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Chapter 2 Types of Transducers Chapter 2 Types of Transducers 2.1 Resistive Position Transducers: The principle of the resistive position transducer is that the physical variable under measurement causes a resistance change in the sensing element. A common requirement in industrial measurement and control work is to be able to sense the position of an object, or the distance it has moved. Fig (2-1) Resistive Positive Transducer or Displacement Transducer One type of displacement transducer uses a resistance element with a sliding contact or wiper linked to the object being monitored. Thus, the resistance between the slider and one end of the resistance element depends on the position of the object. Figure (2-1) (a) shows the construction of this type of transducer. Figure (2-1) (b) shows a typical method of use. The output voltage depends on the wiper position and therefore is a function of the shaft position. This voltage may be applied to a voltmeter calibrated in inches for visual display. Typical commercial units provide a choice of maximum shaft strokes from an inch or less to 5 feet or more. - 13 - Deviation from linearity of the resistance versus-distance specification can be as low as 0.1% to 1.0% consider Fig. (2-1) (b). If the circuit is unloaded, the output voltage V0 is a certain fraction of VT, depending on the position of the wiper as seen in eqn (1). V0 R2 VT R1 R2 (1) In its application to resistive position sensors, this equation shows that the output voltage is directly proportional to the position of the wiper, if the resistance of the transducer is distributed uniformly along the length of travel of the wiper, that is, if the element is perfectly linear. Example (1) A displacement transducer with a shaft stroke of 3.0 in. is applied in the circuit of Fig. The total resistance of the potentiometer is 5 k , and the applied voltage VT=5.0V. When the wiper is 0.9 in. from B, what is the value of the output voltage V0? Solution 0.9 in. x 5000 1500 3.0 in. R 1500 V0 2 VT x 5.0 V 1.5V RT 5000 Example (2) A resistive position transducer with a resistance of 5000 and a shaft stroke of 5.0 in. is used in the arrangement of Fig. (2-2). Potentiometer R 3R 4 is also 5000 , and VT = 5.0 V. The initial position to be used as a reference point is such that R 1 =R 2 (i.e.. the shaft is at midstroke). At the start of the test, potentiometer R 3R 4 is adjusted so that the bridge is balanced (VE=0). Assuming that the object being monitored will move a maximum distance of 0.5 in. toward A, what will the new value of VE be? If the wiper moves 0.5 in. toward A from midstroke, it will be 3.0 in. from B. Solution R2 3.0 in 5000 300 5.0 in R2 R4 VE VR 2 VE 4 VT VT R1 R2 R3 R4 3000 2500 (5V ) (5V ) 0.5 V 5000 5000 R2 - 14 - This answer is a measure of the distance and direction that the object has traveled. Fig (2-2) Basic Voltage Divider Resistive Transducer 2.2 Pressure Transducer: 1. Bellows. For slightly high pressures, the bellows is a serviceable elastic deformation element. It is more sensitive than any other device of its class. The bellows may be considered to be made of cascaded capsules, as shown in fig.(2-3) In fact, one method of manufacturing the bellows is by fastening together several individual diaphragms. The bellows, however, is a one-piece, collapsible, seamless metallic unit with deep folds formed from very thin-walled tubing. Most commonly used materials are brass, phosphor bronze, hardenable stainless steel, nickel alloy and beryllium copper. The diameter may be as small as 12 mm or as large as 300 mm, and it may have as many as 24 folds or convolutions. Basically bellows is a pressure activated spring, stiffness of which depends on the thickness and type of material. Fig (2-3) The Deflection of the Bellows under Application of Pressure P is given by the Expression - 15 - PR 2 y 2nA 3 Et (2) In equation (2) where in is the number of convolutions in the belows, A is the effective area of the bellows, E is Young's modulus of elasticity, and t is the thickness of wall of the bellows. Generally, only a portion of the total available motion of the bellows (10% of the maximum stroke length) is used, in order to prevent their taking a "set" from being expanded to their limit too frequently. A spring is often used to limit their motion. The larger the diameter of the bellows the lower the pressure that can be measured with it. One side of the bellows is fixed and the pressure is applied inside the bellows from other side, which in turn expands or compresses the bellows depending upon the nature of pressure. A rod fitted on the other side of the bellows moves and transmits the motion to the secondary transducer, as illustrated in fig. (2-4). Fig (2-4) Measurement of Pressure Using Bellows and Potentiometer Two commonly used bellows arrangements are illustrated. In one arrangement the unknown pressure is applied to the inside of the bellows and tends to expan d the bellows against the. pull of the tension spring, as shown in fig. (2-5) (a) as the bellows expands, it actuates a mechanical linkage which moves the wiper of a potentiometer to give an electrical output signal. - 16 - Fig (2-5) (a) The Pressure is applied to the Inside of the Bellows In alternative arrangement shown in fig (2-5) (b) the pressure under measurement is applied to the outside of the bellows, forcing it to contract against the push of a compression spring. As it moves, it actuates a mechanical linkage which moves the core of an LVDT to give an electrical output signal. Fig (2-5) (b) The Pressure under Measurement is Applied to the Outside of the Bellows Main advantages of the bellows are simple and rugged construction, moderate cost, capability of providing large force and wide pressure range. The main draw-backs of the bellows are: i. Ambient temperature compensation is required. ii. Unsuitable for measurement of very high pressures. iii. Unsuitable for dynamic measurements because of their greater mass and longer relative movement. These are widely used for measurement of vacuum and low pressures. - 17 - 2. Bourdon Tubes. Bourdon tube, consists of a tube flattened to have an approximately elliptical cross-section and bent into either a C or twisted tube, or spiral or helical shape, as shown in fig. (2-6) (a.b). These are all formed from seamless metal tubing with wall thickness varying from 0.25 mm to 1.25 mm. The tube is sealed at one end and the other end of the tube is kept open for the application of pressure under measurement. The tube is soldered, or welded to a socket at the base through which pressure connection is made. Material used for bourdon tubes are phosphor-bronze, alloy steel, cold worked brass, beryllium copper, stainless steel and Mohel metal. Selecting of material for bourdon tube depends mainly on the fluid and the pressure for which these are designed. The material used for bourdon tube must have good elastic or spring characteristics for adequate reliability. The wall thickness and material determine the maximum pressure to which such an element may be subjected. A thick walled steel bourdon tube is available for measuring pressure as high as 100 MPa. The fluid whose pressure is being measured is admitted to the inside of the tube at the open end, which is mechanically anchored. The tube then deflects by an amount proportional to the magnitude of the pressure. The deflection is mechanically transmitted to the wiper of a potentiometer or to the core of an LVDT to furnish an electrical signal, as illustrated in figs.(2- 6) (a) and-(b). (a) Bourdon Tube Linked to a Potentiometer - 18 - (b) Bourdon Tube Linked To LVDT Fig (2-6) (a.b) Bourdon Tubes are Useful for Measurement of Pressures Higher than that can be measured with a Bellows Figs.(2-6) (a) and (b) illustrates how a C-shaped bourdon tube could be linked to a potentiometer or to an LVDT. C-type bourdon tubes cover pressure ranges 35 kPa to 100 MPa, and with a 50 mm bending diameter have a useful travel of approximately 3 mm. Such a tube has a hysteresis error of approximately 1-2% of full-scale deflection. The commercial bourdon pressure gauges have near elliptical xsection and the tube is usually. bent into a C-shape of arc length between 180 to 270, as shown in fig.(2-7) As the fluid under pressure enters the bourdon tube, it tries to be 'reformed' and owing to availability of a free tip, this action causes the tip to travel in free space and the tube unwinds. The simultaneous action of bending and tension due to internal pressure makes a non-linear movement of the free tip. This travel is suitably guided and amplified for useful measurement of the internal pressure. Though the actual tip travel, due to development of compound stress in the bourdon tube, is non-linear but for practical of compound stress in the bourdon tube. Is non-linear but for practical purposes for a small travel of the tip this can be considered to be linear, and parallel to the axis the link. The main requirement in the design of this gauge is that whenever the same pressure is applied, the movement of the tip should be same and on withdrawl of the pressure the tip should return to the initial point. The schematic arrangement of a complete gauge is illustrated in - 19 - fig.(2-7) The applied pressure P1 acts inside the tube, and P2 acts at the outside. The deflection y of the tube tip or end is a function of (P1 - P2), and is amplified by the lever, quadrant, pinion, and pointer arrangement. A flat spiral spring is commonly employed for taking up backlash between the quadrant gear and the pinion. Fig (2-7) Bourdon Tube with Mechanical Amplification Increased sensitivity, better linearity, and higher accuracy can be achieved by extending the length of the bourdon tubes in the form of a flat spiral or helix as shown in figs.(2-8) (a) and (b). An increased displacement of the free end can be achieved by increasing the number of turns in the spiral or helix and so there is no need for further amplification i.e. the gear sector and pinion arrangement is not required for further amplification as in case of C-type bourdon tube. Fig (2-8) (a) A Spiral Type Bourdon tube (b) Helical-Shaped Bourdon Tube - 20 - A spiral type bourdon tube is made by winding several turns of the tube with its flattened x-section in the form of a spiral. On applying pressure under measurement to the spiral, it tends to unwind causing a relatively long movement of the tip. The displacement of the tip can be used for indication or transmission. The accuracy of spiral tube is higher than that of Gtype tube owing to absence of magnifying elements and is typically approximately ± 0.5%.Helical-shaped bourdon tube is made of coiled tube into multi-turn helix with 6 to 10 turns. The displacement of the tip of helical tube is larger than that of spiral tube. The accuracies obtainable with helical bourdon tubes are of the order ± 0.5 to ± 1 % of span. Its advantages are high range capabilities (in the ratio as high as 10: 1); its adaptability for high pressure service and its stability in fluctuating pressure applications. Advantages and disadvantages of bourdon tubes are given below advantages. 1. Cheap in cost and simple is construction. 2. Availability over wide range of pressure. 3. High sensitivity and good repeatability. 4. Good accuracy except at low pressures. 5. Easily adaptable for design for obtaining electrical outputs. Disadvantages. 1. Prone to shock vibration and shock resistance. 2. Low spring gradient limiting their use for precision measurements upto a pressure of 3 M Pa. 2.3 Strain Gauge Transducers: The strain gauge is an example of a passive transducer the; uses electrical resistance variation in wires to sense the strain produced by a force on the wires. It is a very versatile detector and transducer for measuring weight pressure mechanical force, or displacement. The construction of a bonded strain gauge fig (2-9) shows a finewire element looped back and forth on a mounting plate, which is usually cemented to the member undergoing stress a tensile stress tens to elongate - 21 - the wire and thereby increase its length and decrease its cross-sectional area. The combined effect is an increase in resistance as seen from eqn (3). R L A (3) Fig (2-9) Resistive Strain Gauges; wire Construction Where: = the specific resistance of the conductor material in ohm meters (product) L = the length of the conductor in meters A = the area of the conductor in square meters As a consequence of strain two physical qualities are of particular interest: (1) the change in gauge resistance and (2) the change in length. The relationship between these two variables expressed as a ratio is called the gauge factor. K. Expressed mathematically as K R / R L / L (4) Where:K = the gauge factor R = the initial resistance in ohms (without strain) R = the change in initial resistance in ohms L = the initial length in meters (without strain) L = the change in initial length in meters Note that the term L / L in the denominator is the same as the unit strain G. Therefore. Eq (5) can be written as - 22 - K R / R G (5) Robert Hooke pointed out in the seventeenth century that for many common materials there is a constant, ratio between stress and strain. Stress is defined as the internal force per unit area. The stress equation is can be written as Eq (6). S F A (6) Where:S = the stress in kilograms per Square meter F = the force in kilograms A = the area in square meters The constant of proportionality between stress and strain for a linear stress-strain curve is known as the modulus of elasticity of the material. E or Young's modulus Hooke's law is written as can be written as Eq (7). E S G (7) Where:E =Young's modulus in kilograms per square meter S = the stress in kilograms per square meter G = the strain (no units) For strain gauge applications, a high degree of sensitivity is very desirable. A high gauge factor means a relatively large resistance change for a given strain. Such a change is more easily measured than a small resistance change. Relatively small changes in strain can be sensed, as shown in Examples. Example (3) A resistant strain gauge with a gauge factor of 2 is fastened to a steel member, which is subjected to a strain of 1 X 10-6. If the original resistance value of the gauge is 130 . Calculate the change in resistance. - 23 - Solution R / R R / R L / L G R KGR (2) (1x10 6 ) (130) 260 Example (4) A round steel bar, 0.02 m in diameter and 0.40 m in length, is subjected to a tensile force of 33.000 kg, where E = 2 x 1010 kg/m2. Calculate the elongation, L, in meters. Solution 0.02 m D 4 2 A( 3.14 x 10 m 2 2 S F/A E G L / L 33.000kg x 0.40m FL L AE (3.14 x 10 4 m 2 ) (2 x 1010 kg / m 2 ) K 2 2 2.1 x 10 3 m 2.3.1 Types of Strain Gauges: These strain gauges are mainly of four types namely:1. Wire strain gauges. 2. Foil strain gauges. 3. Thin film strain gauges and. 4. Semiconductor strain gauges. 1. Wire Strain Gauges. Wire strain gauges are normally of smaller size, and are subject to minimal leakage, and can be employed in high temperature applications. The characteristics that should be possessed by wire strain gauges inorder to give excellent and reproducible results are as follows: i. The element of the wire strain gauge should be of low resistance temperature coefficient so that measurement accuracy is not affected by variations in temperature. ii. Wire strain gauges should have a high value of gauge factor, G so that a large change in resistance is obtained for a particular value of strain resulting in high sensitivity. iii. Wire strain gauges should be of resistance as high as possible (of the order. of 100-1,000 ) so that accuracy of measurement is - 24 - not affected due to small variations in resistance of measuring circuit. However, higher resistance of strain gauge results in lower sensitivity. So higher bridge voltages are employed so that high sensitivity is achieved but the bridge voltage is also restricted by the maximum current carrying capacity of wires which is typically 30 mA. iv. Wire strain gauges should be of linear characteristics for its entire range inorder to have easy calibration. v. Wire strain gauges should not have any hysteresis or creep effect, in its performance. vi. Wire strain gauges should have very good frequency response as these are frequently employed for dynamic measurements. Wire strain gauges are of two types namely (a) unbonded wire strain gauges and (b) bonded wire strain gauges. 2. Foil Strain Gauges. It is basically an extension of the bonded wire strain gauge differs in construction and has certain advantages. The bonded wire strain gauges have been completely superseded by foil strain gauges. In such gauges, metal foils are used instead of wire, as shown in fig.(2-10) The required grid pattern is formed from a very thin foil of the same material as that used in wire strain gauges by photo-etching processes Fig (2-10) Foil Strain Gauge That permits great flexibility with regard to shape. The thickness of foil varies from 2.5 microns to 6 microns. Dimensions of a single - 25 - bonded foil strain gauge can be as small as 0.8 mm x 1.6 mm. The length of the grid versus the width is designed to concentrate the strain sensing grid over the high-strain area. The foil is often specially heat treated before use in order to optimize mechanical properties and the thermal coefficient of resistahce. The photo-etching process employed for making foil strain gauges allows the manufacture of sensing grids in virtually any two-dimensional pattern. Normally, a geometric pattern is, developed that will provide maximum electrical and mechanical efficiency from the sensing element. Foil strain gauges with gauge resistance values of 120, 350 and 1000 are common. The maximum gauge current is about 30 mA, maximum strain for ± 1 per cent linearity is about ± 0.3 per cent, and strain variation upto at least 50 kHz can be measured. The advantages, that foil strain gauges posses over wire strain Gauges, are Enumerated Below: 1. Width of foil gauge is many times of its x-section, so a larger ratio of the bonding area to the x-sectional area is achieved. This in turn enables higher heat dissipation-and better bonding. Thus these gauges have low hysteresis and creep effects. 2. The larger ratio of surface area to x-sectional area provides superior mechanical stability under prolonged strain and higher temperature conditions. So they can be used fog higher currents. 3. In foil strain gauges, terminals have no stress concentration because of absence of joints resulting in longer life. 4. Response of the foil gauges to traverse strain can be reduced by making the perpendicular sections of the foil wide. 5. The strain reproducibility is excellent The foil strain gauges are employed for both stress analysis as well as for construction of transducers. 3. Thin Film Strain Gauges. A thin-film strain gauge is produced by depositing a thin layer of metal alloy on an elastic metal specimen by means of vacuum deposition or sputtering process. This technique, - 26 - relatively new and extensively used, produces a strain gauge that is molecularly bonded to the specimen under test, so the draw-backs of the epoxy adhesive bond are eliminated. This technique is most widely used for transducer applications such as in diaphragm-type pressure gauges. For producing thin film strain gauge transducers, first an electrical insulation such as a ceramic is deposited on the stressed elastic metal member such as a diaphragm or beam and then strain gauge alloy is deposited on the top of the insulation layer. Both layers may be deposited either by vacuum deposition or by sputtering process. In the vacuum deposition or evaporation process the diaphragm is placed in a vacuum chamber with some insulating material. Heat is applied until the insulating material vaporizes p and then condenses, forming a thin dielectric film on the diaphragm. Then suitably shaped templates are placed over the diaphragm, and the evaporationcondensation process is repeated with the metallic gauge material, forming the. Desired gauge pattern on top of the insulating substrate. In the sputtering process, a thin dielectric layer is again deposited in vacuum over the entire diaphragm surface; however, this detailed mechanism of deposition is quite different from the evaporation process,. In the process the gauge or insulating material is held at -ve potential and the target (transducer diaphragm or beam) is held at a +ve potential. Molecules of gauge or insulating material are ejected from the -ve electrode owing to the impact of positive gas ions (argon) bombarding the surface. The ejected molecules are accelerated toward the transducer diaphragm or beam and strike the target area with kinetic energy of magnitude several times greater than that possible with any I other deposition process. This produces, superior adherence to the specimen under test. For achieving maximum bridge sensitivity (millivolt output), minimum heating effect and stability, the four strain gauges, the wiring between these gauges, and the balance and temperature compensation - 27 - components are all integrally formed during the deposition process. This ensure the same composition and thickness throughout. The thin-film strain gauge transducers have several advantages over others. They are rugged and have very low hysteresis-and creep. The sensitivity is also high-because of a higher gauge factor and high resistance. A resistance as high as 5 k can be produced in order to permit increased input and output voltages with low power consumption. They can operate over a wide temperature range from - 200 C to 400 C with good stability. 4. Semiconductor Strain Gauges. Semiconductor strain gauges are based on the piezoresistive property of doped silicon and germanium and that is why the transducers based on semiconductor gauges are often called piezo-resisrive transducers, they are made of films of germanium or silicon base materials as shown in fig (2-11). Under strained condition, resistivity of any material changes and this is called the piezo-resistive property of material. In metal alloy strain gauges, variation in resistance is caused, under strained condition, mainly because of change in geometrical shape and very less due to change in resistivity of the material. The gauge factor of metal alloy strain gauges is found to be about 2.0. But in semiconductor strain gauges, variation in resistance, under strained condition, is mainly due to change in resistance i.e. most of the resistance variation comes from peizo-resistance effect. The p-type gauges increase resistance with applied tensile strain while the n-type decrease resistance. Their big advantage is a very high gauge factor. A typical semiconductor strain gauge has a gauge factor of 100 to + 150 with a maximum strain of 0.003 and a temperature range of -10 to + 70° C. In addition to the high gauge factor, other advantages are low cross-sensitivity, freedom from hysteresis a creep effects, chemical inertness and good fatigue life unfortunately, the high gauge factors accompanied by high temperature sensitivity, non-linearity, and mounting difficulties. - 28 - Fig (2-11) Semi-conductor Strain Gauges 2.3.2 Merits of Semiconductor Strain Gauges: 1. These gauges permit measurement of very small strain, as small as, 0.01 micron owing to their high gauge factor lying between - 100 to + 150. 2. As semiconductor strain gauges can be manufactured in very small sizes ranging from 0.7 to 7 mm, so they are very useful in the measurement of highly localized strains. 3. They are chemically inert and have low cross-sensitivity. 4. They have got frequency response upto 102 Hz. 5. They are almost free from hysteresis and creep effects because of integrated format of the actual gauge itself. 6. Their fatigue life is much higher than that of wire and foil gauges due to the perfect elastic deformation of the silicon filament. Their fatigue life is more than 10 106 operations. 7. The drift owing to moisture absorption and noise produced by imperfect insulation of-lead wires are relatively less than that in wire gauges because of higher strain sensitivity. Demerits of Semiconductor Strain Gauges: They are expensive, brittle, highly sensitive to temperature variations and have poor linearity. Semiconductor strain gauges are often used in high-output transducers as load cells. These gauges are extremely sensitive, with gauge factors from 50 to 200. They are however, affected by temperature fluctuations and often behave in a nonlinear manner. The strain gauge is generally used as one arm of a bridge. The simple arrangement is shown - 29 - in Fig. (2-12) (a) can be employed when temperature variations are not sufficient to affect accuracy significantly, or in applications for which great accuracy is not required. However, since gauge resistance is affected by temperature, any change of temperature will cause a change in the bridge balance conditions. This effect can cause an error in the strain measurement. Thus, when temperature variation is significant, or when unusual accuracy is required an arrangement such as that illustrated in Fig. (2-12) may be used. Here two gauges of the same type are mounted on the item being tested close enough together that both are subjected to the same temperature. Consequently, the temperature will cause the same change of resistance in the two, and the bridge balance will not be affected by the temperature. However one of the two gauges is mounted so that its sensitive direction is at right Angles to the direction of the strain. The resistance of this dummy gauge is not affected by the deformation of the material. Therefore, it acts like a passive resistance (such as R3 of Fig. (2-12) (b) regards to the strain measurement). Since only one gauge responds to the strain, the strain causes bridge unbalance just as in the case of the single gauge. Fig (2-12) Basic Gauge Bridge Circuits - 30 - 2.4 Piezoelectric Transducers: When a mechanical pressure is applied to a crystal of the Rochelle salt quartz, or tourmaline type, a displacement of the crystals causes a potential difference to occur. This property is used in piezoelectric transducers: in these transducers a crystal is placed between a solid base and force-summing member, as shown in Fig. (2-13). Externally applied forces exert pressure to the top of the crystal. This produces an electromotive force across the crystal proportional to the magnitude of the applied pressure. Fig (2-13) Elements of a Piezoelectric Transducer For a piezoelectric element under pressure, part of the energy will be converted to an electric potential that will appear on opposite faces of the element, analogous to the charge on the plates of a capacitor. The rest of the applied energy is converted to mechanical energy, analogous to that of a compressed spring: When the pressure is removed, the piezoelectric element will return to its original shape and also lose its electric charge. From these relationships the following formulas have been derived for the coupling coefficient k as seen in eqn (8) and (9). k k Mechanical energy converted to electrical energy Applied mechanical energy Electrical energy converted to mechanical energy Input electrical energy - 31 - (8) (9) An alternating voltage applied to a crystal causes it to vibrate at its natural resonance frequency. Since the frequency is a very stable quantity, piezoelectric crystals are used principally in high - frequency accelerometers. The output voltage is typically on the order of 1 to 30 mV per gram of acceleration. The device needs no external power source and is therefore self-generating. The principal disadvantage of this transducer is that voltage will be generated only as long as the pressure applied to the piezo electric element is changing. Example (5) Solution A certain crystal has a coupling coefficient of 0.32. How much electrical energy must be applied to produce an output of 1 in of mechanical energy? 1 ft 1 Ib 1.356 J 1 in. = in. x x x 12in 16 1 ft Ib = 7.06 x 10-3 J 2.4.1 Merits, Demerits and Applications of Piezoelectric Transducers Merits: 1. Piezoelectric transducers are generally small in size, light in weight and very rugged in construction. 2. These are self generating transducers as they do not need external power. 3. These transducers can operate over a wide range of temperature without appreciable temperature induced errors. Quartz devices can be employed over a temperature range of - 200 to + 300C; whereas ceramic devices. are limited to + 100° C. 4. These transducers have very good high frequency response. They provide flat frequency response from 1 Hz to 20 kHz, the natural frequency being of the order of 50 kHz. 5. Their outputs are quite large; for example, a quartz crystal 2.5 mm thick has a sensitivity of 125 mV/kPa and for a crystal area of 1,000 mmz, sensitivity is 125 V/kN. - 32 - Demerits: 1. On application of a constant deflection to the transducer, it develops voltage across its terminals and the charge leaks off slowly through the leakage resistance of the transducer but this decay of charge is very slow on account of very high leakage resistance (of the order of 1014 ohms) of the transducer. However, when a voltmeter or any other voltage measuring device is connected across the terminals of the transducer the charge leaks off very rapidly. This prevents the measurement of static displacement. Some commercially available systems employing quartz elements of very high leakage resistance and input amplifiers of very high input impedance achieve an effective total resistance of 1014 ohms which gives reasonably slow leakage to allow static measurements. 2. The output voltage is affected by temperature variations of the crystal. 2.4.2 Applications of Piezoelectric Transducers: 1. These transducers are mainly used for measurement of force and pressure. Because of simple and robust construction and having high stiffness, they can be employed for measurement of force over a wide range - from about 1 N to 200 N with linearity approaching t 1 per cent. 2. These transducers, because of their high frequency response, are mainly employed in high frequency accelerometers. In this application their output voltage is typically of the order of 1- 300 mV per g of acceleration. 3. Piezoelectric transducers can also be used for measurement of temperature. A special cut of crystal gives a very linear and sensitive relation between resonant frequency and temperature approximately of the order of 1 kHz per °C. Temperature can be measured with a linearity of 0.05% and a resolution of 0.0001C for the range from - 40C to + 230C. - 33 - 4. Quartz crystals can be employed as mass to frequency convertor. A crystal-controlled electronic oscillator uses a thin quartz plate. The natural frequency of mechanical oscillations of the plate determines the frequency of electrical oscillations. 5. Because of their unusual rugged construction they are widely employed in difficult applications, such as ballistics, blasts, explosions, internal combustion, fuel injection, flow instabilities, high-intensity sound, and hydraulic or pneumatic pulsations-in connection with problems which may be, encountered in connection with guns, shock tubes, closed bombs, rocket motors, internal combustion engines, pumps, compressors, pipe lines, and oil exploration. 2.5 Capacitive Transducers: The capacitance of a parallel-plate capacitor is given by eqn (10). C kA o ( farads) d (10) Where:k = dielectric constant A = the area of the plate, in square meters o = 8.854 X 10", in farads per meter d = the plate spacing in meters Since the capacitance is inversely proportional to the spacing of the parallel plates, any variation in d causes a corresponding variation in the capacitance. Figure (2-14) shows several forms of capacitive transducers. A rotary plate capacitor is shown in fig (2-14) (a) one that is not unlike the variable capacitor used to tune radio transmitters and receivers. The capacitance of this unit is proportional to the amount of area on the fixed plate, which is covered "shaded" by the moving plate. This type of transducer will give signals proportional to curvilinear displacement or angular velocity. - 34 - A rectilinear capacitance transducer is shown in Fig. (2-14) (b), and it consists of a fixed cylinder and a moving cylinder. These pieces are configured so that the moving piece fits inside the fixed piece but is insulated from it. Figure (2-14) (c) shows a transducer that varies the spacing between surfaces, that is, the thin diaphragm. The dielectric is either air or vacuum. Such devices are often used as capacitance microphones. Fig (2-14) Capacitance Transducers Example (6) An electrode-diaphragm pressure transducer has plates whose area is 5 x 10-3 m2 and whose distance between plates is 1 X 10-3 m. Calculate its capacitance if it measures air pressure. The dielectric constant of air is k =1. Solution C kA o d (1) (5 x10 3 m 2 ) (8.854 x 10 12 F / m) 1 x10 3 m 44.25 pF Capacitance transducers can be used in several ways. One method is to use the varying capacitance to frequency-modulate an RF oscillator. This method is the one employed with capacitance microphones like Fig (2-14) (c). Another method is to use the capacitance transducer in an AC bridge circuit. The capacitance transducer has excellent frequency response and can - 35 - measure of static and dynamic phenomena. Its disadvantage is sensitivity to temperature variations and the distorted signals owing to long lead length. 2.5.1 Merits, Demerits and Applications of Capacitive Transducers Merits: 1. These transducers have very high impedance so loading effects are minimum n the measuring circuits. 2. These transducers have excellent frequency response (as high as 50 kHz) and so can be used for measurement of both static and dynamic phenomena. 3. These transducers are not affected by stray magnetic fields. That is why the capacitive transducers are used for applications where stray magnetic fields make the inductive transducers useless. 4. These transducers are extremely sensitive. 5. A resolution of the order of 2.5 microns can be achieved with such transducers. 6. These can be operated with very small forces so they are very useful for small systems and they need small power to operate them. Demerits: 1. Output impedance of capacitive transducer is very high so its measuring circuit becomes very complicated. 2. Insulation resistance of the system cannot be neglected because of high output impedance of the transducer so it reduces its sensitivity. Moreover with change in physical conditions e.g. humidity, temperature etc this resistance changes its value and so introduces error in measurement. 3. Stray capacitance including due to cables etc. in parallel with the output impedance of the transducer also causes error and introduces non-linearity. In order to reduce the effects of stray capacitances, frames should be earthed. - 36 - 4. Electrostatic screening should be provided for capacitive transducers in order to avoid any pickup. 5. The screened cable connector to the transducer can be a source of error because its capacitance varies with the movement between the cable conductors and cable dielectric. 6. Capacitance of capacitive transducers changes with change in temperature or on account of presence of small external matter e.g. dusts particles and moisture etc. Hence error is introduced in measurement. 7. Since the displacement, in general, is small and a large sensitivity is usually needed, so adequate design is required for accurate measurements. 2.5.2 Applications of Capacitive Transducers: 1. Capacitive transducers can be employed for measuring both linear and angular displacements. The capacitive transducers are highly sensitive and can be employed for measuring extremely small displacements such as 0.01 pm. On the other hand they can be employed for measuring large distances up to about 30 m as in airplane altimeters. 2. Capacitive transducers can be employed for measuring force and pressure, which are first converted into displacement and the displacement, make the capacitance to change. 3. Capacitive transducers can also be employed for measuring pressure directly in II those cases in which permittivity of a medium changes with pressure such as in case of Benzene permittivity varies by 0.5% in the pressure range of 1 to 1,000 times the atmosphere pressure. 4. Capacitive transducers can be employed for measuring humidity since the permittivity of gases varies with the variation in humidity. Though the variation in capacitance due to variation in humidity is quite small but is detectable. - 37 - 5. Capacitive transducers can also be employed to measure density, volume, level of liquid, weight etc but with mechanical modifiers 6. The most commonly used microphones are of three types namely: I. Capacitor microphones. II. Carbon microphones and. III. Dynamic microphones. I. Capacitor Microphones. The operation of a capacitor microphone is based on the fact that the capacitance between two plates varies as the distance between the plates is varied. The capacitor microphone uses a metal diaphragm as one plate (moving plate) and a rigid metal plate as the other capacitor plate (fixed plate) as illustrated in fig.(2-15) A constant voltage of 200 to 500 V is maintained across the capacitor plates. The variations in the air pressure in a sound wave striking the diaphragm makes the diaphragm in or out and this, in turn causes the variation in the capacitance. The varying voltage produced due to the incident sound exists as an ac component superimposed on the do level. The ac component is then amplified and delivered to the measuring or recording instrument. The instrument used for measuring output of the capacitor microphone should be of very high input impedance in order to reduce loading errors because a capacitor appears as a high output impedance source. An emitter follower is usually located close to the microphone in order to reduce the inherently high output impedance and reduce the distortion caused' by the noise. Fig (2-15) Capacitor Microphone - 38 - Capacitor microphones perform the most accurate conversions of sound vibrations in air to electrical signals and as such, they are widely used as the standard for precise acoustical measurements. The frequency range is up to 50 kHz. They are reasonably sensitive-a typical sensitivity is -50 db. The disadvantages of capacitor microphones are that (i) they are expensive and (ii) the high voltage supply is often inconvenient to provide. II. Carbon Microphones. These microphones detect sounds by variations in the resistance of carbon granules and operate on the fact that with the variation in the density of the carbon granules, which is caused by the variations in the air pressure of the incident sound waves, the resistance varies. The carbon microphone is provided with a moving diaphragm which is mounted so as to compress together carbon granules with in the housing when sound waves strike it. The device is connected externally to a constant voltage source, and the variation in current due to variation in the resistance of carbon granules is, therefore, a function of variation in sound. As in the capacitor microphones, the ac signal' is separated from the do level, amplified and then delivered to the measuring or recording device as shown in fig (2-16). Fig (2-16) Carbon Microphones Carbon microphones have low output impedance, high sensitivity of the order of -400 db and limited frequency range-maximum of about 5 kHz. - 39 - The non-linearties of variation in carbon resistance prevent the signal from being a faithful replica of the sound vibrations and they find little application in the field of sound measurements. However, the device is quite suitable for transmission of voice and so they are used in almost all telephones. The fact that they are cheaper, highly reliable, and very rugged also makes them more suitable for such applications. III. Dynamic Microphones. The dynamic microphone operates on the principle of electromagnetic transconduction. Such a microphone makes use of a metal diaphragm mechanically linked to a moving coil surrounded by a permanent magnet. The diaphragm and the coil are suspended so that they can move back and forth. The motion of the coil, which is produced due to variations in the air pressure of the incident sound waves, in the magnetic field produces a varying voltage, whose magnitude obviously depends upon the pressure intensity of the sound waves, across the coil. The signal (voltage developed across the coil) is amplified and delivered to the measuring or recording device. The dynamic microphones are self- generating transducers and they have low output impedance, low sensitivity of the order of - 80 db and a frequency response of maximum 20 kHz. They are seldom used in precision measurements as shown fig (2-17). Fig (2-17) Dynamic Microphone The dynamic microphone can also be used as an inverse transducer causing a sound to be produced by applying a varying voltage to the coil. This is the principle on which a loudspeaker operates. - 40 - 1. Vibration Pickups. The transducers that can use for transforming the sound of solid vibrations to electrical signals are called the vibration pickups. Vibration pickups are piezoelectric type. The piezoelectric type vibration pickup operates on the fact that crystalline materials develop a voltage across themselves when deformed from their natural shapes. The deformation need only to be of the order of pm for producing this effect. If the applied force that deforms the piezoelectric crystal has a time-varying magnitude (i.e., as a force on account of the vibration of a piece of material t0 which the crystal is attached), the output voltage from the crystal will also have time varying form which is patterned after the time-varying form of the force. The piezoelectric type vibration -pickup is shown in fig (2-18). The crystals used in the construction of ac pickups are generally made quartz or Rochelle salt. The quartz crystals are accurate but expensive also. Ever Rochelle salt crystals are hampered to the fact that they melt at 65C and limited because of high humidity conditions. Fig (2-18) Piezoelectric Type Vibration Pickup These are self-generating microphones and have been developed for use in a wide variety of situations. They have linear output over a wide range of amplitude, a low sensitivity of the order of - 50 to - 100 db and a frequency response extending to the ultrasonic region, above 100 kHz. The problems with such devices are high output impedance. dependence on temperature, and sensitivity to vibrations. These devices are extensively used in sound measurement systems. - 41 -