The other problem, creep, refers to a gradual change in the length of the gauge element which does not correspond to any change of strain in the material that is being measured. This also should be very small, of the order of 0. Both hysteresis and creep increase noticeably as the operating temperature of the gauge is raised. A load cell is a force transducer that converts force or weight into an electrical signal. Basically, the load cell uses a set of strain gauges, usually four connected as a Wheatstone-bridge circuit. The output of the bridge circuit is a voltage that is proportional to the force on the load cell.

This output can be processed directly, or digitized for processing. Though the principles of the method are quite ancient, its practical use had to wait until suitable lasers and associated equipment had been developed, along with practicable electronic methods of reading the results. When waves meet and are in phase a , the amplitudes add so that the resultant wave has a larger amplitude. If the waves are in antiphase b , then the resultant is zero or a wave of small amplitude. All waves exhibit interference Figure 1.

When two waves meet and are in phase peaks of the same sign coinciding , then the result is a wave of greater amplitude, a reinforced wave. This is called constructive interference. If the waves are in opposite phase when they meet, then the sum of the two waves is zero, or a very small amplitude of wave, and this is destructive interference.

The change from constructive to destructive interference therefore occurs for a change of phase of one wave relative to another of half a cycle. If the waves are emitted from two sources, then a movement of one source by a distance equal to half a wavelength will be enough to change the interference from constructive to destructive or vice versa. If the waves that are used have a short wavelength, then the distance of half a wavelength can be very short, making this an extremely sensitive measurement of change of distance.

The wavelength of red light is about nm, i. This method would have been used much earlier if it were not for the problem of coherence. The set-up of laser and glass plates is shown in a. The light is therefore the sum of all the pulses from the individual atoms, rather than a continuous wave. The laser has completely changed all this. The laser gives a beam in which all the atoms that contribute light are oscillating in synchronization; this type of light beam is called coherent.

The interferometer makes use of both of these properties as illustrated in Figure 1. Since this is a light beam, this implies that the illumination on the screen will change between bright and dark. The interferometer is often much too sensitive for many purposes. This is the average distance over which the light remains coherent, and is usually at least several metres for a laser source. This change of phase can be used to detect small movements by using the type of arrangement shown in Figure 1.

When a ray of light passes from an optically dense highly refractive material into a less dense material, its path is refracted away from the original direction a and more in line with the surface. The sensor must be calibrated over its whole range, because there is no simple relationship between the amount of movement and the amount by which the light is delayed.

For a solid, the amount of stress would be calculated, either from knowledge of force and area of cross-section, or from the amount of strain. Where the stress is exerted on a wire or girder, the direct calculation of stress may be possible, but since strain can be measured by electronic methods, it is usually easier to make use of the relationship shown in Table 1. Young's modulus is a quantity that is known for each material, or which can be measured for a sample of material. The stress is stated in units of 12 Table 1.

The measurement of pressure in liquids and gases covers two distinct ranges. Pressure in liquids usually implies pressures greater than atmospheric pressure, and the methods that are used to measure pressures of this type are similar for both liquids and gases. For gases, however, it may be necessary also to measure pressures lower than atmospheric pressure, in some cases very much lower than atmospheric pressure.

The best-known principle is that of the aneroid barometer, illustrated in Figure 1. The diaphragm is acted on by the pressure that is to be measured on one side, and a constant usually lower pressure on the other side. In the domestic version of the barometer, the movement of the diaphragm is sensed by a system of levers which provide a pointer display of pressure.

For electronic measurement, the diaphragm can act on any displacement transducer and one well-suited type is the capacitive type, illustrated in Figure 1. Reducing the spacing between the diaphragm and the backplate will increase the capacitance, in accordance with the formula shown in Figure 1. The domestic barometer uses an aneroid capsule with a low pressure inside the sealed capsule. This is an inside-out arrangement as compared to the domestic barometer. The pressure to be measured is applied inside the capsule, with atmospheric air or some constant pressure applied outside. The formula relating capacitance to spacing is shown in b.

The movement of the diaphragm causes considerable changes in the reluctance of the magnetic path, and so in the inductance of the coil. This provides a very sensitive detection system, and one which is fairly easy to calibrate. Although the thin metal corrugated diaphragm makes the device suitable only for detecting pressures of about atmospheric pressure, the use of a thicker diaphragm, even a thick steel plate, can permit the method to be used with very much higher pressures. For such pressure levels, the sensor can be made in the form of a small plug that can be screwed or welded into a container.

The smaller the cross-section of the plug the better when high pressures are to be sensed, since the absolute amount of force is the product of the pressure and the area of cross-section. The materials used for the pressure-sensing plate or diaphragm will also have to be chosen to suit the gas or liquid whose pressure is to be measured. For most purposes, stainless steel is suitable, but some very corrosive liquids or gases will require the use of more inert metals, even to the extent of using platinum or palladium. The method can also be used for gases, and for a range of pressures either higher or lower than atmospheric pressure.

Another transducing method uses a piezoelectric crystal, usually of barium titanate, to sense either displacement of a diaphragm connected to a crystal, or pressure directly on the crystal itself. As explained earlier, this is applicable more to short duration changes than to steady quantities. For a very few gases, it may be possible to expose the piezoelectric crystal to the gas directly, so that the piezoelectric voltage is proportional to the pressure change on the crystal. For measurements on liquids and on corrosive gases, it is better to use indirect pressure, with a plate exposed to the pressure which transmits it to the crystal, as in Figure 1.

This type of sensor has the advantage of being totally passive, with no need for a power supply to an oscillator and no complications of frequency measurement. Piezoresistive, piezoelectric, and capacitive pressure gauges can be fabricated very conveniently using semiconductor techniques. Piezoelectric and capacitive pressure-sensing units can be created using the same methods. Pressures that are only slightly lower than the atmospheric pressure of around kPa can be sensed with the same types of devices as have been described for high pressures. Pressure sensors and transducers for this range are more often known as vacuum gauges, and many are still calibrated in the older units of millimetres of mercury of pressure.

The conversion is that 1 mm of mercury is equal to The high-vacuum region is generally taken to mean pressures of 10 3 mm, of the order of 0. Of some 20 methods used for vacuum measurement, the most important are the Pirani gauge for the pressures in the region 1 mm to 10 3 mm about Pa to 0. A selection of measuring methods is illustrated in Table 1. All vacuum gauge heads need recalibration when a head is replaced. The Pirani gauge, named after its inventor, uses the principle that the thermal conductivity of gases decreases in proportion to applied pressure for a wide range of low pressures.

The gauge Figure 1. Gauge type Pressure range Pa Diaphragm Manometer Pressure balance Radioactive ionization gauge Compression gauge Viscosity gauge Pirani gauge Thermomolecular gauge Penning gauge Cold-cathode magnetron gauge Hot-cathode ionization gauge High-pressure ionization gauge Hot cathode gauge Modulator gauge Suppressor gauge Extractor gauge Bent beam gauge Hot-cathode magnetron gauge 10 5 10 5 1 10 2 10 6 10 6 10 3 10 7 10 7 10 8 10 5 10 4 10 7 10 8 10 9 10 10 10 11 10 11 to to to to to to to to to to to to to to to to to to 10 2 10 3 10 5 10 5 10 3 10 3 10 4 10 1 10 1 10 2 1 10 10 2 10 2 10 2 10 2 10 2 10 2 Figure 1.

Commercially available Pirani gauges, such as those from Leybold, are robust, easy to use, fairly accurate, and are not damaged if switched on at normal air pressures. The ionization gauge operates by using a stream of electrons to ionize a sample of the remaining gas in the space in which the pressure is being measured. The positive gas ions are then attracted to a negatively charged electrode, and the amount of current carried by these ions is measured. The range of the gauge is to about 10 7 mm 0. The most serious problem in using an ionization gauge is that it requires electron emission into a space that is not a perfect vacuum.

If this can be done, then the ionization gauge can have a long and useful life. With a constant high current of electrons to the anode, positive ions from the remaining gas are attracted to the grid and the resulting grid current is measured and taken as proportional to gas pressure. A common variation on the ionization method is the Penning gauge, which uses electron emission from a point a cold-cathode emitter.

If the electron beam is taken through a longer path, more atoms can be bombarded, and more ions generated from a given volume of gas, and so the sensitivity of the device is greatly increased. This is the magnetron principle, used in the magnetron tube to generate microwave frequencies by spinning electrons into a circular path that just touches a metal cavity, so that the cavity resonates and so modulates the electron beam.

Gauges of this type can be used down to very low pressures, of the order of 10 11 Pa. On the other end of the pressure range, a radioactive material can be used as a source of ionization, and this allows measurements up to much higher ranges of pressure, typically up to 10 5 Pa. The piezoelectric device used for pressure sensing is also a useful transducer, and can be used in either direction.

The conversion of energy from an electrical form into stress can be achieved by the magnetically cored solenoid, as illustrated in Figure 1. The amount of force can be large, so that stress can be exerted causing strain on a solid material. If the core of the solenoid is mechanically connected to a diaphragm, then the force exerted by the core can be used to apply pressure to a gas or a liquid.

In general, though, there are few applications for electronic transducers for strain or pressure and the predominant use of devices in this class is as sensors. Chapter 2 Position, direction, distance and motion 2. In this chapter we shall look at the methods that are used to measure direction and distance so that position can be established either for largeor small-scale ranges of movement. For a three-dimensional location, three axes, labelled x, y and z, can be used. Figure 2. For a three-dimensional location, an additional angle is used. Calculate the position of the star at the time of your observation, using the Almanac.

From this position calculation, calculate for each star you have observed what altitude and azimuth direction you should have observed. Plot each offset on a chart as a line of position. Find your true position as the point where several lines of position cross. Starting with the most ancient method, observation of stars, otherwise known as Celestial navigation, depends on making precise angle measurements.

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The basic two-dimensional requirements are a time measurement and tables of data. The simplest form of celestial navigation is the observation of local noon. Navigation by the local noon method is simple, but it is not necessarily always available, and although it has been the mainstay of navigation methods in the past, it was superseded several centuries ago by true celestial navigation, which relies on making a number of observations on known stars. The advantage of using stars is that you do not have to wait for a time corresponding to local noon. The process is summarized in Table 2.

The size and direction of this correction can be obtained from tables of magnetic constants the magnetic elements that are published for the use of navigators. The drift speed and direction of the magnetic north pole can be predicted to some extent, and the predictions are close enough to be useful in fairly precise navigation in large areas on the Earth's surface.

The principle is illustrated in Figure 2. Since the electrons are negatively charged, the top of the slab is negative and the bottom positive. If the main carriers are holes, the voltage direction is reversed.

By using an analogue to digital converter for angular rotation, the direction can be read out in degrees, minutes and seconds. Magnetic compasses served the Navy well in the days of wooden ships, and when iron later, steel construction replaced wood, magnetic compasses could still be used provided that the deviation between true magnetic north and apparent north distorted by the magnetic material in the ship could be calculated and allowed for, using deviation tables.

This compass model was superseded, in , by the Sperry type of gyrocompass. Full acceptance of gyrocompasses did not occur until errors caused by the ships' movement could be eliminated. The magnetic portion of the wave will induce signals in a coil, but the phase of these signals depends on the direction of the transmitter. By combining the signals from the two aerials, and turning the coil, the direction of the transmitter can be found as the direction of maximum signal.

Gyrocompass design was considerably improved for use in air navigation in World War II. The gyrocompass has no inherent electrical output, however, and it is not a simple matter to obtain an electrical output without placing any loading on the gyro wheel. Laser gyroscopes making use of rotating light beams have been developed, but are extremely specialized and beyond the scope of this book. Radio has been used for navigational purposes for a long time, in the form of radio beacons that are used in much the same way as light beacons were used in the past.

The classical method of using a radio beacon is illustrated in Figure 2. The signal from the coil aerial is at maximum when the axis of the coil is in line with the transmitter, and the phase of this maximum signal will be either in phase with the signal from the vertical whip aerial or in antiphase, depending on whether the beacon transmitter is ahead or astern of the coil. By using a phase-sensitive receiver that indicates when the phases are identical, the position of maximum signal ahead can be found, and this will be the direction of the radio beacon.

The original Watson-Watt system used multiple-channel reception with two dipoles, arranged to sense directions at right angles to each other and a single whip aerial connected to separate receivers. A later improvement used a single channel, and modern methods make use of digital signal processing to establish direction much more precisely. A geostationary satellite is one whose angular rotation is identical to that of the Earth, so that as the Earth rotates the satellite is always in the same position relative to the surface of the planet.

The navigation satellites are equipped with transponders that will re-radiate a coded received signal. At the surface, a vessel can send out a suitably coded signal and measure the time needed for the response. This time can be very short, of the order of microseconds or less, so that the duration of the wave pulse must also be very short, a small fraction of the time that is to be measured. Both radar and sonar rely heavily on electronic methods for generating the waveforms and measuring the times, and although we generally associate radar with comparatively long distances, we should remember that radar intruder alarms are available whose range is measured in metres rather than in kilometres.

The time required for a pulse of microwave signal to travel to the target and back is displayed in the form of a distance on a cathode ray tube. The air pressure, however, alters with other factors such as humidity, wind-speed and temperature, so that pressure altimeters are notoriously unreliable.

Even if such an altimeter were to give a precise reading, the height that it measures will either be height above sea-level or the height relative to the altitude of the place in which the altimeter was set, rather than true height. It is, in fact, remarkable that air travel ever became a reality with such a crude method of height measurement. Position measurement on a smaller scale e. In this case, we shall start with the sensors for short distance movements, because for motion over large distances the distance travelled will generally be calculated by comparing position measurements rather than directly.

Sensors for small distances can make use of resistive, capacitive or inductive transducers in addition to the use of interferometers see Chapter 1 and the millimetrewave radar methods that have been covered earlier. The methods that are described here are all applicable to distances in the range of a few millimetres to a few centimetres. Beyond this range the use of radar methods becomes much more attractive.

A simple system of distance sensing is the use of a linear in the mechanical sense potentiometer Figure 2. The output can be displayed on a meter, converted to digital signals to operate a counter, or used in conjunction with voltage level sensing circuits to trigger some action when the object reaches some set position.

The main objections to this potentiometric method are: that the range of movement is limited by the size of potentiometers that are available although purpose-built potentiometers can be used , and that the friction of the potentiometer is an obstacle to the movement.

The precision that can be obtained depends on how linear in the electrical sense the winding can be made, and 0. The advantage of this type of sensor is that the output can be a steady DC or AC voltage that changes when the displacement changes. A change in the position of the moving plate will cause the voltage between this plate and the centre tap of the transformer to change phase, and this phase change can be convened into a DC output from the phase-sensitive detector.

An alternative that is sometimes more attractive, but often less practical, is the use of a capacitive sensor. The type of circuit arrangement is illustrated in Figure 2. Because the capacitance between plates is inversely proportional to plate spacing, this method is practicable only for very short distances, and is at its most useful for distances of a millimetre or less.

An alternative physical arrangement of the plates is shown in Figure 2. The most commonly used methods for sensing distance travelled on the small scale, however, depend on induction. The basic principle of induction methods is illustrated in Figure 2. If one coil is supplied with an AC signal, then the amplitude and phase of a signal from the second coil depends on the position of the ferromagnetic core relative to the coils. The range of movement for this type can be considerably greater than for the previous type. An AC voltage is applied to one coil, and the position of the core determines how much will be picked up by the other coil.

In addition, the shape of the graph means that even if the range is restricted the output is never linearly proportional to the distance. Movement of the core alters the voltage levels and phases of the voltages across the outer coils, and these voltages can be converted into DC by the phase-sensitive detector. The principle is illustrated by the circuit diagram shown in Figure 2. The other two coils are connected to a phase-sensitive detector, and as a core of ferromagnetic material moves in the coil axis, the output from the detector will be proportional to the distance of the core from one end of the coils.

As the name suggests, the output from the phase-sensitive detector will be fairly linearly proportional to distance, and there are considerable advantages as compared to other types of distance sensors, as follows. Virtually zero friction, since the core need not be in contact with the coils, and so no wear. Linear output. Very high resolution, depending mainly on the detector. Good electrical isolation between the core and the coils. No risk of damage if the core movement is excessive. Strong construction that is resistant to shock and vibration.

The performance of the AC types is always superior, but in some systems where, because of lack of space, no separate AC supply can be provided, the DC type must be used. Typically, a frequency of 5 kHz is used for the AC drive. Because of the seven advantages listed above, the LVDT has superseded most other types of distance sensors. For very small distances, the strain gauge see Chapter 1 can be used; laser interferometers are applicable when very precise changes must be sensed, and radar methods are used for longer distances.

One peculiar advantage of the laser interferometer is that its output can readily be converted to digital form, since it is based on the counting of wavepeaks. Most sensors give analogue outputs, and where a sensor is described as having a digital output, this usually implies that an analogue to digital conversion has been carried out. The interferometer is one of the few sensors which is capable of providing a genuinely digital output. Another is the linear digital encoder, and since digital methods are of everincreasing importance in measurement and control, a description of this device in detail is appropriate here.

The simplest form of encoder of this type is optical, and the principle is illustrated in Figure 2. A glass strip is printed with a pattern of the form shown, using large blocks rather than the more practical lines, alternately opaque and transparent. The next strip in turn has bars that are twice the width of its predecessor and so on. The number of strips determines the number of binary digits in the output and the number of increments of position that can be detected.

The optical linear encoder is read by using a sensor for each strip or track. Moving the glass strip between a light source and a set of photocells will result in outputs from each photocell that will make up a binary number. The main problem of using binary code with this system is that incorrect readings can be obtained when the position of the slide is such that sections overlap the photocells. The resolution is equal to the width of the units mark.

The photocells must be placed almost in contact with the encoder slide, and with suitable light shielding to ensure that stray light does not cause false responses. One problem that arises with optical linear or angular encoders is the suitability of the coding system. The usual binary number system is often termed code, in recognition of the fact that each digit place represents a doubling or halving of the value of the adjacent place.

This can mean that some changes of number can involve changes in more than one of the digits. Denary binary Grey code Denary binary Grey code 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 change from to , in which each of four digits has changed simply to indicate a value change of just one unit. For this reason, another code, the Grey code illustrated in Table 2. ICs exist which will convert Grey code into normal binary, so that arithmetic can be carried out on the numbers if needed. For some applications, conversion may not be necessary. The linear digital encoder systems provide a set of binary digital signals directly, but since this requires a slide which is very precisely printed and which will use one detector for each binary digit, less direct conversion methods are often used.

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A slide using only a single set of equally spaced markings can be used in conjunction with a two-phase pick-up system to provide pulse signals whose phasing can be used to indicate direction and whose count indicates distance moved. A system of this type has only a single output to a counter with a second connection if direction is to be sensed , and the counter will then convert into binary code. This type of system is considered more fully under the heading of Rotation later in this chapter.

Another optical method that is particularly useful for small displacements, particularly vibration amplitudes, is the optical grating method whose principles are illustrated in Figure 2.

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The two slides each have identical thin line patterns printed on them. When one slide moves relative to the other, the amount of light passing through varies considerably depending on the relative positions of lines and spaces in the two slides. Large movements are read in terms of the number of complete waves of output from the photocell, small movements in terms of the amplitude of the signal. The mass that is used as part of an acceleration sensor must therefore be supported in the vertical plane, and the type of support that is used will depend on whether accelerations in this plane are to be measured.

This in turn will stretch or compress the spring, and the amount of this displacement can be measured by any of the usual methods, usually by an LVDT. If the acceleration to be measured is always in a horizontal direction, then the mass can be supported on wheels, ball bearings or air-jets, depending on the sensitivity that is required. Since a force on the mass is to be sensed, the mass will also have to be coupled to a sensor. The method of sensing force is to measure the displacement of the mass against the restoring force of a spring, so that the outline system for a horizontal accelerometer is as sketched in Figure 2.

The weight of the mass is supported on ball bearings, and the mass is held in the horizontal plane by springs. In Figure 2. The amount of linear movement will be proportional to the force, so that any sensor for linear displacement can be used to give an output that is proportional to acceleration. Suitable transducers include potentiometers, capacitive distance gauges, inductive gauges and LVDTs for the larger ranges of movement that are possible.

Sensors for acceleration that use this spring and displacement principle are generally intended for the measurement of very small accelerations, usually in one plane. If only a single dimensional acceleration can be measured, the acceleration in any other direction will produce a false reading, equal to the component of acceleration in that direction. If the mass can be supported in a cradle of springs and three displacement sensors connected, one for each axis of motion two horizontal and one vertical , then the outputs can be used to compute the magnitude and direction of an acceleration that can be in any direction.

A strain-gauge sensor can be connected to an inertial mass, with or without spring suspension in order to measure acceleration, but the most common type of accelerometer uses an inertial mass coupled to a piezoelectric crystal. The principle is that some crystalline materials such as quartz silicon oxide , Rochelle salt and barium titanate are composed of charged particles ions which do not move uniformly when the crystal is stressed. The voltage is proportional to the strain of the crystal and can be very large, of the order of kilovolts for some ceramic crystal types, if the strain of the crystal is large.

The use of an inertial mass bonded to a piezoelectric crystal therefore provides an accelerometer that requires no springs or special supports for the mass. It is even possible to obtain two-dimensional signals from one crystal, and the system will respond to a very wide range of accelerations. The snag is that the piezoelectric crystal is, from the circuit point of view, a capacitor, and the signal is in the form of a charge. The connection of a resistance to the contacts on the faces of the crystal will therefore allow this capacitance to discharge with a time constant equal to CR seconds, where C is the capacitance between the crystal faces in mF and R is the resistance between the faces in MO.

As it happens, most accelerations are not sustained. The only steady and constant value of acceleration that we normally encounter is the acceleration of gravity, and most of our acceleration measurements are on accelerations that are caused by short-duration forces, such as those encountered when one object hits another. To put this into perspective, an acceleration of only 1 g for 10 s corresponds to falling a distance of about m in a vacuum.

In general, unless you are working with propulsion systems for outer space, the measurement of small accelerations that are applied for long periods will be of no practical interest. When an accelerometer of any type produces an electrical output, this output can be used for computing other quantities. One of these quantities is speed or, more correctly, velocity because an acceleration exists when a change of direction or a change of speed, or both, take place.

The relationship between speed or velocity value and acceleration is shown in Figure 2. A second integration of the voltage output the speed output will produce a signal proportional to distance, so that this quantity can also be found by using an analogue computing action on the output of the accelerometer. If the starting point of the motion is rest no starting speed , then no constants need to be fed in.

If quantities are expressed in digital terms, then a digital computer can be used to calculate the integral values. The quantities that are used to measure rotation correspond to the quantities that are used in the measurement of linear motion in such a way that the same types of equations can be used, substituting the rotational quantities for the linear ones.

To convert from degrees to radians, divide the angle in degrees by If the rotating object is a wheel and is in contact with a surface, then Figure 2. The sensors for angular motion are also very closely related to those that are used for linear motion. For sensing and measurement purposes only a minimum of power must be used, so that a miniature AC generator called the tacho-generator is normally used. The construction 42 Figure 2. The frequency of the output signal is proportional to the revolutions per second of the shaft that is coupled to the tacho, so that a frequency-sensitive detector can be used to give a DC output proportional to angular frequency.

The tacho can be used over a wide range of angular velocity values, and if the frequency detector is reasonably linear then the readings can be of high precision. The drawback for some applications is the need to make a mechanical coupling between the tacho and the revolving shaft. A drag system involves a frictional coupling between the rotating shaft and some object that is restrained and whose displacement can be measured.

One version of this is the drag cup, whose principle is illustrated in Figure 2. The motion of the shaft is communicated by the viscosity of the oil to a turning force torque on the cup, and the displacement of the cup against the spring is measured by the sensor. Since displacement should be proportional to torque, which in turn should be proportional to rotational speed of the shaft, output from the sensor is proportional to rotational speed over a small range of speeds. The range is small because the assumption that torque is proportional to rotational speed holds good for only a small range of speeds, and the system is best suited for slow rotations.

Another version of this method that is much more versatile is the magnetic disc type. The method can be converted to electrical output by dispensing with the pointer and mounting the cup and its retaining spring on to the shaft of a potentiometer. This has been extensively used in car speedometers, and can be adapted to electronic measurement by replacing the disc and its mountings by a sensing coil.

This is the scheme that has been used for many years for car speedometer heads, and it operates best at a medium range of angular speeds. One particular advantage is that no contact is needed, though there must not be any metal between the magnet and the disc. A piezoelectric pulse can be operated, as indicated in Figure 2. The disadvantages are that there is only one pulse per revolution, and that the contact between cam and crystal causes a frictional drag on the rotation of the shaft.

In addition, the friction on the shaft is fairly large compared to the alternative system of magnetic pulsing. The magnetic pulse system uses a permanent magnet mounted on a wheel or shaft and passing over a coil at one part of the revolution. As the magnet moves, a voltage is induced in the coil, so providing a signal for each revolution.

Angular displacement measurement methods fall into two groups: those for very small angular displacements that are temporary, and those for large displacements. Temporary small displacements are of a degree or less, and the shaft or other rotating object returns to its original position following the rotation. Such small displacements are sensed by variants of the methods used for small linear displacements, such as capacitive, strain gauge and piezo sensors. The rotary digital encoder can be used to provide a direct digital output, using a wheel of the form shown in Figure 2.

The digital encoder can also be used to measure angular velocity and acceleration, and this makes it particularly useful for a very wide range of 46 Figure 2. This usually implies input to a computer that can run suitable software. In practice, optical encoders often use methods that are closer to analogue than to strictly binary digital methods, employing a disk on which the sectors are equally spaced Figure 2.

Such encoders can be obtained in the open form, allowing the disk to be attached to any rotating object, or as sealed units with a shaft that must be coupled to the rotating object. In this example, only a 16position disk is shown, but practical examples would use eight tracks to obtain positions. Miniature varieties can be used up to speeds of 30 rpm, and the unenclosed disks can typically be used up to 12 rpm. Although the signals are square-waves at the lower speeds of rotation, they become approximately sinusoidal at higher speeds.

For the simplest applications in sensing shaft speed, either of the phase outputs can be fed into a comparator, Figure 2. A counter can be connected to the output of the comparator in either case. The waveforms for this circuit Figure 2. When the rotation is clockwise, the A signal is high and the B signal low just before the rising edge of the clock pulse the delay in the OR gate will ensure that the clock is slightly delayed with respect to the signals at J or K , and this makes the Q output high.

One particularly useful sensor for angular displacement is the synchro, also known as the selsyn. This makes use of inductive principles, and a simple synchro system is illustrated diagrammatically in Figure 2. The aim is to sense an angular displacement, convert it to phase changes in electrical signals, and reproduce the same angular displacement at a receiver.

As the diagram shows, a rotor is fed with an AC signal, typically a 1 kHz sine wave. This is a form of rotary LVDT that uses three stator coils and one rotor. The rotor is fed with an AC supply often at high frequency , and the connection of the stator coils ensures that when one rotor is moved, the other slave units will respond with an identical rotor movement. The coils of this transmitter synchro are connected to the corresponding stator coils of a receiver synchro, whose rotor is fed with AC whose phase is locked to the phase of the AC used for the transmitter.

Any movement of the rotor of the transmitter synchro will cause a change in the amplitudes and phases of the voltages induced in the stator coils of the transmitter, and these same voltages and phases will exist across the receiver coils. The device can have very low friction, and because the transmission is electrical, and because each unit is fed from a mains supply, the sensitivity can be high and the amount of torque fairly large.

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The device is used for diverse purposes, such as to transmit the angular position of a radar aerial, the direction of a wind vane, or the reading of a compass. As Figure 2. For static torque used, for example, to determine to what extent a nut or a bolt has been tightened, simple torque wrenches depend on a spring balance whose scale has been calibrated in terms of torque. Other static torque systems make use of a similar type of force measurement, using a strain gauge mounted on a shaft so as to measure strain in the direction of the circumference of the shaft.

This is often the most practical arrangement for analogue measurements, since strain is proportional to stress caused by force. For a digital system, the use of an angular digital encoder and computer allows torque readings to be calculated. The measurement reliability can be improved by digitally processing the signals, but the method is not really useful for transient torque changes. A more modern approach does not use mechanical coupling, and depends on the measurement of stator currents and voltages in an electric motor.

The associated circuitry then computes the torque values, allowing for fast changes to be measured. In addition to position, direction, distance and motion of an object, it may be necessary to sense the near presence of an object. This requires proximity detection, and the topic is discussed in Chapter 6. Chapter 3 Light and associated radiation 3. The place of light in the range of possible electromagnetic waves is shown in Figure 3.

This range of wavelengths, i. One is that this range of waves is not generated or detected by the conventional electronic methods that are used for waves in the millimetre to kilometre range. One such problem is coherence, mentioned earlier in conjunction with laser interferometers. Light from a small portion of a source, such as light passing through a pinhole, can be coherent over a short distance a fraction of a millimetre , but only laser light is coherent over distances of a metre or more.

Light is a very small part of this complete spectrum, and the waves that can be used for radio communication are at the lower frequency end. Like any other form of radiated wave, light can be polarized, and this is a topic that is of importance in some applications. Normal unpolarized light consists of waves whose direction of oscillation can be in any plane at right angles to the direction of motion Figure 3. When such light is passed Figure 3. Light is electromagnetic radiation that consists of an electric oscillation and a magnetic oscillation. The magnetic oscillation is always at right angles to both the electric oscillation and the direction of the beam.

When two sheets of such materials are placed in the path of a light beam and arranged so that their directions of polarization are at right angles, no light will pass through the second polarizer. Materials that polarize light in this way are generally crystals or other materials that contain lines of atoms at a critical spacing. If polarized light is beamed on another sheet of polarizing material, the amount of light that passes through the material depends on the angle of the sheet, because two sheets of polarizing material with their planes of polarization at right angles will not pass any light Figure 3.

Like radio waves, light can also be polarized in other ways circular, elliptical polarization , but plane polarization of light is the most common. When light travels through transparent materials, however, the velocity is reduced, and the factor by which the velocity is reduced is called the refractive index, a number that is always greater than unity. In general, the interaction between an electromagnetic radiation and a material can be expected to be critical when the wavelength of the radiation is of a value similar to the distance between atomic particles in the material.

Light radiation carries energy, and the amount of energy carried depends on the square of the amplitude of the wave. In addition, the unit energy depends on the frequency of the wave. This concept of unit quantum energy is seldom considered when longer wavelengths are being used, but it determines, to a very considerable extent, what can be done using light waves and particularly the sensing and transducing actions.

Any hot object, meaning an object whose temperature is greater than that of absolute zero, will radiate energy, but the spectrum of that energy, meaning the relative percentage of the energy that is radiated at each detectable frequency, will depend on the temperature of the object. When an object and its surroundings are at the same temperature, each radiates to the other and the amount of energy leaving the object is balanced by the amount entering, keeping the temperature constant.

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Figure 3. The upper curve is for an object at a higher temperature, radiating more power overall and with the peak at a shorter wavelength higher frequency. Since any object hotter than absolute zero will radiate, the radiation temperature is measured in Kelvins degrees absolute which for all practical purposes are calculated by adding to Celsius temperature. At low absolute temperatures, the radiation is predominantly in the far infrared, with no trace of near IR which would be easier to detect or visible light. As the temperature is raised, the spectrum shifts towards the higher frequencies and the absolute amount of energy at each frequency increases.

In other words, as an object is heated, it radiates very much more energy and the energy is predominantly of a shorter wavelength. The amount of energy radiated is proportional to the fourth power of the absolute temperature, so that an object at K is radiating 16 times as much as one at K. As the temperature increases, the spectrum continues to shift, with the simple relationship that the wavelength of the peak multiplied by the absolute temperature is a constant double the absolute temperature and you halve the wavelength of the predominant radiation.

In addition, the bandwidth of the spectrum increases. Temperatures of K or so will provide light that is predominantly blue, approaching the spectrum of sunlight. The spectrum of any radiation can therefore be described very compactly in terms of its colour temperature, meaning the temperature to which a perfectly radiating object a black body would need to be raised to radiate in the same way.

Fluorescent tubes, for example, can give light of a high colour temperature but are themselves cool to touch. In this example, the discrepancy is due to the small fraction of the contents of the tube that is actually radiating. There will usually be a discrepancy between actual temperature and colour temperature for any radiating material. Another important point relating to the use of photocells is their wavelength at peak sensitivity. For many types of sensors, this may be biased to either the red or the violet end of the visible spectrum, and some sensors will have their peak response for invisible radiation either in the infrared or the ultraviolet.

A few devices, notably some silicon photodiodes, have their peak sensitivity for the same colour as the peak sensitivity of the human eye. This makes the devices more suitable for use in automated processes that once involved visual inspection, but such replacements are not always successful. The reason is that although the peak sensitivity of the sensor may match that of the eye, the sensitivity at other colours may not follow the same pattern as that of the eye.

Figures 3. A simple type of photoemissive cell is illustrated in Figure 3. The photoemissive action is the release of electrons into the surrounding vacuum when the material is struck by light. This release of electrons will take place whether the electrons have anywhere to go or not, but unless there is a path provided, all the electrons will lose energy and return to the emitting surface, often termed the photocathode. The cell must be contained in an evacuated enclosure, and consists of a nickel rod anode with a nickel sheet cathode coated with a photoemissive material such as caesium.

This, however, is true only if the light is of a frequency that will release electrons. For any photoemitting material there will be a threshold frequency of light. Below this threshold frequency, electrons will not be emitted no matter how intense the light happens to be, so that, in general, photoemitters do not respond to infrared, particularly the far infrared. Planck's theory was that energy existed in units just as materials exist in atoms, and he named the unit the quantum. The quantum is a unit of action, a physical quantity that was not considered of practical interest prior to Planck's theory.

The size of the quantum for a light beam is equal to the frequency of the light multiplied by a constant that we now call Planck's constant. We touched on this idea when considering laser interferometry, because the factor that prevents light from most sources from being coherent is that it is given out in these quantum-sized packets rather than as a truly continuous beam. Mixed photocathode materials containing antimony along with the alkali metals caesium, potassium and sodium, have been the most successful emitters in terms of providing an electrical output that is reasonably well maintained for the visible frequencies of light.

This does not imply, however, that the output is by any means uniform. The photoemissive cell is used in a circuit of the type shown in Figure 3. Some circuits make use of the current through the cell directly, but the most common circuit is as shown here, using a load resistor in series with the cell and amplifying the voltage signal. This is particularly useful when the incoming light is modulated in some way so that the electrical output will be an AC signal, such as that in use as a cinema soundtrack transducer.

For measuring purposes, any photoemitter detector will have to be calibrated for each light colour for which it will be used, and if a reasonably high precision is needed, this calibration will be a long and tedious matter. The electrons emitted from the transparent photocathode are multiplied in the dynode stages to provide a much greater output current than would be obtained from the original photocurrent. Materials that are good photoemitters are usually good secondary emitters as well.

Photoemitters are still used where a fast response is needed, because many competing devices are solid-state rather than high-vacuum, and the speed of electrons in a solid is very much lower than the speeds that can be obtained in a vacuum. Even for cinema soundtracks, however, the vacuum photocell has now been replaced, and at the time of writing, vacuum devices are found only in old equipment and in instruments intended for specialized use.

For these reasons, then, more detailed descriptions of vacuum photoemissive cells will not be given here. However, the photomultiplier obtains very much greater sensitivity from a photocell at very little cost in noise or time delay. The principle, illustrated in Figure 3.

Secondary emission occurs when a material is struck by electrons and releases more electrons than strike the surface initially. This means that an electron beam from a cathode can be directed to a secondary emitting surface and be re-emitted as a beam that contains a much larger number of electrons. In practical terms, this means a beam at a higher current.

It is mechanically and electrically rugged, and has a good record of reliability. The alternative name is LDR light-dependent resistor. Since, in addition, the materials are comparatively easy to prepare in a practical form, the use of photoresistive or photoconductive materials is very common. The two names should really be synonymous, but some lists show devices under one name or the other. The most common form of photoconductive cell is the cadmium sulphide cell, named after the material used as a photoconductor.

This is often referred to as an LDR light-dependent resistor. The cell is then encapsulated in a transparent resin or encased in glass to protect the cadmium sulphide from contamination by the atmosphere.

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The cell is very rugged and can withstand a considerable range of temperatures, either in storage or during operation. The voltage range can also be considerable, particularly when a long track length of cadmium sulphide has been used, and this type of cell is one of the few devices that can be used with an AC supply. Table 3. Peak spectral response Cell resistance at 50 lux Cell resistance at lux Dark resistance Max.

A typical spectral response graph was illustrated earlier in Figure 3. In such applications, the main drawback of the LDR, which is a comparatively long response time, is not a drawback. These times are reasonable when compared to the operating times of the relays that the ORP12 is so often used to operate, but they make any type of use with modulated light beams out of the question.

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