Young's modulus. Both 7r and Y depend
on
1. Basic material, now mostly silicon
2. Majority carriers, i.e. p or n
3. Crystal orientation given by Miller indices like (100) or (111)
4. Angle between the current and stress; the stress may be tensile, shear or volume
compression
5. Degree of doping indicated by the room-temperature resistivity p0
6. Size and shape of the resistor
In general, both the stress and the current are along the length of the piezoresistor. Then,
the relation for the longitudinal piezoresistance coefficient is given by
where 11"11 , 11"12 , 11"44 are the fundamental piezoresistive coefficients, the subscripts referring
to the current and stress directions
a1, /31, /1 are the direction cosines of the current with respect to the
crystallographic axes

For a shear stress perpendicular to the current direction, the relation for the transverse
piezoresistive coefficient is given by
7r1 = 7r12 + (?rn - 7r12 - 7r44)(aia~ + f3?(3~ +1hn
Table 5.11 gives an idea about the characteristics of lightly doped silicon and germanium at
moderate strain at the room temperature. In general, the sensitivity and thermal coefficient
of doped semiconductors decrease with higher doping.
Table 5.11 Relevant piezoresistive characteristics of lightly doped silicon and germanium at moderate
strain at the room temperature. Crystal orientations are (111) for all, except n-Si for which
it is (100)
Characteristic (unit) p-Si n-Si p-Ge n-Ge
Unstrained resistivity (x 10- 3 Q-m) 78 117 150 166
7r11 (x 10- 12 m2 /N) 66 -1022 -106 - 52
7r12 (x 10- 12 m2/N) -11 534 50 55
7r44 (x 10- 12 m2/N) 1381 -136 986 -1387
Pu 175 -133 102 -157
Young's modulus (x 109 N/m2) 187 130 155 155
Poisson's ratio 0.180 0.278 0.156 0.156
Nonlinearity. The variation of piezoresistivity with strain at moderate doping is far from
linear. For example, the fractional resistivity variation of lightly doped p-Si at moderate
tensile stress and at the room temperature can be written as
dp = 175s + 72625s2
p
At higher stress levels, the nonlinearity can be even higher and more temperature dependent.
Of couse, the nonlinearity as well as temperature dependence can be lowered by higher doping
but at the expense of sensitivity. Figure 5.24 shows a qualitative picture of the variation.
Light doping
Temperature
Fig. 5.24 Sensitivity vs. temperature plots for p-Si at different degrees of doping.
Despite the fairly large stress sensitivity of simple resistors, they are preferably used in
more complex configurations eliminating certain cross sensitivities and thermal effects.

Transducers 153
Typical applications of piezoresistors are as strain gauges which are used in pressure
transducers and accelerometers.
Surface Acoustic Waves
In 1887, Lord Rayleigh25 discovered the surface acoustic wave (SAW) mode of propagation.
Named after their discoverer, Rayleigh waves have a longitudinal and a vertical shear
component that can couple with a medium in contact with the surface of the device
(Fig. 5.25). Such coupling strongly affects the amplitude and velocity of the wave. This
feature enables SAW sensors to directly sense mass and mechanical properties.
z
l(y
x
Fig. 5.25 Surface acoustic wave propagation, shown in an exaggerated way.
The wave has a velocity that is nearly 5 orders of magnitude less than the corresponding
electromagnetic wave, making Rayleigh surface waves among the slowest to propagate in solids.
The wave amplitudes are typically around 10 A and the wavelengths range from 1- 100 µm .
Fabrication of the SAW sensor
The SAW sensors are made by a photolithographic process. Initially a piezoelectric substrate
is carefully polished and cleaned. Then a metal, usually aluminium, is deposited uniformly on
the substrate. Next it is coated with a photoresist, baked to harden it and then exposed to
UV light through a mask with opaque areas corresponding to the areas to be metallised on the
final device. The exposed areas undergo a chemical change that allows them to be removed
with a developing solution. Finally, the remaining photoresist is removed. The pattern of
metal remaining on the device is called an interdigital26 transducer, or IDT. By adjusting the
length, width, position, and thickness of the IDT, the performance of the SAW sensor can be
maximised. The diagram of a SAW sensor is shown in Fig. 5.26.
Among the piezoelectric materials chosen for the substrate, the most common are quartz
(Si02), lithium tantalate (LiTa03 ), and, sometimes, lithium niobate (LiNb03 ).
Principle of operation
The input IDT of the sensor provides the electric field necessary to generate an oscillation in the
piezoelectric substrate through the inverse piezoelectric effect. Thus a travelling acoustic wave
25 Lord Rayleigh (John William Strutt), a British Physicist (1842- 1919) worked on the theory of waves. He
became the Cavendish Professor of Physics at Cambridge and was awarded the Nobel prize in Physics (1904)
for his discovery of the gas Argon.
26 The word digit literally means a finger of a human being. So, interdigital signifies a pattern that resembles
the interwoven fingers of both hands.

Power
supply
Input IDT
Absorber
Output IDT
Surface wave
Piezoelectric substrate
Fig. 5.26 Diagram of a surface acoustic wave sensor.
Load
is formed. The wave propagates to the other end of the substrate, where it is converted back
to an electric field by the output IDT. Since this is a longitudinal wave, alternate compression
and stretching of the substrate take place in the transverse direction. These produce alternate
polarisations in the opposite directions on the surface of the substrate. The fingers of the
output IDT are so spaced that they are able to capture these charges to produce a voltage.
Applications
The SAW sensors generally operate from 25- 500 MHz. They are sensitive, to varying degrees,
to perturbations from many different physical parameters. The range of phenomena that can
be detected by them can be greatly expanded by coating the devices with materials that
undergo changes in their mass, elasticity, or conductivity upon exposure to some physical or
chemical stimulus. For example, these sensors become
• Pressure, torque, shock, and force detectors under an applied stress that changes the
dynamics of the propagating medium.
• Mass, or gravimetric, sensors when particles are allowed to come in contact with the
propagation medium thus changing the stress on it.
• Vapour sensors when a coating is applied that absorbs only specific chemical vapours
and changes the mass of the coating.
• Biosensors, if the coating absorbs specific vapours of biological fluids.
One disadvantage of these devices is that the Rayleigh waves are surface-normal waves,
making them unsuitable for liquid sensing. When a SAW sensor is in contact with a liquid,
the resulting compressional waves cause an excessive attenuation of the surface wave.
Two interesting applications of the SAW sensor are as band-pass filters in mobile telephones
and sensing device in touch-screen displays.
Optical Effects
Detectors based on opticl effects can be classified as shown in the tree diagram of Fig. 5.27.
Photographic film, photopolymers, etc. can be called chemical detectors. They do not give
a signal output in the usual sense as do the other types.

Transducers
Optical detector
--------
Chemical Electronic
--------
Photon Thermal
--------
External photoeffect
I
Phototube
Photomultiplier tube
Internal photoeffect
I
Photoconductor
Photovoltaic cells
Photodiode
Phototransistor
Fig. 5.27 Optical detectors tree.
155
In thermal detectors, the absorption of light raises the temperature of the device and this,
in turn, results in changes in some temperature-dependent parameter (e.g. electrical conduc-
tivity). Some of the better known thermal detectors are the thermocouple, the bolometer
and pyroelectric detectors. The last type can be made with response times in the nanosecond
region and with a wavelength response up to 100 µm. They have proved very useful as low
cost, robust infrared detectors.
The operation of photon detectors is based on the photoeffect, in which the absorption of
photons by some materials results directly in an electronic transition to a higher energy level
and the generation of mobile charge carriers. The photoeffect takes two forms:
• External photoeffect: The process involves photoelectric emission in which the photo-
generated electrons escape from the material (the photocathode) as free electrons.
• Internal photoeffect: In the internal photoeffect, the photoexcited carriers (electrons and
holes) remain within the material.
We will consider the external photoeffect, which can be called photoemissive effect, first.
External photoeffect: Photoemission
When irradiated by electromagnetic radiation of very short wavelength, such as visible or
ultraviolet light, electrons are emitted from matter-metals and non-metallic solids, liquids
or gases-as a consequence of their absorption of energy. This phenomenon is called the
photoelectric effect or photoemissive effect (Fig. 5.28). Emitted electrons are referred to as
photoelectrons. The effect was first observed by Heinrich Hertz27 in 1887.
The photoelectric effect requires photons with energies from a few electron volts to over 1
MeV in high atomic number elements. In photoelectric emission, the photo-generated electrons
escape from the material (the photocathode) as free electrons with a maximum kinetic energy
given by the photoelectric equation of Einstein:
Emax = hv- cp
where the work function cp is the energy difference between the Fermi level and he continuum
of the material. The study of the photoelectric effect led to important consequences in
27 Heinrich Rudolf Hertz (1857-1894) was a German physicist who carried out important experiments to
prove the electromagnetic nature of light.

Ejected
electrons
from the
surface I
I
0 I
0 I
0
Vacuum
Fig. 5.28 Schematic diagram showing emission of photoelectrons.
understanding the quantum nature of light and electrons, and led to the formation of the
concept of wave- particle duality of matter.
Observations. The remarkable aspects of the photoelectric effect are:
1. The electrons are emitted immediately. There is no time lag between the irradiation of
the substance and the ejection of electrons from it.
2. If the intensity of the light is increased, the number of photoelectrons also increases, but
not their maximum kinetic energy.
3. An impinging red light (.A = 700 nm) will not cause the ejection of electrons, no matter
whatever its intensity is. A green (.A = 550 nm) or violet (.A = 400 nm) light will
eject electrons. But their maximum velocities are greater the shorter the wavelength
(Fig. 5.29).
700 nm
1.77 eV
Vmax = 6.22 X 17
5 mis
Vmax = 2.96 X 105 mis/
550nm /
2.25 ,v ,o 400 = .. /c
/// 3.1 eV ..·····
Cesium, ¢ =2.1 eV
Fig. 5.29 Schematic representation of emission of photoelectrons for incidence of different wavelengths
of light. </>indicates the value of the work function for potassium.
Theoretical explanation. In 1905 Einstein28 gave a very simple interpretation of the
photoelectricity phenomenon. He assumed that the incoming radiation should be thought of
as quanta of energy hv, with v the frequency. In photoemission, one such quantum is
absorbed by one electron. If the electron is deep inside the material, some energy will be lost
as it moves towards the surface. This is usually called the work function, cp. The most
28 Albert Einstein (1879- 1955) was a German-born theoretical physicist who is often regarded as the father
of modern physics. He received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and
especially for his discovery of the law of the photoelectric effect".

Transducers 157
energetic electrons emitted will be those very close to the surface, and they will leave the
surface with kinetic energy
Emax = hv- r.p
where h is the Planck constant and v is the frequency of the incident photon. The work
function satisfies the relation
r.p = hv0
where v0 is the threshold frequency for the metal. The maximum kinetic energy of an ejected
electron is then
Emax = h(v- vo)
Since kinetic energy is a positive quantity, we must have v > v0 for the photoelectric effect to
occur.
Stopping potential. Let a light source illuminates a plate X, and another plate electrode Y
collects the emitted electrons. We apply a voltage between X and Y, change it slowly and
measure the current flowing in the external circuit between the two plates.
If the frequency and the intensity of the incident radiation are fixed, the photoelectric
current increases gradually with an increase in the voltage until the photoelectric current
attains a saturation value and does not increase further whatever the voltage. The saturation
current depends on the intensity of illumination, but not its wavelength.
If we now apply a negative voltage to Y with respect to X and gradually increase it, the
photoelectric current decreases until it is zero, at a certain negative voltage. The minimum
negative voltage at which the photoelectric current becomes zero is called stopping potential
or cut off potential. It may be observed that for a given frequency of the incident radiation,
the stopping potential V0 is
1. fudependent of its intensity.
2. Related to the maximum kinetic energy of the photoelectron that is just stopped from
reaching Y If m is the mass and Vmax is the maximum velocity of photoelectron emitted,
then
If e is the charge on the electron, then the work done by the retarding potential in
stopping the electron= eV0 , which gives
(5.42)
Eq. (5.42) shows that the maximum velocity of the emitted photoelectron is independent
of the intensity of the incident light. Hence
he
Emax = eVo = er.p = -
Ao
Ao = he = 1.2431 µm
er.p r.p

Photoemissive materials. Many metals are photoemissive when irradiated with photons of
moderate energy. The work functions and corresponding threshold wavelengths of a few
common elements are listed in Table 5.12.
Table 5.12 Work functions and threshold wavelengths for a few common elements
Element cp (eV) Ao (µm) Element cp (eV) Ao (µm)
Aluminum 4.08 0.3025 Magnesium 3.68 0.3354
Beryllium 5.0 0.2468 Mercury 4.5 0.2742
Cadmium 4.07 0.3032 Nickel 5.01 0.2463
Calcium 2.9 0.4256 Niobium 4.3 0.2870
Carbon 4.81 0.2566 Potassium 2.3 0.5366
Cesium 2.1 0.5877 Platinum 6.35 0.1943
Cobalt 5.0 0.2468 Selenium 5.11 0.2415
Copper 4.7 0.2626 Silver 4.73 0.2609
Gold 5.1 0.2420 Sodium 2.28 0.5413
Iron 4.5 0.2742 Uranium 3.6 0.3428
Lead 4.14 0.2981 Zinc 4.3 0.2870
Photoemissive transducers. The photoemissive transducers that we will consider are
1. Phototube
2. Photomultiplier tube
Phototube. Photoemissive devices usually take the form of vacuum tubes called phototubes
(Fig. 5.30). It works on the basic principle of light striking the cathode which causes the
emission of electrons. Emitted electrons travel to the anode which is kept at 70- 180 V. As a
result, an electric current proportional to the photon flux incident on the cathode is created
in the circuit.
(a)
Evacuated glass
envelope
Anode
(b)
Fig. 5.30 {a) Schematic diagram of a phototube, {b) symbolic representation of a phototube.
The quantum yield K>. is defined as
K>. = Number of electrons released
Number of photons absorbed

Transducers 159
The value of K;.. lies between 0 and 0.5. Pure metals are rarely used as cathodes since they have
low quantum yields ("-' 0.1) and high work functions (<p = 2.1 eV for Cs) which makes them
useful only in the visible and ultraviolet regions of the spectrum. However, semiconductors can
operate with higher quantum yields and lower work functions corresponding to wavelengths
up to about 1.1 µm. Typically cathodes are made of materials like Cs3 Sb, NaO, AgOCs.
The responsivity R;.. is defined as
where X;.. is the output signal like voltage, current, charge
<I>>. is the incident flux in W
The generated current ia is given by the relation
where 'r/ is the anode collection efficiency (0- 1) which is dependent on its design and bias
e is the electronic charge
The responsivity vs. A is called the spectral response. The relative spectral response of various
photoelectric transducers is shown in Fig. 5.31.
1015 A
1014
<!)
1013
VJ
i::
0
0..
VJ
<!)
1012
....
(;J
:::
()
<!)
0.. 1011
en
E
1010
109
200 600 1000 1400 1800 2200
Wavelength (nm)
Fig. 5.31 Relative spectral response of various photon transducers. A: photomultiplier tube, B: CdS
photoconductive cell, C: GaAs photovoltaic cell , D: CdSe photoconductive cell, E: PbS
photoconductive cell, F: Si photodiode.
Photomultiplier tube. The photomultiplier tube (Fig. 5.32) makes use of the photoelectric
effect to convert small intensities of light into electrical current.
Electrons dislodged by the photoelectric effect from the photoemissive cathode travel down
a special tube consisting of secondary electron generating dynodes. Dynodes are usually made
of materials like MgO or GaP. Each dynode is biased on the order of 100 V more positive

Quartz envelope
,__~~---'~-Photoemissive cathode
- - - Incident light
Anode
Fig. 5.32 Diagram of a photomultiplier tube. The numbers 1, 2, 3, ... indicate dynodes.
than the previous to accelerate electrons from dynode to dynode (Fig. 5.33). The gain per
dynode is typically 2- 5 and the total gain is 106- 108 . So, by the time it gets to the end, a
single electron can gather a hundred million other electrons. The charge pulse at anode is a
few nanosecond wide.
Quartz envelope
To readout
l
Fig. 5.33 Biasing of dynodes and output from a photomultiplier tube. The numbers 1, 2, 3, .. . indicate
dynodes.
Internal photoeffect
Among the transducers that utilise internal photoeffect, we will consider the following:
l. Photoconductor
2. Photovoltaic transducer

Transducers 161
3. Photodiode
4. Phototransistor
Photoconductor. Photoconductivity is one of the internal photoeffects in which a material
becomes more electrically conductive when irradiated by light of suitable waveband such as
visible, ultraviolet, infrared or gamma radiation. Such a device is called a photoresistor, or a
photoconductor or sometimes a light dependent resistor (LDR).
Construction. Photoconductors are typically made by depositing thin films of
photoconductive substances on a glass or plastic substrate. Electrodes are deposited on the
photoconductive surface and are made of materials which give an ohmic contact, but with
low resistance compared with that of the photoconductor. Gold is typically used because its
Fermi level29 matches those of intrinsic semiconductors and therefore, no rectification of
signals takes place at the points of contact. The electrodes are usually interdigital, i.e. in the
form of interlocked fingers, as shown in Fig. 5.34.
Electrodes
Encapsulation
Fig. 5.34 Photoconductor.
The design of the electrode system affects the resistance and voltage ratings of the cell.
Different resistances and voltage ratings can be achieved on a film of a given size. A device
with a small number of widely spaced electrodes will have a higher resistance and voltage
rating than a device using the same film with a large number of closely spaced electrodes.
Devices can be made for end on or side illumination. The encapsulation is hermetically sealed
so that it is resistant to humidity and corrosive atmosphere.
Principle of operation. Photoconductor detectors rely directly on the light-induced increase in
the conductivity, an effect exhibited by almost all semiconductors. The absorption of a photon
results in the generation of a free electron excited from the valence band to the conduction
band, and a hole is generated in the valence band. An external voltage source connected to the
material causes the electrons and holes to move, resulting in a detectable electric current. The
detector operates by registering either the current (which is proportional to the photon flux)
or the voltage drop across a series resistor. Unlike the quantum efficiency for the photoelectric
effect, for example, the gain in a photoconductor may be larger than unity. The semiconducting
material may take the form of a slab or a thin film.
29 Top filled electron energy level at 0 K.

Photoconductive materials. Photoresistors are available in many different types. Inexpensive
cadmium sulphide (CdS) ones can be found in many consumer items like camera light meters,
clock radios, burglar alarms and automatic ON/OFF street lights.
CdS LDRs have a long life, typically up to 10,000 hours. Their response is temporarily
impaired by exposure to strong light, but they recover by themselves and are not damaged.
Damage may be caused by electrical overload. So, the applied voltage and current for the
required illumination must be known. If in doubt a series resistor can be incorporated to limit
the current. Overheating can cause damage, but the device is usually vibration resistant.
A few classic examples of photoconductive materials are listed in Table 5.13
Table 5.13 A few classic photoconductive materials and their uses
Material Comments
Polyvinylcarbazolea Conductive polymer used extensively in photocopying (xerography).
Lead sulphide Used in infrared detection applications, such as heat-seeking missiles
Sidewinder (USA) and Atoll (Russia).
Selenium Employed in early television and photocopying.
Ge:Cu Among the best far-infrared detectors available. They are used for
infrared astronomy and infrared spectroscopy.
a Commonly called OPC (organic photoconductor).
The photoconductive cells usually have high gains (103-104 ) but poor response times
(rv50 ms).
Photovoltaic transducer. The photovoltaic cell is another transducer which utilises the internal
photoeffect.
Principle of operation. The photovoltaic cell is a p-n junction structure where photons
absorbed in the depletion layer generate electron-hole pairs which are subject to the local
electric field within that layer. Because of this field, the two carriers drift in opposite
directions and an electric current is induced in the external circuit.
Construction. Photovoltaic cells are fabricated from thin layer of crystalline semiconductor,
e.g. Se, Si, Cu2 0 as well as from ternary and quaternary compound semiconductors such
as InGaAs, HgCdTe and InGaAsP sandwiched between two different metal electrodes. Pure
selenium, a p-type semiconductor, is coated on a metal base such as aluminium or brass. Then
cadmium is diffused into selenium to form a p-n junction as cadmium oxide forms then-layer.
This layer is sometimes called the barrier layer. On top of it is coated a thin layer of silver or
gold which forms the metal layer as well as an electrode. The entire cell is encapsulated in a
plastic case. Devices are often constructed in such a way that the light impinges normally on
the p-n junction instead of parallel to it. A typical construction is shown in Fig. 5.35.
Solar cell. A basic photovoltaic cell is also called a solar cell. For solar cells, a thin
semiconductor wafer is specially treated to form an electric field, positive on one side and
negative on the other. A number of solar cells electrically connected to each other and
mounted in a support structure or frame is called a photovoltaic module. Modules are

Transducers 163
Glass Thin layer of silver
Barrier layer
Selenium -++----.i:z::z::;:::z::::zzzz::z::;:::z:J
Aluminium Plastic case
+
Fig. 5.35 Schematic diagram of a photovoltaic cell.
designed to supply electricity at a certain voltage, such as a common 12 volt system. The
current produced is directly dependent on how much light strikes the module. Multiple
modules can be wired together to form an array. In general, the larger the area of a module
or array, the more electricity will be produced.
Multijunction solar cell. In a single-junction photovoltaic cell, only photons whose energy is
equal to or greater than the band gap of the junction can free an electron-hole pair for an
electric circuit. In other words, the photovoltaic response of single-junction cells is limited
to the portion of the sun's spectrum whose energy is above the band gap of the absorbing
material, and lower-energy photons are not used.
One way to get around this limitation is to use two (or more) different cells, with more
than one band gap and more than one junction, to generate a voltage. These are referred to as
multijunction cells (aka cascade or tandem cells). Multijunction devices can achieve a higher
total conversion efficiency because they can convert more of the energy spectrum of light to
electricity.
Eg1 > Eg2 > Eg3
Junction 1
Eg2 t - - - - - - - - - - - - i
Junction 2
Junction 3
Fig. 5.36 Functioning of a multijunction cell.
As shown in Fig. 5.36, a multijunction device is a stack of individual single-junction cells in
descending order of band gap (E9 ). The top cell captures the high-energy photons and passes
the rest of the photons on to be absorbed by lower band gap cells.
Multijunction materials. Much of today's research in multijunction cells focusses on gallium
arsenide as one (or all) of the component cells. Such cells have reached efficiencies of around
35% under concentrated sunlight. Other materials studied for multijunction devices have been
amorphous silicon and copper indium diselenide.

Photodiode. A photodiode is sort of a miniature solar cell that consists of an active p- n
junction which is operated in reverse bias [Fig. 5.37(a)] . The light incident on the junction
generates a reverse current which is proportional to the intensity of illumination.
-
Reverse current
(a)
:;(' 800
E
';:;" 600
i::
~
8 400
<!)
</>
....
~ 200
<!)
i:i:::
2000 4000 6000
Light intensity (lumen/m2)
(b)
Anode --ct--Cathode
(c)
Fig. 5.37 Photodiode: (a) operation , (b) response curve, and (c) symbol.
Its linear response [Fig. 5.37(b)] to light makes it a useful photodetector for some
applications. It is also used as the active element in light-activated switches. The symbol of
a photodiode is shown in Fig. 5.37(c).
The photodiode response is fast- on the order of nanoseconds. But it is not as sensitive as
a phototransistor. However , its linearity of response can be utilised to construct simple light
meters.
Phototransistor. Phototransistors are designed specifically to take advantage of the fact that
like diodes, all transistors are light-sensitive. The most common variant is an n-p-n bipolar
transistor with an exposed base region. When light strikes the base, a voltage is applied to
the base. So, a phototransistor amplifies variations in the light striking it. A phototransistor
may or may not have a base lead. If it does, the base lead allows us to bias the light response
of the phototransistor.
Of course, photodiodes also can provide a similar function, but with much lower gain.
Which means, photodiodes allow much less current to fl.ow than do phototransistors.
The illustration given in Fig. 5.38, where both circuits are equivalent, helps us to understand
the difference between a photodiode and a phottransistor. It suggests that the phototransistor
is basically a combination of a photodiode and a transistor which not only detects the light
intensity like a photodiode, but also amplifies the generated current.
(a) (b)
Fig. 5.38 (a) Phototransistor and (b) an equivalent circuit with a photodiode.
Table 5.14 offers a comparison between the characteristics of different photon detectors.

Transducers 165
Table 5.14 Typical characteristics of photon detectors
Type D*a RA b Linear range Spectral range Rise timec Output
(cm Hz1/ 2 w-1) (decades) (nm) (ns)
Phototube 10s-1010 0.001-0.1 d 5 200-1000 1-10 Current
Photomltiplier 1012_1017 10-105d 6 110-1000 1-10 Current,
tube charge
Photoconductive 109-1012 104-106• 5 750-6000 50-106 Resistance
cell change
Photovoltaic 10s-1011 100-106" 3 400-5000 103 Current,
cell voltage
Si 1010-1012 0.05-0.5d 5-7 250-1100 1-10 Current
Photodiode
a Measure of minimum detectability: D = 1/<I>n; D* is normalised D for area A (cm2 ) and
bandwidth !lf (Hz) [DA1/2(tJ.J)l/2].
b Values indicate range for several different types.
c Time for output to rise from 10-90% of final value for instantaneous increase in radiant power.
dAjW
·v;w
5.3 Selection of Transducers
It is important to remember that since transducers constitute the sensing element in an
instrumentation system, the precision of the data produced by the instrumentation system
depends, in most of the cases, on the capability of the transducer. For example, a precise
temperature control can hardly be achieved if the transducer used is a simple bi-metallic
strip. Therefore, the selection of a proper transducer is important from the standpoint of
required precision.
The following points should be considered while selecting a transducer:
Fundamental parameters. These include
(a) Type of measurand
(b) Range of measurement
(c) Required precision, which includes
(i) Allowable nonlinearity effects
(ii) Allowable dead-zone effects
(iii) Frequency response
(iv) Resolution.
Environment. This includes consideration of
(a) Ambient temperature
(b) Corrosive or non-corrosive atmosphere
(c) Shock and vibration to withstand.

Physical conditions. These are
(a) Room or available space to mount the transducer
(b) Whether the measurement is static or dynamic
(c) How much energy can be extracted from the measurand to carry-out measurement
without much loading.
Compatibility with the next stage. Normally, some standard signal conditioner and display
devices are used with a transducer, unless they are custom-built to suit the requirements
of the transducer. In the former case, the transducer should be so chosen as to meet the
requirements of the next stage, such as
(a) Impedance matching
(b) Excitation voltage matching
(c) Sensitivity tolerance matching.
These criteria, of course, are not exhaustive but they may offer some guidance as regards
selection of a suitable transducer.
Transducers can be constructed from various materials and in many designs. But to gain
acceptance in the field of instrumentation they must conform to the following six cardinal
requirements:
1. Ruggedness to withstand overloads
2. Linearity
3. Repeatability
4. Stability and reliability
5. Good dynamic response
6. Convenient instrumentation
5.4 Smart Sensors and IEEE 1451 Standard
Ordinary sensors or transducers help sense and/or control process parameters like temperature,
pressure, strain, flow, pH, etc. Smart sensors provide functions beyond those. A smart sensor
1. Acquires data
2. Conditions the signal
3. Converts the measurement into the attribute's units
4. Transmits the data to a network by wireline or wireless method
An example will perhaps make the concept clear. Suppose, we are measuring the temp-
erature of a measurand with the help of thermocouple that generates a particular voltage
corresponding to a particular temperature. If the thermocouple is connected to network, the
network controller needs to convert it to represent the data in degrees Celsius or Fahrenheit
('attribute's units'). A smart sensor incorporates a look-up table or transducer electronic
data sheet (TEDS) that performs the conversion and presents the data in appropriate unit
of temperature to the network controller. To perform the latter task, the smart sensor also
possesses a built-in digital interface that provides a communication channel with the network
control. A functional smart sensor system thus consists of two main components, namely

Transducers 167
1. Transmitter interface module (TIM) that contains physical transducer and data acquisi-
tion system, and
2. Network capable application processor (NCAP) where control and data correction take
place.
Diagrammatically the system can be represented as shown in Fig. 5.39.
Address
logic
Transducer interface
(wired/wireless)
NCAP
Commands
Object model
Network
Fig. 5.39 Smart sensor system. XDCR = transducer.
The TIM and NCAP perform the following functions:
TIM NCAP
1. Analogue signal conditioning 1. Message encoding and decoding
2. Triggering 2. Detection and control of TIMs
3. Analogue to digital conversion 3. Correction and interpretation of TEDS data
4. Command processing 4. Message routing and interface control
5. TEDS storage
6. Data transfer and communication
With the advancement of digital communication, increasing demand for networked
configuration to connect sensors and actuators and proliferation of smart sensor
manufacturers, the IEEE30 introduced a standard, called IEEE 1451, to address the
following requirements:
1. Network and vendor independent plug-and-play TIMs without having to add special
drivers or profiles. The features that enable plug-and-play operation are TEDS and the
basic command set.
2. Analogue or digital interfaces so that sensors or actuators can be easily connected by
either wireline or wireless method.
3. Installation, upgradation, replacement and/or movement of sensors with minimum effort.
4. Elimination of manual data entry and system configuration steps which are error prone.
30 Institute of Electrical and Electronics Engineers (USA).

Be it mentioned here that IEEE 1451 is not another field network. It is an open standard
that may be used with multiple networks.
Smart sensors, though very elegant, are finding it hard to make inroads to existing industries
owing to (i) the great technological leap and (ii) the cost associated with the replacement of
entire existing software and hardware infrastructures.
The new standard, referred to as IEEE P1451.4, provides many of the features of IEEE
1451 such as automatic detection, configuration and calibration while retaining the existing
measurement architectures. It is backward compatible to traditional sensors and measurement
architecture while allowing integration of smart sensors.
In the following chapters we will discuss a few transducers and associated methods of
measurements and other relevant matters. For our convenience we will deal with the
measurement of a few physical quantities because the techniques involved in these
measurements are of representative character.
Review Questions
5.1 What is transducer? What is the difference between sensor and transducer? Name some
of the active transducers which are used in the measurement of temperature.
5.2 What is 'transducer'? Define active and passive transducers with examples and state
the role of each in measuring system.
5.3 Match the following:
Phenomenon
(a) Applied force causes emf
(b) Applied voltage causes vibrations
(c) Temperature difference causes emf
(d) Light causes current
5.4 Match the devices with the sensors:
Name
(i) Seebeck effect
(ii) Hall effect
(iii) Photoelectric effect
(iv) Magnetostriction
(v) Piezoelectric effect
(vi) Inverse piezoelectric effect
(a) High frequency vibration
(b) Load cell
(e) Strain gauge
(c) Gauss meter
(d) Large displacement
(f) Hall element
(g) Potentiometer
(h) Piezoelectric crystal
5.5 Match the devices with quantities measured:
(a) Rotameter (e) Relative humidity
(b) Hydrometer (f) Density
(c) Sling psychrometer (g) Dynamic pressure
(d) Piezoelectric transducer (h) Flow rate

Transducers
5.6 Match the transducers with the materials used:
(a) Permalloy
(b) Advance
(c) Phosphor bronze
(d) Quartz
(e) Piezoelectric
(f) Magnetostrictive
(g) Strain gauge
(h) Spring
5.7 In the context of transducers, indicate the correct choice:
169
(a) A photoconductive transducer works on the principle that when a light beam strikes
(i) the material, its resistance decreases, which is sensed by an external circuit
(ii) the barrier between transparent metal layer and a semiconductor material, a
voltage is generated
(iii) the barrier between transparent metal layer and a semiconductor material, a
current is generated in the external circuit
(iv) the cathode, it releases electrons, which are attracted towards the anode,
thereby producing electric current in the external circuit
(b) Identify the correct set of matches:
(a) Mean free path (p) Optical pyrometer
(b) Humidity (q) Knudsen gauge
(c) Heat transfer coefficient (r) Sling psychrometer
(d) Intensity of radiation (s) Hot wire anemometer
(i) (a)-+ (p), (b)-+ (q), (c)-+ (r), (d)-+ (s)
(ii) (a)-+ (q), (b)-+ (p), (c)-+ (s), (d)-+ (r)
(iii) (a)-+ (r), (b)-+ (s), (c)-+ (p), (d)-+ (q)
(iv) (a)-+ (q), (b)-+ (r), (c)-+ (s), (d)-+ (p)
(c) Identify the correct set of matches:
(p) Thermocouple (1) DC bridge
(q) Strain gauge (2) Phase sensitive detector
(r) Piezoelectric sensor (3) Charge amplifier
(s) LVDT (4) Cold junction compensation
(5) Instrumentation amplifier
(i) (p)-+ (2), (q)-+ (3), (r)-+ (5), (s)-+ (1)
(ii) (p)-+ (1), (q)-+ (5), (r)-+ (2), (s)-+ (3)
(iii) (p)-+ (4), (q)-+ (1), (r)-+ (2), (s)-+ (5)
(iv) (p)-+ (4), (q)-+ (1), (r)-+ (3), (s)-+ (2)

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