TRANSDUCER ELEMENTS

Prepared By: Dr Sam Sung Ting

ANALOG TRANSDUCERS

• Electromechanical Types

In such transducers, an electrical output is produced due to an input of mechanical

displacement or strain. The mechanical displacement or strain input in turn may be produced by a

primary sensor due to the input physical variable which may be pressure, flow, etc.

Figure 4.1 shows the scheme for measurement using an electrochemical transducer.

In each case, the input physical variable results in a displacement of an elastic member. In Fig.

4.2 (a), the force applied results in a displacement of the elastic member. In Fig. 4.2 (b), an elastic

diaphragm converts pressure input into deflection or displacement. Similarly, a bimetallic strip of

brass an invar alloys gets deflected due to the change of temperature, due to the different in

coefficient of expansion of the two materials. In each case, an electrochemical transducer may be

employed to convert the displacement into an electrical signal, that can be related to the force,

pressure or temperature input desired.

• Since displacement or motion is an input to an electromechanical transducer, this may be treated

as a basic parameter, derivable from several types of physical inputs. The transducer discussed

here are also known as motion transducers.

• The following factors have to be kept in mind, while considering the selection of motion

transducers, for a given application:

1. Magnitude of motion – whether the transducer is meant for measuring small, medium or large

motions.

2. Type of input – output relation – whether the output is proportional to displacement motion its

rate of change with time, viz. velocity or rate change of velocity, viz. acceleration.

3. Static and dynamic characteristics – whether the transducer can measure static or dynamic or

both types of displacements.

4. Attachment or proximity type – whether the transducer has to be attached to the moving object

or kept in close proximity to it.

5. Self-generating or external power source type – whether a power output is needed to energise

the transducer or the same is generated due to the input motion itself, within the transducer.

6. Type of associated circuit – whether the circuit to be used along with the transducer for

producing a measurable output is of a simple or complicated type.

• Potentiometric Resistance – Type Transducer

A wire-wound potentiometer may be used as a transducer for converting mechanical displacement

to an electrical output.

This may be of linear or angular type.

As shown in Fig. 4.3, the motion of the object changes the effective resistance and hence the

voltage output eo between points b and c.

Thus, the output voltage appears as shown in Fig. 4.3 and is directly proportional to the dynamic

displacement of the moving object.

The value of the potential between points b and c, at the starting position, may be large,

compared to the change in the potential due to the motion.

• Inductive – Type Transducers

In these types of transducers, the magnetic characteristics of an electric circuit change due to the

motion of the object. These may be classified into two types:

1. Self-generating types, in which a voltage signal is generated in the transducer, because of

relative motion of a conductor and a magnetic field. Electrodynamics, electromagnetic and eddy

circuit types of transducers belong to this category.

2. Non-self-generating or external power source types of transducers, in which an external source

is needed to energies a coil/coils, the inductance of which would change due to the motion of the

object. The following types of transducer belong to this category: attachment type inductance

transducer, air gap type, LVDT type and magneto-strictive type of transducer.

• Self-generating types

Figure 4.5 shows an electrodynamic type of transducer. A coil wound on a hollow cylinder of non-

magnetic material moves in the annular space of a fixed magnet.

The voltage generated in the coil is proportional to the rate of change flux and hence the velocity

of the moving object. The coil cylinder has to be attached to the moving object and thus this is a

contact or attachment type transducer.

Figure 4.6 shows an electrodynamic transducer for measuring rotary motion. The coil moves in

the annular space between a magnet and soft iron core, generating a voltage in the coil.

Figure 4.7 shows an electromagnetic transducer, in which a voltage is induced in the coil when

the magnetic flux about it is varied due to the motion of the object, which has to be for a

ferromagnetic material.

This is a proximity type velocity transducer and is linear only for small motions, as the flux

intensity changes due to the change in air gap.

Figure 4.8 shows an eddy-current-type transducer.

A non-ferrous plate moves in a direction perpendicular to the lines of flux of a magnet.

Eddy currents are generated in the plate.

These are proportional to the velocity of the plate. These eddy currents set up a magnetic field in

a direction opposing the magnetic fields that creates them.

• Non-self generating types

An inductance transducer of attachment type is shown in Fig. 4.9 (a).

The core, made of high permeability steel, is attached to the moving object. The motion changes

the length of the core inserted in the coil and thud the inductance of the coil gets changed due to

the change of reluctance of the magnetic flux path.

When the core moves up and down, the inductance of one half increases while that of the other

half decreases. The two inductances L1 and L2 from the adjacent arms of a Wheatstone

bridge, as in Fig. 4.9 (b).

Figure 4.10 shows a variable inductance for measuring angular displacement or torsional motion.

One half of the core is made of magnetic material while the other half of non-magnetic material.

The inductances of the halves of the coil depend upon the amount of magnetic material in their

flux paths. The associated circuit for the same is identical to that Fig 4.9 (b).

In the variable inductance transducer, shown in Fig. 4.11, a small air gap in the magnetic flux path

of an elecromagnet is varied.

The inductance of one coil increases while that of the other decreases.

With the circuit being similar to that of other inductance transducers discussed earlier, the output

is proportional to the displacement of the object.

In linear variable differential transducer (LVDT) type of transducer, shown in Fig. 4.12, a soft

iron core provides the magnetic coupling between a primary coil and two secondary coils,

connected in series opposition.

When the core is central and both secondaries are identical, the voltage across them are equal in

magnitude. However, the output is zero as both the secondaries are in series opposition. As the

core moves up or down, the induced voltage of one secondary coil increases while that of the

other decreases. The output voltage, which is modulated, is the difference of the two, since

secondaries are in opposition. The associated circuit is similar to that discussed ealier. The output

is proportional to the displacement of the iron core. The device is very sensitive and is linear

over a wide range of motion.

Magnetostrictive type of transducer, shown in Fig. 4.14, is based on the principle that the

magnetic permeability of a ferromagnetic material, like Ni, changes when the material is

subjected to mechanical stress.

The magnetic permeability of Ni increases when the material is subjected to compression and

decreases due to the tension. Thus, the inductance of the coil would change, due to compression

or tension of the probe.

The magnitude and frequency of the exciting current determines the coil inductance and a change

in the same can be measured. Such transducer can be used for measurement of force, motion,

etc.

These have high mechanical impedance and thus resonant frequency is high, with a good

dynamic response. However, these transducer need individual calibration due to the fact that

these transducer depend on the change of a physical property of a material, which may differ.

• Capacitive Type Transducer

This is a displacement-sensitive transducer. Due to the motion, there is a change in

the capacitance between two plates. Suitable circuitry is used to generate a voltage,

corresponding to the capacitance change.

The capacitance C between two plates is given by

(4.1)

where C is capacitance, pF

A is area of plates, cm²

d is distance between plates, cm

ɛ is dielectric constant of the medium between the plates (= 1 for air)

Capacitance C between plates A and B may change due to the change of gap as shown in Fig. 4.15 or due to the change in area as shown in Fig. 4.16 as a result of motion of member A. Figure 4.17 shows to top view of an are-change type of capacitive transducer, which can be used measuring rotational motion.

Figure 4.18 shows an associated circuit for capacitive transducer, using an ac

carrier frequency oscillator, with the transducer forming one arm of a Wheatstone

bridge. A change in the capacitance, causes modulation of the oscillator carrier

frequency. A phase-sensitive demodulator is used to eliminate the carrier

frequency signal.

• Piezo-Electric Transducer

This operates on the principle that when a crystalline material like quartz or barium titanate is

distorted, an electrical charge is produced.

Referring to Fig. 4.21, application of a force P causes deformation xi, producing a charge Q, where

Q = K1xi (4.6)

K1 is called the charge sensitivity constant.

The crystal behaves as if it was a capacitor, carrying a charge across it. Voltage eo, across the

crystal, is given by:

(4.7)

C being capacitance of the crystal, and K the voltage sensitivity constant equal to K1/C.

As before, (4.8)

C being the capacitance of the crystal (pF), ɛ the dielectric constant of the crystal material, A its

area (cm²) and t its thickness (cm). If A is in square metre (m²), t in metre (m) and C in farads (F),

Eq. (4.8) becomes:

(4.9)

Relation between force P and deformation xi is:

(4.10)

E being the Young’s modulus of the crystal material.

Table 4.2 gives the properties of some typical piezo-elecric materials.

• Resistance Strain Gauges

These types of transducers are based on the principle that if a conductor is stretched or compressed, its resistance will change, because of change in its length, area and resistivity. The resistance R of a conductor of cross-sectional area A, length L, made of a material of resistivity ρ is

(4.20)

Gauge factor F of the conductor is defined as

(4.21)

∆R being change in resistance R due to axial ɛa, which is ∆L/L.

With the application of ,mechanical strain, ρ, L and A may change as above. The corresponding expression for ‘F’ is derived as below :

Substituting the expressions for derivatives from Eq. (4.20),

Dividing by expression for R from Eq. (4.20),

Area A = CB² , where B is geometrical dimension of the strain gauge cross-section, and C

is a constant whose value depends on the section, equal to π/4 for circular section of diameter B

and 1 for square section of sides B each.

or

Thus,

Finally,

For metallic strain gauges, the two terms viz. (1 + 2v) are higher than the third term while

for semi-conductor strain gauges, the third term due to change in resistivity due to strain is much

higher compared to (1 + 2v). The change in resistivity due to the strain is called Piezo-resistivity.

The value of F for Cu-Ni alloy gauge is 2 to 3 while that for semi-conductor is 100 to 200.

In the latter case, the value of F is positive for silicon doped with small amounts of p type

materials while it is negative for silicon doped with N type materials. The negative value implies

decrease resistivity with tensile strain.

In practice, the conductors used are in the form of thin wires or foils. Strain gauge transducers are

of two types:

1. Unbonded strain gauge, and

2. Bonded strain gauge.

• Unbonded strain gauges

In an unbonded strain gauge, a resistance wire is stretched between two frames, one being the

moving frame and the other, the fixed one as in Fig. 4.28. Typical dimensions of the wire are : 25

mm length and 25 µm diameter. The flexure plates act as springs between the two frames. The

wires are under preload, which is greater than any compressive load expected. An input motion as

shown in Fig. 4.28 would stretch wires 1 and 3 and reduce tensions in wires 2 and 4. Motion in the

opposite direction does the reverse. The wires are connected in a Wheatstone bridge

arrangement as shown in Fig 4.28 (b). With this type of transducer one can measure very small

motions, of the order 50 µm and very small forces. These transducers may be used to measure

force, pressure, acceleration, etc.

• Bonded resistance strain gauges

Transducers, using bonded resistance gauges are widely used for measurement

of several physical variables like strain, force, torque, pressure, vibrations,

etc. These gauges may be of metallic or semiconductor materials, and are in the

form of a wire gauge (about 25 µm diameter) or thin metal foil or small rods (in

the case of semiconductor gauges), as shown in Fig. 4.29. These gauges having

paper or some other material backing, are cemented or bonded to the surface,

whose strain is to be measured, as shown in Fig. 4.30. Once bonded, the gauges

undergo the same strain as that in the member surface. These are very sensitive

and when used with electronic equipments, strain as low as 10-7 may be

measured.

Gauges made of copper-nickel alloys have a gauge factor of 2-3 while semiconductor gauges

have gauge factors of 100-200.

Table 4.3

Gauge current is usually limited to 10-30mA, depending on the test duration, in order to

prevent wire damage. Bakelite base gauges can with stand somewhat higher values of current.

Care has to be taken while bonding the gauges. The surface of the member has to be

thoroughly cleaned. Later, the adhesive has to be applied and allowed to set, according to

manufactures’ instructions. Then, the connecting leads are soldered to the gauge and securely

fixed to the test member, as in Fig. 4.30. Finally, the gauge continuity and insulation resistance are

checked.

In the subsequent figures, the strain gauges shown in Fig. 4.29 are represented by

rectangles, with the longer side being along the length of the wire, foil or semiconductor.

Gauge backing

material

Adhesive Wire materials Remarks

Paper or silk

Bakelite

Glass weave

Nitrocellulose

Epoxy

Ceramic cement

Cu-Ni alloy

Cu-Ni alloy

Ni-Cr alloy

Useful up to 60°C

Useful up to 200°C

Useful up to 400°C

• Ionisation Transducer

This works on the principle of development of voltage across two electrodes placed in an ionised

gas, the magnitude of which depend on the electrode spacing and state of balance, which can

change due to the motion to be measured.

The transducer consists of a glass tube (Fig. 4.54) containing gas under reduced pressure.

A dc voltage is developed across the internal electrodes A, when the tube is subjected to an

electric field due to external electrodes B, connected to a radio frequency (RF) voltage source.

The gas in the tube gets ionised and the dc voltage produced depends on the electrode spacing,

being zero at null position. As in Fig. 4.54, the motion xi of the tube relative to the fixed external

electrodes varies the output voltage. The balance between the electrodes may also be changed

as in Fig. 4.55 by changing either capacitance C1 or C2 (C1 in Fig. 4.55 shown), due to the motion

xi, to be measured. This produces an output eo.

• Mechano-Electronic Transducer

This type of transducer, which is of electronic displacement type, depends on the principle

that the plate current depends on the spacing between an anode and a cathode in a diode or a

triode. Figure 4.56 shows such a transducer, consisting of an evacuated tube, in which the

cathode C is fixed and the position of the anode can be changed by the input motion xi, which

causes deformation of an elastic diaphragm producing a change in plate current, which can be

measured. This can be used for measuring displacement, pressure, force, etc.

Table 4.1 compares the above and other features of various motion transducers.

• DIGITAL TRANSDUCERS

Introduction

The transducers described so far are analog ones, i.e. their output varies continuously according

to the input. In digital transducers, however, the output is discrete and may give frequency type

output or a digitally coded output. of binary or some other type: The main advantages of digital

transducers are

l. Use of digital computers, along with the transducers, for data manipulation, is made

easier.

2. Digital signals—pulse count frequency or sequences of digitally codes outputs—are not

dependent on signal amplitudes and are thus easy to transmit without distortion and

external noise.

3. Increased accuracy in pulse count is possible.

4. There are ergonomic advantages in presenting digital data.

Digital transducers range from frequency domain or frequency generating types of

transducers to digital encoders. Alternatively, an instrument may incorporate an analog transducer

and an analog-to-digital (A-D) converter, giving a digital output, Figure 4.61 shows such an

arrangement. Various types of A-D conveners are described in Chapter 5.

• Frequency Domain Transducers

In these transducers, the output is in the form of pulses or sinusoidal wave forms, the

frequency of which is a measure of the magnitude of the physical variable. Frequency can be

measured by a frequency or pulse counter. Three types of frequency domain transducers have

been described below, viz. electro- magnetic frequency domain transducer, opto electrical

frequency domain transducer and vibrating string transducer.

• Electromagnetic Frequency Domain Transducer

This type of transducer can be used for speed measurement, as shown in Fig. 4.62. The

device consists of a permanent magnet or a solenoid. On the rotating shaft whose speed is to

be measured, a gear of ferromagnetic material is attached. As each gear tooth passes in front of

the magnet, the gap length changes. This changes the flux density and a voltage pulse is induced

in the coil. Pulse frequency equals speed N times the number of teeth T. The form of the output

signal is also shown in Fig. 4.62. Thus, pulse frequency is a measure of speed of rotation.

• Opto-Electrical Frequency Domain Transducer

Figure 4.63 shows an opto-electrical frequency domain transducer for the measurement of

speed of rotation of a shaft. The shaft has half dark and half white or shining portions. Every

time the latter portion is Ill front of the light source, the reflected light falling on the photo-electric

transducer, gives an electrical pulse output. The frequency of the pulses is thus a measure of the

speed of rotation.

For measurement of linear motion, an arrangement using the opto-electrical device is

shown in Fig. 4.64. This uses a transparent scale with a grating. The moving object is attached to

the transparent scale. Light from a source passes through the scale and a slit and then falls on a

photo-electric transducer. The slit width is such that a motion equal to the pitch of the grating

produces one complete cycle of light and darkness at the photo-electric cell. Thus, a pulse output

is obtained. From the number of output pulses, the change in motion of the scale and the Object

attached to it can be determined.

• Vibrating String Transducer

This is essentially used to measure the force applied to a metal string, which is kept vibrating, the

frequency of which is dependent on the force applied. The natural frequency f of a string of length

L and area of cross-section a is given by

where P is the force applied and ρ the mass density of the wire material.

The arrangement is shown in Fig. 4.65. One end of the string is fixed and the other

can be moved relative to it, due to the force applied. An electromagnetic transducer

picks up the vibrations; the output of which after amplification is fed to an

electromagnetic vibration generator, which maintains the string vibration at its natural

frequency f. Frequency f gets changed due to change in magnitude of force P. The

frequency is measured by a frequency counter and is a measure of the force applied

on the string. Initial string vibrations are obtained by an electro-magnetic device that

plucks the wire on application of a pulse. The transducer can be used for force and

displacement measurements.