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1 CHAPTER 7: TRANSDUCERS In general terms, the transduction process involves the transformation of one form of energy into another form. This process consists of sensing with specificity the input energy from the measurand by means of a "sensing element" and then transforming it into another form by a "transduction element." The sensor-transduction element combination shown in figure below will henceforth be referred to as the "transducer". Measurand relates to the quantity, property, or state that the transducer seeks to translate into an electrical output. Transducers may be classified as self-generating or externally powered. Self-generating transducers develop their own voltage or current and in the process absorb all the energy needed from the measurand. Externally powered transducers, as the name implies, must have power supplied from an external source, though they may absorb some energy from the measurand. I. TRANSDUCTION MECHANISMS Capacitive Thermoelectric effects (Seebeck and Peltier) Inductive and electromagnetic Resistive Ionization effects Resistive and thermoresistive Photoelectric effect Piezoresistive effect Photoresistive effect Hall effect Photovoltaic effect Lateral effect Acoustooptic effect Extrinsic, interferometric and evanes- Fluorescence and fluorescence quenching cent effects in optical fiber Field effect Magnetoresistive effect Doppler effect Tunneling effect EE Transducers 125

2 II. MEASURANDS Displacement Atomic and surface profiles Position Gas concentration and ph Velocity ph and partial pressure of O 2 and CO 2 Acceleration in blood Force and load Infrared radiation Strain Torque Rotation and encoding Magnetic field Vibrations Acoustic fields Flow Medical imaging Temperature Non-destructive testing Pressure Audio fields and noise Vacuum Rotation and guidance III. SELECTION OF TRANSDUCERS When selecting a transducer, in addition to the question of cost, careful attention must be given to the following Sensitivity Range Physical properties Loading effect and distortion Frequency response Electrical output format Output impedance Power requirements Noise Error or accuracy Calibration Environment EE Transducers 126

3 IV. CLASSIFICATION OF TRANSDUCERS EE Transducers 127

4 Before discussing the transduction principles, we first examine several methods for combining individual transduction principles into one single compound transducer. These composite methods are employed to reduce or even totally eliminate certain restrictions associated with individual transducers. A widespread method is to use 2 identical transducers in a balanced configuration shown in Figure 3.1 below. If the transducers have the same transfer characteristic, the output y of the balanced configuration is: y = f(x) f(-x) Here f(x) may be the non-linear transfer function that we intend to linearize. Let assume that f(x) can be expressed with a Taylor expansion in the following form: Using the balance equation above, we find: f(x)= a 0 +a 1 x+a 2 x 2 + a 3 x 3 + a 4 x 4 + a 5 x 5. y = 2a 1 x + 2a 3 x 3 + 2a 5 x 5 + Evidently, the constant (or offset) a 0 and the even terms a 2 x 2, a 4 x 4, disappear when balancing the two transducers. If the non-linearity of f(x) does not contains any uneven terms, we will obtain a perfectly linear system. The systems then referred to as a difference configuration. However, usually balancing will only improve the linearity of the system over a limited range of the input quantity x. Such system is called a differential configuration. The balanced configuration is not sensitive to external disturbances, since it inherently makes use of parallel compensation. The configuration is immune to additive disturbances when the transducers T and T have the same sensitivity to these disturbances. In order to be immune to multiplicative disturbances, the transducers T and T must have disturbance coefficients with the same magnitude, but opposite signs. A second commonly used configuration is the feedback configuration of 2 transducers T1 and T2 in Figure 3.2 below. The purpose of the system is to convert an input signal x into an electrical output signal y. We could use a single transducer T1 for this. Assume T1 is unsuitable to be used directly, due to an unacceptably large non-linearity and has too large a sensitivity to disturbances. If we have a second transducer, capable of the reverse conversion (conversion of y to x) and this conversion is linear and not susceptible to disturbances, then when we combine both transducers T1 and T2 (with an amplifier to increase the loop gain) in the feedback configuration, we can realize a compound transducer for conversion of measurement signal from x into y, with the same characteristics as the employed reverse transducer. The necessary conditions for achieving this EE Transducers 128

5 are a large gain and a quasi-static dynamic behavior for T1, T2 and A. In practice, though, the dynamic behavior of especially T1 and T2 is often of a higher order and, therefore, the situation may not be as ideal as described above. Finally, the reliability of the transducers is often a problem. Sometimes this can be solved by using several transducers which all measure the same quantity. This redundant configuration greatly improves the reliability of the system at, of course, an increased cost. V. MECHANOELECTRIC TRANSDUCERS These transducers measure mechanical quantities. 1. Displacement transducers Displacement transducers can measure either linear displacement (translation) or angular displacement (rotation). They can also be classified according to the principle of transduction on which they are based. We can distinguish between, for instance, resistive, capacitive, inductive and optical translation or rotation transducers. These mechanical transducers are also referred to as gauges or sensors. a. Resistive displacement transducers The potentiometric transducer is a popular type of displacement transducer. For measuring translation it is, in fact, no more than a sliding potentiometer. For measuring rotation, a rotating potentiometer can be used. Usually the potentiometers are wire-wound to achieve a better accuracy, temperature coefficient, etc. However, a limitation of wire-wound displacement transducers is their finite resolution. The maximal resolution R = x/ax is equal to the number of turns on the potentiometer body. Metal film potentiometers do not have this limitation. A disadvantage of all transducers of the potentiometric type is that mechanical wear and chemical corrosion can change the transfer characteristic over the lifetime of the transducer. Another type of resistive displacement sensor makes use of the fact that the electrical resistance of a conductor depends on the dimensions of the conductor. The resistance R is a function of the cross sectional area of the conductor, its length l and its resistivity ρ. EE Transducers 129

6 R=R(A,l,ρ) If the conductor is mechanically strained or compressed, the parameters A, l, and ρ, and as a consequence R, will change. This enables one to measure very small displacements. Figure 3.4a shows a piece of wire (stain gauge) which is elongated a distance l by applied tensile stresses. Figure 3.4(b) shows the meanders of a metal foil strain gauge are made extra wide when they turn, in order to reduce the sensitivity of the strain gauge to strain perpendicular to the main axis of operation. If, besides the magnitude of the strain, we also wish to measure the direction of the strain, a combination of strain gauges is used, arranged in a certain geometric pattern, for instance 3 strain gauges oriented at 120 degrees angles with respect to one another. This arrangement is known as a strain gauge rosette. b. Capacitive displacement sensors b. Capacitive displacement transducers Capacitance C is a function of distance d between the electrodes of a structure, the surface area A of the electrodes and the permittivity ε of the dielectric. C=C(d,A,ε) Therefore the capacitance can be changed when the three variables are changing. Figure 3.6 shows the displacements sensors using the detection of capacitance and the applicable capacitances for each displacement. It is shows that the variable distance transducer has a non-linear characteristics and can be linearized by using it in a balanced configuration. EE Transducers 130

7 The force F(x) causes the movement of sensor with a constant voltage across the capacitor is given by: c. Inductive displacement sensors It is not only possible to vary the self-inductance of a single coil as a function of the displacement to be measured, it is possible to vary the mutual inductance between two coils as a function of the displacement. An obvious way of varying the inductance of a coil is to vary the effective number of turns, Figure 3.8(a), and vary the magnetic resistance (reluctance) of the yoke by means of an air gap of variable width, Figure 3.8(b). The displacement of the second transducer, based on variable reluctance, is incorporated in a bridge network to obtain a linear transfer characteristic. d. Optical displacement sensors Displacement can also be detected optically, by means of an encoding strip (translation) or a rotary encoder (rotation). Figure 3.10(a) shows an optical displacement sensor which utilizes an encoder strip consisting of rows of alternating transparent and opaque bars. The position of the strip is converted directly to a digital signal with a narrow beam of light and a number of light sensors. The digital code is determined by the position of the transparent and opaque bars on the strip. EE Transducers 131

8 2. Velocity transducers There are two transducers used to measure velocity: translational and angular transducers. The measure of velocity is often converted to a frequency measurement. The conversion is performed by a strip or disc on which a large number of marks (detection elements) have been put at equal distances x. The velocity can be calculated from v= xn/t = xf, in which n is the number of detection element which passes the detector in t seconds and f is the frequency of output signal. The detection can be performed optically, mechanically, inductively or capacitively. a. Measurement of velocity by differentiation or integration: For linear velocity v(t) dx(t) v (t) = dt For angular velocity ω(t): d!(t) "(t) = dt where x(t) is the linear displacement where θ(t) is the rotation angle. From these two equations, it is evident that we can obtain a signal, for the velocity of an object, by calculating the derivative of the output signal of a displacement sensor. It is simple to design an electronic circuit for differentiating an electrical signal. Another possibility for obtaining the velocity is by integrating of the linear acceleration a(t) t v(t) =! a(t)dt + v(0) or of an angular acceleration α(t): The integration can be performed by a relative simple analogue electronic circuit. It should be noted that the differentiator and integrator circuits having a disadvantage of increasing or decreasing very slowly, even when the input is zero, due to leakage or drop. b. Inductive velocity transducers: In this kind of transducers, the velocity of the measurement object is made to give rise to a change of magnetic flux Φ, which induces an electrical potential in a conductor. The induced voltage of Figure 3.11(a) in turn i of the coil of this inductive velocity pick up is given by: For a total of n turns, the coil terminal voltage is: 0 t "(t) =!#(t)dt + "(0) 0 Vi = d$ i dt n EE Transducers V = 132 " d$ i i i= n dt

9 Since ΦI=ΦI(x), in which x is the position of the magnet with respect to the center of the coil, and x=x(t), we find: n d$ n = i dx d$ V " = i i v" = vk(x) i= n dt dt i= 1 dx Thus, the output voltage V is proportional to the velocity v of the magnet for a given value of x. The sensitivity of the transducer is equal to k. Unfortunately, since k=k(x), the transducer is non-linear. Therefore, again this type of transducer is often used in a balanced configuration. Since the magnet is moving here the velocity sensor is referred to as a magneto-dynamic transducer. 3. Acceleration transducers Transducers for measuring acceleration rely on the measurement of the force F required to give a known mass (the seismic mass m) the same acceleration, a, as the measurement object. From the force and the mass, the acceleration is determined: a=f/m. The extra mass has to be kept to a minimum, especially when the measurement object is highly elastic or has a low mass (extra mass influences the measure acceleration). VI. THERMO-ELECTRIC TRANSDUCERS 1. Resistive temperature sensors a. Metal: The electrical resistance of any material depends to a certain extend on the temperature and can be used to convert a temperature measurement into a measurement of resistance. Depending on the material used, we can distinguish two kinds of thermometers: metal thermometers and semiconductor thermometers. The resistive of pure metals can be written in the form of power series: 2 2 R(T) = R(T0 )[1 + #(T T0 ) + &(T T0 ) + %(T T0 ) +...] EE Transducers 133

10 in which R(T) is the resistance of the sensor at temperature T and R(T 0 ) is the resistance at certain reference temperature T 0. If the temperature range is not too large, the first 2 terms of the expansion will suffice, the sensor is approximately linear. The most frequently used metals are platinum and nickel. The measurement range of a platinum sensor runs from 70K to 1000K and nickel from 200K to 500K. At T 0 =273K: α Pt =3.85 x 10-3 K -1 α Nt =6.17 x 10-3 K -1 β Pt =-5.83 x 10-7 K -2 γ Pt =-3.14 x K -3 b. Semiconductors: In both intrinsic and extrinsic semiconductors, this effect is overshadowed by a much stronger effect: the number of free charge carriers depends on the absolute temperature. The higher the temperature, the larger the number of electrons which cross the band gap from the valence band into the conduction band (intrinsic) or the larger the number of activated donor and acceptor atoms (extrinsic). The number of free charge carriers increases according to: n=n 0 e -Eg/2kT in which E g is the energy required for the crossing the band gap and k is Boltzmann s constant ( x J/K). Thus the resistance of a semiconductor will decrease as the temperature increases, the semiconductor has a Negative Temperature Coefficients (NTC-resistor). The resistance of a semiconductor can be expressed as: R(T)=Ae B/T The coefficients A and B also depend on the temperature and therefore a more accurate expression is given by: B(1/ T 1/ T0 ) R(T) = R(T0 )e Obviously, a semiconductor sensor is highly non-linear. The temperature coefficient is given by: In practice, the value of the coefficient B lies between 2700K and 5400K at a temperature of 300K. Thus, at 300K, the temperature coefficient ranges from 3 x 10-2 K -1 to 6 x 10-2 K -1. At 300K, a semiconductor sensor is an order of magnitude more sensitive than a metal sensor. Such a semiconductor temperature-sensing resistor is often referred to as thermistor. More improvement in the making of thermistors yields better linear characteristic. 2. IC temperature sensors 1 dr(t) B #(T) = = R(T) dt 2 T An alternative temperature sensor can be found in the bipolar transistor. Such a sensor makes use of the fundamental band gap voltage of silicon, which depends in the temperature. Two EE Transducers 134

11 bipolar transistors located close together, on the same IC, are biased to different collector current. If the ratio of the (collector) current densities (the transistors may have different areas) is equal to r, the difference between the base-emitter voltages of the two transistors is equal to (kt/q)ln(r). This base-emitter voltage difference is a linear measure of absolute temperature. Addition electronic circuits amplify this voltage to provide a practical output value. Typical IC sensor specifications are: range -55 o C to 150 o C, non-linearity over the entire range of approximately 0.3K, sensitivity 10mV/K or 1uA.K, instability over 1000hr of operation ±0.08K, dissipation 1.5mW to 3mW. 3. Thermal couples When two different metals are brought into atomic contact with each other, an electrical potential difference is generated. This so-called junction potential depends only on the nature of the two metals and on the absolute temperature. The surface area of the junction has no influence. For many combinations of metals the junction potential difference is approximately linearly proportional to the absolute temperature of the junction, provided that the temperature range is not too large. When two junctions are connected in series, as illustrated in Fig. 3.16(a), a net thermo voltage V will result if the two junctions are at different temperatures. This configuration is called a thermocouple. Several characteristics of thermocouples have been plotted in Fig. 3.16(b). The thermovoltage is a measure of the temperature difference between the two junctions. The output voltage of a thermocouple can be written more accurately as a power series of the temperature difference T-To, with To a certain calibration temperature than it can if it is assumed to be proportional to temperature: i.e. As n increases, this expression will describe the behavior of a given thermocouple more and more accurately. Every thermocouple (so every combination of two metals) is characterized by its own series of temperature independent coefficients a i (i = 1,..., n). An inaccuracy of ±l% requires roughly eight coefficients (n=8) for most materials. The coefficient a 1 is referred to as the Seebeck coefficient. Fig. 3.16(c) shows how this coefficient would depend on the temperature if a thermocouple were to be described by only one single coefficient, a 1. EE Transducers 135

12 If we are dealing with a large temperature range, we must use more than one coefficient for reasons of accuracy. There are four physical effects that contribute to the output voltage of the thermocouple. -Seebeck effect. This is the desired effect which is measured when no current is allowed to flow through the thermocouple. It arises from the temperature dependence of the junction potential difference. This junction potential difference originates from the difference in Fermi levels of two dissimilar metals. The higher the temperature, the larger the number of electrons with a higher energy level than the Fermi level. This causes the junction potential difference to become temperature dependent. -Peltier effect. When a current flows through a junction of two dissimilar metals, the temperature of the junction will change. Depending on the direction of the current, the junction will become either warmer or cooler than ambient. This effect is caused by the fact that with every electrical conduction process there is also transportation of heat. In a metal, thermal conduction as well as electrical conduction are caused by free electrons. The Peltier effect is undesirable in a thermocouple since it gives rise to a temperature error. -Thomson effect. If a current is flowing through a uniform metal conductor in the direction in which there is a negative temperature gradient, thermoelectric heat will be generated. If the direction of the current is reversed, heat will be extracted from the conductor. This reversible effect also originates from the fact the electrical conduction process in a metal is accompanied by the transfer of heat and, inversely, heat conduction is accompanied by electrical conduction. This effect also gives rise to errors. -Joule heat. With the last two effects, we assumed that no heat was generated by the dissipation of electrical energy in the electrical resistance of the metals. If the total resistance is R, then, per second, I 2 R joules is dissipated. The thermocouple will therefore heat itself up. Thus, the clear conclusion is that no current may flow through the thermocouple when one is interested in accurate temperature measurements; the measurement circuit must have a high input impedance. An additional source of measurement errors is moisture. Moisture can create a galvanic element with both metals, which generates a galvanic cell voltage many times larger than that of the thermocouple. Therefore, thermocouples are often supplied in a waterproof case. If we wish to measure the absolute temperature as opposed to a temperature difference by means of a thermocouple, we must hold one of the junctions at a fixed known reference temperature. This can be achieved by controlling the temperature of one of the junctions with a thermostat. It is also possible to compensate the temperature of the reference junction, as indicated in Fig The temperature of the reference junction is measured here by a resistance sensor R(T), which is connected to a bridge network. The output voltage of the bridge is connected in series with the thermocouple such that it compensates for the temperature of the reference junction. Of course, the temperature sensitivity of the reference junction must oppose that of the bridge network. The temperature measured by the active junction AB is usually located some distance away from the rest of the circuitry. The metal of the thermocouple junction is usually too EE Transducers 136

13 expensive to use for long interconnections and, therefore, two wires A'B' of a cheaper metal are used for the interconnections. Provided that these two wires A' and B' have the same thermoelectric characteristics as the two wires A and B of the measurement junction, no error will be introduced. It can be seen that when two (other) metal conductors are connected in series with the two junctions of the thermocouple, as in Fig. 3.17, the new junctions will not contribute a net potential difference, as long as the new junctions are kept at the same temperature (isothermal). The extra junction potentials will cancel each other. Temperature differences between these new junctions will cause measurement errors. If the cable which connects the two junctions of the thermocouple has the same thermoelectric characteristics it is referred to as compensation cable. 4. Radiation thermometers A radiation thermometer absorbs a fraction of the infrared radiation emitted by the measurement object. A radiation thermometer for high temperatures is usually called a pyrometer. The radiation is usually focused on the actual thermal detector by means of a concave mirror (as illustrated in Fig. 3.18(a)). If the temperature of the measurement object is lower than that of the detector, it will supply heat energy to the object, causing the detector to cool. The use of lenses is avoided, especially for low temperatures, since lenses which easily transmit heat radiation (diathermanous infra-red lenses) are very expensive. Other pyrometers are based on quantum detectors. This principle of operation relies on the electrons of the material being excited by infrared radiation. This can only occur when the quantum energy E of the radiation quanta is equal to or larger than a certain threshold energy Eo. This threshold energy corresponds to the transition of electrons to a higher energy state. With: EE E hc Transducers 0 = hf0 = 137 0

14 This threshold energy is related to infrared radiation above a certain minimal frequency fo or below a certain maximal wavelength λ 0 Fig. 3.18(b) shows the spectral sensitivity of this kind of quantum detector. Photodiodes are used as quantum detectors for near infrared radiation; photoresistors are used in the far infrared region. Quantum detectors respond quickly, but only measure radiation in a limited band of wavelengths. Pyrometers are used for measuring extremely high temperatures (T>1000K) when no other means are available. They are also used for measuring objects with a high thermal resistance, such as plastics, rock, etc. Besides the described methods for converting a temperature into an electrical signal, there are many more. One is the (quartz) crystal thermometer which is based on the temperature dependence of the resonance frequency of a piezoelectric crystal. The crystal is used to determine the frequency of an oscillator accurately. This frequency can be determined by the enumeration method, resulting in a small inaccuracy of only 0.01K and a very high resolution of 10 4 in the range from -80 C to 250 C. These excellent specifications are realized by cutting the quartz crystal very accurately with respect to the crystal orientation axes. This is done in such a way that the temperature sensitivity of the resonance frequency is maximal and as stable as possible. A calibration curve of temperature versus frequency is recorded and built into the instrument (PROM) to increase the accuracy even further. VII. MAGNETOELECTRIC TRANSDUCERS The induction of a magnetic field can be measured with transducers referred to as magnetometers or magnetic field sensors. The magnetic induction B is expressed in teslas (T). Sometimes, it is also referred to as the magnetic flux density. A unit which is consistent with this terminology is the weber per square meter with, of course, 1T = 1Wb/m2. Sometimes a rotating coil (with area A, n turns and angular frequency ω) is used for measuring the induction B of a static magnetic field. Assuming the coil is so small that the induction is constant across the surface area of the coil and B n is the component of B perpendicular to the axis of rotation, the flux Φ through the coil is equal to Φ = B n A sin θ(t), where (θ) is the instantaneous angle between the coil and B n. With θ(t) =ωt, the induced ac voltage is given by: d$ V = n = nbn"cos("t) dt We can determine B n from this expression. Induction sensors always require a changing flux. The change in magnetic flux can obviously also arise from an alternating magnetic field in a static coil. Another type of magnetometer is based on the influence of a magnetic field on the electrical resistance of a material. As early as 1856 W. Thomson (Lord Kelvin) discovered that if one exposes a current conducting body to a magnetic field the electrical resistance changes. This effect, called the magnetoresistive effect, was only used much later for realizing transducers. It was not until the American physicist E. F. Hall had discovered the so called Hall effect that an explanation for this phenomenon could be given. EE Transducers 138

15 The Hall effect is a result of the Lorentz force, exerted on charge carriers in solids. When a platelet of conducting material is positioned in a magnetic field (as sketched in Fig. 3.19), the charge carriers will be deflected in a direction perpendicular to the direction of motion of these charge carriers and perpendicular to the induction vector B of the magnetic field. The Lorentz force acting on a charge q with velocity v is equal to: F l =q(vb) As the charge carriers are deflected, a transverse charge gradient will build up, resulting in an electrical field E across the plate. This field will subject the charge carriers to an opposing force F e which is given by: F e =qe At a certain point, equilibrium is reached between the Lorentz force and the force produced by the electrical field, so F e = F l and therefore: E=vB Assuming the charge carriers all have approximately the same velocity v, the current density J is equal to nqv, with n the concentration of charge carriers. If, in addition, we assume that B is perpendicular to v, as in Fig. 3.19, then E = JB/nq. The factor 1/nq is called the Hall coefficient and usually denoted by R H. With I=bdJ and V =Eb we find: V = 1 IB nq d = RH For semiconductor materials, in which the majority charge carriers are holes (p-type semiconductors), q is positive and the output voltage of the Hall plate will have the polarity indicated in Fig If the majority charge carriers are electrons (n-type semiconductors) the polarity will be opposite. The Hall coefficient is large for semiconductors, since the concentration n of charge carriers is much smaller in semiconductors than in metals. Obviously, a Hall plate can measure static magnetic fields, without any moving or rotating parts. A Hall plate is also suitable for high-frequency measurements; it has a wide frequency range (up to several GHz). Furthermore, the disturbance to the magnetic field, caused by the Hall plate is very small. In addition to measuring magnetic fields directly, Hall plates are often used for measuring large DC currents and in current probes for oscilloscopes. IB d EE Transducers 139

16 VIII. TRANSDUCER SELECTION The selection of a transducer begins with the specifications of the physical quantity to be measured. The user must ascertain the required accuracy of the measurement, the duration of the test, and may need to consider cyclic behavior or other factors. In addition, consideration needs to be given to the environment in which the transducer is placed. Finally, the calibration procedure should be considered. Each of these categories is discussed as part of the selection criteria for transducers. The general selection criteria listed in this section should be considered representative; additional factors may be necessary for specific transducers. MEASUREMENT REQUIREMENTS The measurement requirements for a transducer are as follows Range: The range is the set of values a transducer is designed to measure. The minimum and maximum values of the transducer's range are called the endpoints. Some transducers can be adjusted to cover a different range by attenuating the measurand -for example, a sensitive radiation transducer can be used if the measured quantity is attenuated using radiation-absorbing filters. It is not always possible to find a single transducer to cover the entire range of measurand values; in these cases transducers with overlapping ranges must be selected Input threshold The input threshold is the smallest detectable value of the measured quantity starting near the zero value of the variable. For an input to be discerned, it must be possible to assign a unique number to the input. The selection of a transducer requires that it respond in a discernible manner to the threshold. Dynamic behavior The dynamic behavior of a transducer specifies how the transducer can respond to a changing input. No transducer could follow an instantaneous change. (For that matter, no measurand can change instantaneously!) The transducer's dynamic performance is usually specified as a frequency response or response time, depending on the type of transducer. The response time is the time required to reach a specified percentage (typically 90% to 99%) of the final value for a given change of the input. The response time is measured in much the same way as the time constant for an RC or RL circuit. (Recall that the time constant is the time required for the output to reach 63% of its final value.) Accuracy and resolution Accuracy is the difference between the measured and accepted value. The accuracy requirements for a particular measurement can greatly affect the total cost of the measurement system. In addition, certain transducers, such as strain gages and pressure transducers, have a fatigue life that can change the accuracy, depending on the duration and cyclic behavior of the measurand. In some cases, the accuracy isn't as important as the ability to detect a small change (resolution), as when quantities are being compared. For example, in underground-tank testing, the interface between the liquid and air can be located by observing the small temperature difference between the air and liquid. In other cases, consistency is the most important criterion. Other accuracy errors include nonlinearities due to a zero shift or drift due to aging, which can affect the long-term repeatability of measurements EE Transducers 140

17 Repeatability and hysteresis errors Repeatability is the maximum difference between consecutive measurements of the same quantity when the measured point is approached each time from the same direction for full-range traverses. It is usually expressed as a percentage difference of the full-scale output. Hysteresis error is the maximum difference between consecutive measurements for the same quantity when the measured point is approached each time from a different direction for full-range traverses. An example is when backlash in gearing causes the readings of a dial to be different, depending on whether the gearing was turned in one direction or the other. OPERATIONAL AND ENVIRONMENTAL CONSIDERATIONS The operational and environmental considerations for a transducer are as follows Natural hazards The transducer, wiring, and connectors must all be able to withstand the effects of exposure to the required environment. Natural hazards include the effects of dust and dirt, high or low temperatures, water (including salt water), and humid conditions. Wire insulation is available that is resistant to these effects as well as solvents, acids, bases, and so forth. In contrast, the transducer should not present a hazard to the environment in which it is placed-including causing electrical problems such as explosion hazard or shock hazard. Human-caused hazards Human-caused hazards include high-radiation environments, corrosive or dangerous chemicals, immersion, abrasion, vibration, and explosive environments, to name a few. The electrical signal from the transducer may be interfered with if the signal cables are routed in an electrically noisy environment, another possible hazard for proper operation, particularly with transducers that have a low output signal. Power requirements Power requirements depend on the type of transducer. Passive transducers, such as photocells, convert some of the incident source energy into electrical energy. Others require a source of excitation, which can be a dc or ac source. If the transducer is being operated in a remote or noisy environment, the power leads become a source of potential problems. Signal-conditioning requirements If the transducer produces a very small signal or it is located at a remote location or in a noisy environment, amplification or other signal conditioning may be required at the transducer. The transducer output may need to be converted into a compatible format for the remainder of the instrumentation system. Physical requirements In some installations, the space available may be limited or the measurand may be over a limited region. If the quantity to be measured is concentrated, such as in the case of a collimated light source, the physical size of the transducer can affect the output. Loading effects Loading effects cause the measurand to be disturbed in some manner by the presence of the transducer. All measurements in some way modify the quantity to be measured. For example, a rotating-vane flowmeter extracts a small amount of the energy from the fluid to turn the vane and EE Transducers 141

18 thus changes the flow from its undisturbed value. Loading can also occur in the electrical-measuring circuit. Electrical loading can occur when a transducer with an equivalent high Thevenin resistance is connected to an amplifier with a finite input impedance. In this case the transducer signal is reduced by the connection to the amplifier. Many transducers have a very high equivalent Thevenin resistance (ph electrodes, for example), so it is important to be aware of the need for compatible amplifiers. Human factors Human factors that need to be considered in the selection of a transducer are the operating skill of the persons installing and using the transducer, the ease of installation, the cost of the transducer, and the required maintenance. CALIBRATION REQUIREMENTS Our final consideration for selecting a transducer is the calibration requirements. The calibration interval and type of calibration necessary need to be considered. The calibration interval is determined by the operating life of the transducer and other factors such as long-term sensitivity shift, zero shift, and the accuracy requirements of the application. The calibration interval, complexity, and need to refer to calibration data can affect the total cost of the transducer. The ideal calibration will precisely predict the response of the transducer in the application setting. This prediction may be difficult, particularly when there are large differences between the calibration process and the application such as different loading, dynamic response, or environmental conditions. Calibration methods vary widely, depending on the transducer, but should be made in a manner that is traceable to NIST. The errors associated with the standard should be much smaller than the transducer that is being calibrated. The calibration can consist of comparing the transducer to a known reference instrument or a physical standard (such as a known mass for a load cell) or using a physical reference (such as the triple point of water for a temperature transducer). Frequently, the physical parameter is varied and the response of the transducer is observed and compared to a known reference. Generally, the specific calibration points should extend over the full range of the measurand to avoid the need for extrapolation. For example, a pressure transducer should be subjected to the same range of pressures in the calibration process that it will be subjected to in its intended application to reveal any nonlinearities or other problems. The data should be taken in both an increasing and decreasing direction to reveal any hysteresis present. Data taken during calibration is called a calibration record. A line connecting the data points is called a calibration curve for the particular transducer. If the calibration of the transducer is not done under the same conditions as the operating conditions, systematic error can result whenever the transducer is used. For example, a radiation transducer that is calibrated with a radio- active source that has a different spectrum than the spectrum that is to be monitored will lead to flawed data if the difference is not accounted for. A calibration performed in a manner that gives the transducer time for the output to settle to a fixed value is called a static calibration. Transducers used in dynamic measurements can be tested for their response with a dynamic calibration. A dynamic calibration is often a comparison of the transducer that is being calibrated with a known reference transducer that is faster. Another dynamic test is called a step-function response test. In it, the transducer is subjected to a rapid change in the input measurand, typically from 10% to 90% of the transducer's range. For example, a temperature transducer is very quickly moved to a much warmer or colder environment and its response is observed. The time required for the output to settle to the new temperature is a measure of the transducer's response time. EE Transducers 142

19 IX. BRIDGE MEASUREMENT Many transducers - such as strain gages, resistance temperature devices, and certain displacement transducers-use resistive transduction principles. Typically, these transducers produce a very small resistance change in response to the measurand. A circuit that can detect these very small changes is the Wheatstone bridge. Because of their great sensitivity and other advantages, bridge circuits are widely used for transducer measurements. A bridge circuit that consists of four resistance arms with a source of energy (called the excitation) and a detector is shown in Figure This circuit is shown with two pairs of leads to the power supply, a common method of ensuring that the voltage at the bridge is stable. Current to the bridge flows on the excitation leads. Any variation in the voltage due to IR drop in the excitation leads is detected by the sense leads and is used to regulate the supply. Notice that the sense leads carry almost no current, so they have almost no IR drop. Figure 13-4 The balance condition can be detected with great sensitivity using an instrumentation amplifier (IA) connected across the differential output, as shown in Figure For general application, the circuit shown is good choice (CMRR is typically greater than or equal to 110 db). The IA is selected for low-drift, high- common-mode rejection and gain stability. Figure 13-5 EE Transducers 143

20 When a Wheatstone bridge is used to detect the change in resistance of a single resistive transducer, the transducer is placed in one arm of the bridge, and the output of the bridge is observed. Frequently, more than one active transducer is used in a bridge to increase the sensitivity of the measurement. It is not always necessary to balance the bridge to determine the unknown resistance; instead, the magnitude of the off-balance condition can be used as an indicator of the resistance or to detect a change in resistance. The output change is not a linear function of the resistance change (it is approximately linear when Rl» R unknown ), but this non-linearity has some advantages in certain measurements. It is possible to construct bridges that tend to linearize the output of nonlinear transducers such as thermistors. Transducer manufacturers have developed a number of techniques for increasing the linearity, sensitivity, and stability of bridge circuits. These include specialized amplifiers, changing the excitation source, and matching the thermal or other characteristic of the transducer with the bridge resistors. For example, strain gages respond to more than just strain; they also respond to temperature changes. To cancel the temperature effects, a "dummy" gage can be placed in the same environment but not subjected to the strain of the measuring strain gage. The dummy gage is placed on the same side of the bridge as the measuring gage. Temperature effects change the resistance of both gages in a like manner, causing no change in the output. Many resistive transducers produce only a tiny change in resistance for a given input change. For sensitive measurements, the detecting instrument must have good common-mode rejection (CMR) because each side of the bridge includes a common-mode signal from the excitation supply. When the detecting instrument is located some distance from the transducer, an even more serious common-mode problem can occur when ground current causes a common-mode source to appear between the bridge ground and the instrument ground. Notice that the output (signal leads) of the bridge in Figures 13-4 and 13-5 are not connected to circuit ground, a condition referred to as a floating output. When a voltmeter is connected as a detecting instrument to the bridge outputs, the voltmeter signal connections should be isolated from circuit ground; however, there is always some high impedance to ground (Figure 13-6(a)). Assume that the impedance to ground is different between the high and low inputs (the usual case). Current from the common-mode ground source finds a path through the voltmeter's leads and generates a differential voltage due to the impedance difference in the return paths. This means that EE Transducers 144

21 a common-mode signal has been converted into a differential-mode signal, and the meter will respond to this potential. One possible solution is shown in Figure 13-6(b). The excitation supply is floating-in other words, its reference is isolated from the circuit ground by using an isolation transformer or a battery. This method can provide CMRRs greater than 160 db. The left side of the bridge is connected to circuit ground and the right side of the bridge is connected to a single-ended, non-inverting op-amp. Another solution is to use a guarded voltmeter. The guard connection is made so that it shunts common-mode current away from the meter's inputs. One of the best ways to do this is to connect the guard lead to a low-impedance point that is at the same potential as the low side of the meter. This is done by adding a low-impedance divider to the bridge, as illustrated in Figure 13-6(c). Most of the common-mode current will flow through the low-impedance path provided by the voltage divider. There are other variations of sensing circuits that are designed to optimize dc offset, voltage or temperature drift, non-linearity, noise performance, or other characteristic. EE Transducers 145