Hall-Effect Transducers

The material used in the manufacture of Hall-effect devices is a p-type or an n-type semiconductor. Typical examples are indium arsenide, indium arsenide phosphide, and doped silicon. Figure 5.15 shows a section of a p-doped semiconductor subjected to a magnetic field Bz in the z direction and an electric field Ex in the x direction. A current Ix flows in the x direction.

The holes move in the x direction across the magnetic field and experience an upward magnetic force, which results in the accumulation of holes on the top surface and electrons on the bottom face, as indicated in Fig. 5.15.

Figure 5.15 Hall-effect device.

An electric field Ey, known as the Hall field, is set up as a consequence, and this is known as the Hall effect.The corresponding Hall voltage VH=Eyt. Since there is no flow of current in the y direction, the magnetic force equilibrates with the electric force that is exerted on the holes, and as a result the Hall voltage can be expressed as

Figure 5.16 Hall-effect displacement transducer.

Figure 5.16 shows the HET being used to measure small displacements. If the displacement brings magnet 1 close to the transducer, the output voltage will be increasingly positive, and it will be incresingly negative if magnet 2 moves closer to the HET.

The magnetoresistance effect is closely associated with Hall-effect transducers.33 If the length of the device in Fig. 5.15 is made much shorter than its width h, 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 causes an increase in resistance of the device, and this is known as the geometrical magnetoresistance effect.33 Transducers for measuring angular velocity of ferrous gear wheels have been developed based on this effect.

Hot-Wire Anemometer (Thermoresistive Transducer)

The hot-wire (h-w) or hot-film (h-f) anemometer is a thermoresistive transducer used in the microstructure analysis of gas and liquid flows. Consequently it is useful in the study of flow problems related to the design of airplane wings, propellers, ventilation systems, and blood-velocity measurements for medical research.

The anemometers have a very small sensing element, which accounts for their high spatial resolution and fast response. The transduction mechanism in these transducers is the change in resistance of the sensor element, brought about by the convective heat lost because of the velocity of the fluid. The changes in resistance are caused by the thermo resistive effect and are measured with a Wheatstone bridge circuit.

The output of the bridge can be adequately expressed by King’s law,

These transducers consist of a thermoresistive sensing element suspended between two support prongs, a transducer handle, and electrical connections to the support prongs. The h-w transducer most commonly consists of a 5-μm diameter platinum-plated tungsten wire as shown in Fig. 5.14.

sensing element consists of a thin nickel film deposited on a 70-μm-diameter quartz fiber, which is suspended between the two prongs. Typical sensor element resistance for the h-w transducer is 3.5 m, and the velocity measuring range is from 0.2 to 500 m/s.

Thermistors

The thermistor is a thermally sensitive resistor, but unlike the RTD, it exhibits a correspondingly large change in resistance. Its resistance, in general, decreases as the temperature increases. Thermistors are made by sintering a combination of oxides into plain beads or beads in a glass rod.27 Oxides of manganese, nickel, cobalt, copper, iron, and titanium are commonly used.

The resistance vs. temperature relationship for a thermistor can be represented by a third-degree polynomial,as shown below.

Since there are four unknowns, at least four calibration points are required to solve four simultaneous equations to obtain the values of the constants.

The Wheatstone bridge circuit configurations used with strain gages and RTDs are also used with thermistors. In many cases, a single voltage-divider circuit is also used as shown in Fig. 5.13. This circuit has the advantage of providing an output voltage eo(t) that increases as the temperature increases,

By selecting an appropriate value of R, it is possible to operate in the quasilinear region .

Physical Strain Gage Transducers

Strain gages are used in physical transducers to measure the strain induced in a summing device by a displacement, force and load, pressure, or torque. Figure 5.11a shows a simple cantilever. Figure 5.11b shows a type of spring element used in load cells, that is, transducers for measuring loads. In each of these, the bending of a composite beam is utilized to obtain strains of opposite signs designated as T for tensile and C for compressive. When strain gages are fixed at those locations, the bridge output could be doubled or quadrupled if two or four active gages are used.

Semiconductor gages can also be used with various types of spring elements to measure displacements, pressure, temperature, and force.

Thermoresistive detectors

Metals and semiconductors experience an increase in their electrical resistivity when heated, and consequently their resistance increases with temperature.

This transduction mechanism, in metals like nickel, nichrome, tungsten, copper, and platinum, is used in resistance temperature detectors (RTDs). Platinum resistance temperature detectors (PRTDs) yield a reproducible resistancetemperature relationship, and their resistance varies quite linearly with temperature.

The relationship between resistance and temperature for a platinum wire RTD is given by the Callender-Van Dusen equation

The PRTD assembly is composed of a resistance element made from 99.9 percent pure platinum wire, a sheath that encloses the element, and lead wires that connect the element to the external measuring circuitry. RTDs are also made from platinum metal film with a laser trimming system and are bonded directly to the surface under test. Owing to the intimate thermal contact, the self-heating is minimal and therefore they can be operated at a higher excitation voltage.

In most measuring circuits, the PRTD forms an arm of a dc Wheatstone bridge circuit. Since the RTD is connected by wires to the bridge, there is a need to compensate for the wire resistance RL. For this reason, the RTD is supplied in a three-wire (as shown in Fig. 5.12) and a four-wire configuration.

Figure 5.12 A PRTD in a three-wire configuration.

Basic Measuring Circuits

The Wheatstone bridge circuit shown in Fig. 5.10a can be redrawn as in Fig. 5.10b, which shows that the full bridge is made up of two voltage-divider circuits. These circuits are commonly used for static and dynamic strain measurements.

Fig 5.10 (a) Wheatstone bridge circuit.
             (b) The Wheatstone bridge circuit redrawn as two voltage-divider circuits.

The strain-induced incremental output voltage E0, corresponding to changes in resistance of the four arms, is given by 

CLICK TO ENLARGE BELOW IMAGES

Figure 5.11 (a) A simple cantilever-type summing device. (b) A complex summing device.

Semiconductor Strain Gages

Semiconductor strain gages operate on the transduction mechanism known as piezoresistive effect. It is defined as the change in electrical resistivity brought about by an elastic strain field. In some semiconductors the piezoresistive effect is quite large.

Both p-type and n-type silicon are used in the fabrication of these gages. When a semiconductor gage is strained, the distribution of the number of charge carriers and their mobility changes and consequently the resistivity changes. Semiconductor gages also have a gage factor as their figure of merit, which is given by

The first two terms of Eq. 5.8 correspond to dimensional changes similar to wire and foil gages, but the third term is due to piezoresistivity. Also, ∏L is larger than (1+2μ) by a factor of about 100. The magnitude of the gage factor also depends on the direction along which the stress is applied to the semiconductor.

Silicon diaphragms with diffused strain gages are used in miniature pressure transducers.

Foil Strain Gages

Foil gages are fabricated from constantan or nickel-chromium alloy sheet material that is reduced to 0.0025 to 0.0005 mm in thickness. This foil is then laminated to a backing material and coated with photo resist. Using a multiple-image negative of a gage, the composite gage pattern is transferred to the photoresist on the foil using photolithographic techniques.

After developing and chemical etching processes, the gages are completely defined and can be isolated for lead-wire attachment, encapsulation, and establishing the gage factor for the batch of gages. The gage factor for foil gages is also defined by Eq. 5.7.

Figure 5.9 shows a gage pattern of a two-element 90° rosette.23 The axis of the gage on the right is aligned with the principal axis. The gage on the left is automatically aligned to measure the transverse strain due to Poisson’s ratio.

The gage length is an important parameter in gage selection, as it is the effective length, excluding the end loops, over which the transduction takes place. The grid width together with the gage length determines the area of the strain field.

Fig 5.9 A two-element 90° rosette-type foil gage.

For example, when measuring strains in a reinforced-concrete beam in the presence of aggregate and cement-sand mix, one is interested in the average strain, and for this reason long-gage-length gages should be used. Transverse sensitivity is exhibited by foil gages owing to a strain field normal to the principal axial field. Since the grid lines of a foil gage are wide, the transverse strain couple through the backing into the grid, and this causes a change in the resistance of the grid.

Resistance Strain Gages

Carbon granules, packed in a small volume in the shape of a button and connected in series with a voltage source and a load resistor, have been used in the past as microphones. Using this transduction mechanism, carbon-strip strain gages were developed in the early 1930s. These were, in turn, followed by unbonded and bonded wire strain gages, foil strain gages, and semiconductor strain gages.

Wire strain gages. The resistance of a metallic wire is a function of the material.

In unbonded strain gages, as the name implies, the resistance wire is strung between insulated posts. One post is attached to a fixed frame and the other to a frame constrained to move in a fixed direction. Movements that place the wire in tension are measured by the corresponding changes in resistance. This arrangement finds use in certain force and acceleration transducers.

In bonded strain gages, a meandering grid of fine resistance wire is sandwiched between two thin layers of paper and is then impregnated with a resin to provide the necessary strength. The gage is then bonded to the structural members for the determination of the strain at the desired location. The strain sensitivity of an “encapsulated and bonded” gage is defined by the gage factor.

Wire strain gages are rapidly being replaced by foil strain gages, which can be mass-produced using standard photolithographic techniques.

Resistive Transducer (Potentiometric transducers)

Resistive transducers have many and varied applications in the transduction of measurands such as displacements, mechanical strain, pressure, force and load, temperature, and fluid velocity into electrical outputs. The transduction mechanisms are based on the change in resistance brought about by the measured.

 Potentiometric transducers

A potentiometric transducer is a mechanically driven variable resistor. It consists of a wire-wound fixed resistor and a wiper arm that slides over it and in so doing taps a different segment of the resistor, as shown diagrammatically in Fig. 5.8a and b, where K represents a fraction of the resistor that is tapped.

The displacement to be measured is linked by a shaft to the wiper arm, and a measure of the displacement is the fractional resistance KR or the fractional voltage KV.

This is the transduction mechanism. The resolution that one can achieve with this transducer depends on the gage of the nickel alloy or platinum wire used. For extremely fine resolution, the wire is replaced by a metallized ceramic or a film resistor. If the resistance wire is wound on a doughnut-shaped tube, the wiper will measure angular displacements. The output voltage corresponding to a displacement, force, or pressure is a fraction of the external voltage V, and therefore it does not need any amplification to activate external circuitry.

Fig 5.8 Potentiometric displacement transducers. (a) Resistance proportional to displacement or position. (b) Voltage proportional to the same measurands. (c) Displacement is measured around a null position and the output voltage is ±K0V0. K0 is referenced to the center of the resistor.

Carbon granules, packed in a small volume in the shape of a button and connected in series with a voltage source and a load resistor, have been used in the past as microphones. Using this transduction mechanism, carbon-strip strain gages were developed in the early 1930s. These were, in turn, followed by unbonded and bonded wire strain gages, foil strain gages, and semiconductor strain gages.

Electromagnetic Transducer

When a moving conductor of length l or a single-turn coil of the same length moves with a velocity ds/dt across and perpendicular to the lines of magnetic flux of density B, an emf is generated in the conductor (coil) which is given by Faraday’s law as e=Bl ds/dt. Now l ds represents an area through which the flux lines cross during the time dt, and Bl ds is the corresponding differential flux d through that area. The emf generated corresponding to N turns is

Accordingly, the magnitude of the emf depends on the rate of crossing the lines of magnetic flux. This transduction mechanism is utilized in a velocity-measuring transducer. Figure 5.7a shows two coils L1 and L2, which are connected in phase opposition. The measurand is linked to the permanent magnet, which slides freely in the coils. The rate of movement of the magnet determines the velocity of the measurand. The output voltage is proportional to the velocity for all positions of the magnet. These transducers are known as linear velocity transducers (LVTs).

Figure 5.7 Electromagnetic Transducers. (a) Linear velocity transducer (LVT).
                                                      (b) Flow velocity transducer.

Another application of this transduction mechanism is in sensing the flow velocity V of an electrically conducting fluid as shown in Fig. 5.7b. the flow is into the plane of the paper. The magnetic field is normal to the flow. The emf is generated along the diameter a-b normal to the flow and the magnetic field B. The voltage across the electrodes inserted into the flow at a and b is proportional to the flow velocity.

Inductive Transducers

In these transducers, the transduction mechanism is one where the self-inductance of a single coil or the mutual inductance between two coils is changed by a measurand. In general, the measurand could be a linear or rotary displacement, pressure, force, torque, vibration velocity, and acceleration.
The inductance changes are brought about by the movement of a concentric magnetic core.

The inductance of a single coil increases as the core is inserted in the coil and reaches a maximum value when it is centered on the coil length. Similarly, two separate coils L1 and L2 wound on the same bobbin can also be used as a displacement transducer. Any measurand that moves the core directly through a summing device will produce a change in the impedance of the coils that is proportional to the magnitude of the measurand. The coils can be used as the adjacent arms of an impedance bridge. Since L1 increases by the same amount that L2 decreases, or vice versa, the bridge output will be doubled.

A variation of the inductive transducer, shown schematically in Fig. 5.6a, is known as the linear variable differential transformer (LVDT).This transducer consists of a primary coil L1, two interconnected coils L2, L3, and a common magnetic core. The coils are wound on a hollow nonmagnetic glass-filled nylon tube and the core slides coaxially inside the tube. The excitation frequency for coil L1 ranges from 1 to 10 kHz. Coils L2 and L3 are wound in phase opposition in a way that the voltages induced in them by coil L1 are 180° out of phase.

Fig 5.6 Inductive transducers. (a) Linear variable differential transformer (LVDT) (b) LVDT accelerometer.

Consequently, the voltage at terminals c-d is zero when the core is centered inside the tube between coils L2 and L3. When the core is moved away from the null position, the voltage at terminals c-d changes in amplitude and phase (polarity). This change, when brought about by a measurand, is proportional to the magnitude of the measurand. LVDTs are available in linear stroke lengths of ±1 to ±300 mm and sensitivities of 1.7 to 250 mV/V/mm, depending on the stroke length.

The same transduction mechanism is also used in a rotary variable differential transformer (RVDT) to measure angular displacements and torque.To achieve good linearity, the angle of rotation is limited to ±40°. The LVDT can be used with Bourdon tubes, bellows, and proving rings to measure force and pressure.and the leaf springs provide the restoring force. This is an open-loop accelerometer.

Capacitive Transducers

The change in capacitance in response to a measurand has many applications in physical transducers. Displacements, velocity, acceleration, force, pressure, vacuum, flow, fluid level, audio sound field, and relative humidity can be measured using capacitive transducers.

The capacitance between parallel conducting plates with a dielectric material between them is given by

Equation  indicates that the capacitance varies linearly with the area A and the dielectric constant of the material, but it varies inversely with the separation between plates. Any changes in the above-mentioned parameters caused by a measurand, and taken one at a time, provide practical transduction mechanisms.

Fig 5.2 Capacitive Displacement transducers.

Figure 5.2 shows some of the configurations where the changes in Cs are used to measure physical measurands. The first two lend themselves to the measurement of displacement, force, flow, vacuum, and pressure, and the third configuration could be used to measure the changes in the dielectric constant brought about by the absorption of moisture13 or a chemical reaction with the dielectric material.

Fig 5.3.Capacitive pressure Transducer

Figure 5.3 shows the diametrical cross section of a pressure transducer constructed totally from fused quartz, which has a very small temperature coefficient of expansion. The transducer consists of a circular diaphragm rigidly clamped by brazing it to a fused quartz body. A very shallow cavity has been sputter etched in the body to provide the separation Zo between the capacitor plates. This cavity is vented to the atmosphere by a small hole in the body of the structure, allowing the transducer to measure Gage pressure.

The diaphragm has an annular electrode of metalized chrome and gold on the inside face, and a common electrode is deposited on the bottom of the etched cavity. The capacitance of this transducer as a function of the applied pressure is given by

The units of b1 and b2 are meters. Using the  Eq. the capacitance of a circular electrode transducer in the center of the diaphragm can be obtained by setting b1 equal to 0 and b2 equal to the desired radius. This construction is currently used in an invasive blood pressure transducer shown in Fig. 5.4.

Fig 5.4. Blood Pressure Transducer

It has a circular sensing electrode in the center of the diaphragm, an annular reference electrode very close to the clamped edge of the diaphragm, and a full electrode at the bottom of the etched cavity. The reference capacitor changes very little with pressure.

A monolithic capacitor-type accelerometer made from silicon by microma-chining results in a rugged transducer with excellent thermal and elastic stability. Techniques is shown in Fig. 5.5a. It is made up of several differential capacitors, and each capacitor section consists of two fixed outer plates and a center plate that is movable.

Fig. 5.5b shows the deflected position of the center plate when the transducer experiences an acceleration. The deflection, and consequently the capacitance change, is proportional to the acceleration.

In many applications, capacitive transducers are connected in an ac bridge circuit to obtain an electrical output proportional to the measurand. In others it can be made a part of an LC oscillator, where the oscillator frequency is proportional to the magnitude of the measurand. When differential sensing is used, the sensitivity can be doubled and the temperature sensitivity reduced.

Fig 5.5.Capacitive Micro Machined Accelerometer

Classification & Selection of Transducers

We have tabulated the class of transducers and some important measurands are mentioned.The name of each class is keyed to the transduction mechanism, but its explanation is given along with the description of the transducer.

The instrumentation technologist to select the transducer most suitable for the measurand of choice. Moreover, cross indexing to the literature in the reference section is provided, wherever required, to the transducer class-measurand combination.

In addition, the table also includes several other transducers such as

• fiberoptic transducers.

• surface-profiling transducers (SPT).

• wave-propagation transducers (WPT).

• intravascular imaging and Doppler transducers.

• surface acoustic wave (SAW) transducers.

• acoustooptic (AO) transducers.

• Hall-effect transducers.

• ChemFET transducers.

 Selection of Transducers

Research and development in the transducer industry has traditionally been very productive. Many new forms and rapid improvements of old forms are continuously reported. One of the most successful improvements in transducers is the incorporation of integrated circuits for signal conditioning, with the basic transducer unit. These are known as smart transducers.When selecting a transducer, in addition to the question of cost, careful attention must be given to the following

(i)Sensitivity Output impedance

(ii)Range Power requirements

(iii)Physical properties Noise

(iv)Atomic and surface profiles

(v)Gas concentration and pH

(vi)pH and partial pressures of O2 and CO2in blood

(vii)Infrared radiation

(viii)Torque

(ix)Magnetic fields

(x)Acoustic fields

(xi)Medical imaging

(xii)Nondestructive testing

(xiii)Audio fields and noise

(xiv)Rotation and guidance

INTRODUCTION TO TRANSDUCERS

In general terms, the transduction process involves the transformation of oneform of energy into another form. This process consists of sensing withspecificity the input energy from the measurand by means of a “sensing element” and then transforming it into another form by a “transductionelement.”

The sensor-transduction element combination shown in Fig. 5.1 will henceforth be referred to as the “transducer.” Measurand relates to the quantity, property, or state that the transducer seeks to translate into an electrical output.

As an example, consider a “walkie-talkie” intercom set where the loudspeaker also functions as a microphone. At the input end, the loudspeaker functions as an acousto electric transducer and at the output end as an electro acoustic transducer. Moreover, in the reverse direction, the functions of the loudspeakers are interchanged, and for this reason we say that the loud-speaker is a bidirectional transducer and the transduction process is reversible.

Another example of reversible transduction is seen in piezoelectric materials; when an electric voltage is applied to the faces of a piezoelectric substrate, it produces a change in its physical dimensions; and conversely, when the material is physically deformed, an electric charge is generated on these faces.

In this transducer, the sensing and transduction functions cannot be separated as easily, and it represents a good example of a practical transducer used in the field of nondestructive testing (NDT) of materials and in medical ultrasound imaging of body tissues and organs. This is a bidirectional transducer, but most practical transducers are not bidirectional.

Transducers may be classified as self-generating or externally powered.

Fig 5.1. Sensor-Transduction Element Combination

Self Generating Transducer:

Self-generating transducers develop their own voltage or current and in the process absorb all the energy needed from the measurand. Externally powered transducers, as the name implies, must have power supplied from an external source, though they may absorb some energy from the measurand. The Halleffect  transducer and  integrated-circuit temperature transducer are examples of externally powered transducers, whereas the loudspeaker and the piezoelectric substrate are self-generating transducers.

Transduction Mechanisms and Measurands

The operation of a transducer is tightly coupled to one or more electricalphenomena or electrical effects. These effects are listed below. Some relate to more advanced concepts for transducers that are leaving the research and development laboratories and making an entry into the commercial world. In addition, the most useful and important measurands are also listed.

 Transduction mechanisms

(i)Capacitive

(ii)Inductive and electromagnetic

(iii)Resistive and thermoresistive

(iv)Piezoresistive effect

(v)Hall effect

(vi)Lateral effect

(vii)Extrinsic

(viii) interferometric

(ix) evanescent effects in optical fibers

(x) Magnetoresistive effect

(xi)Piezoelectric effect

(xii)Tunneling effect.

(xiii)Thermoelectric effects (Seebeck andPeltier)

(xiv)lonization effects

(xv)Photoelectric effect

(xvi)Photoresistive effect

(xvii)Photovoltaic effect

(xviii)Acoustooptic effect

(xix)Fluorescence and fluorescence quenching effect

(xx)Field effect

(xxi)Doppler effect

 Measurands

(i)Displacement

(ii)Position

(iii)Velocity

(iv)Acceleration

(v)Force and load

(vi)Strain

(vii)Rotation and encoding

(viii)Vibrations

(ix)Flow

(x)Temperature

(xi)Pressure

(xii)Vacuum

(xiii)Relative humidity