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5.7 Bridge Circuits 195 Fig. 5.38. Sensitivity of a disbalanced bridge as a function of impedance ratio. this concept. A control circuit modifies the value of R 3 on the command from the error amplifier. The output voltage may be obtained from the control signal of the balancing arm R 3 . For example, both R v and R 3 may be photoresistors. The R 3 photoresistor could be interfaced with a light-emitting diode (LED) which is controlled by the error amplifier. Current through the LED becomes a measure of resistance R v , and, subsequently, of the light intensity detected by the sensor. 5.7.3 Temperature Compensation of Resistive Bridge The connection of four resistive components in a Wheatstone bridge configuration is used quite extensively in measurements of temperature, force, pressure, magnetic fields, and so forth. In many of these applications, sensing resistors exhibit temperature sensitivity. This results in the temperature sensitivity of a transfer function, which, by using a linear approximation, may be expressed by Eq. (2.1) of Chapter 2. In any detector, except that intended for temperature measurements, this temperature dependence has a highly undesirable effect, which usually must be compensated for. One way to do a compensation is to couple a detector with a temperature-sensitive device, which can generate a temperature-related signal for the hardware or software correction. Another way to do a temperature compensation is to incorporate it directly into the bridge circuit. Let us analyze the Wheatstone bridge output signal with respect to its excitation signal V e . We consider all four arms in the bridge being responsive to a stimulus with the sensitivity coefficient, α, so that each resistor has the value R i = R(1 ± αs), (5.48)
196 5 Interface Electronic Circuits where R is the nominal resistance and s is the stimulus (e.g., pressure or force), and the sensitivity, α, is defined as α = 1 dR R ds . (5.49) An output voltage from the bridge is V out = V e αs + V 0 , (5.50) where V 0 is the offset voltage resulting from the initial bridge imbalance. If the bridge is not properly balanced, the offset voltage may be a source of error. However, an appropriate trimming of the bridge sensor during either its fabrication or in application apparatus may reduce this error to an acceptable level. In any event, even if the offset voltage is not properly compensated for, its temperature variations usually are several orders of magnitude smaller than that of the sensor’s transfer function. In this discussion, we consider V 0 temperature independent (dV 0 /dT = 0); however, for a broad temperature range (wider than ±15 ◦ C) V 0 should not be discounted. In Eq. (5.48), sensitivity α generally is temperature dependent for many sensors and is a major source of inaccuracy. It follows from Eq. (5.49) that α may vary if R is temperature dependent or when dR/ds is temperature dependent. If the bridge has a positive temperature coefficient of resistivity, the coefficient α decreases with temperature, or, it is said, it has a negative TCS (temperature coefficient of sensitivity). Taking a partial derivative with respect to temperature T , from Eq. (5.50) we arrive at ∂V out ∂T = s ( α ∂V e ∂T + ∂α ∂T V e ) . (5.51) A solution of this equation is the case when the output signal does not vary with temperature: ∂V out /∂T = 0. Then, the following holds: α ∂V e ∂T =−∂α ∂T V e, (5.52) and, finally, 1 ∂V e V e ∂T =−1 ∂α =−β, (5.53) α ∂T where β is the TCS of the bridge arm. The above is a condition for an ideal temperature compensation of a fully symmetrical Wheatstone bridge; that is, to compensate for temperature variations in α, the excitation voltage, V e , must change with temperature at the same rate and with opposite sign. To control V e , several circuits were proven to be useful [9]. Figure 5.39 shows a general circuit which incorporates a temperature compensation network to control voltage V e across the bridge according to a predetermined function of temperature. Several options of the temperature compensation network are possible. Option 1: Use of a temperature sensor as a part of the compensation network. Such a network may be represented by an equivalent impedance R t , and an entire bridge can be represented by its equivalent resistance R B . Then, the voltage across the bridge is V e = E R B . (5.54) R B + R t
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HANDBOOK OF MODERN SENSORS PHYSICS,
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HANDBOOK OF MODERN SENSORS PHYSICS,
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To the memory of my father
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Preface Seven years have passed sin
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Contents Preface ..................
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Contents XI 4.5 Lenses ............
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Contents XIII 7.7.1 Micropower Impu
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Contents XV 15 Radiation Detectors
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Contents XVII Table A.9 Physical Pr
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1 Data Acquisition “It’s as lar
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1.1 Sensors, Signals, and Systems 3
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1.1 Sensors, Signals, and Systems 5
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1.2 Sensor Classification 7 oscillo
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1.3 Units of Measurements 9 Table 1
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Table 1.7. SI Basic Units Reference
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2 Sensor Characteristics “O, what
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2.2 Span (Full-Scale Input) 15 Fig.
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2.4 Accuracy 17 2.4 Accuracy Avery
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2.6 Calibration Error 19 To compute
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2.8 Nonlinearity 21 Fig. 2.4. Trans
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2.12 Resolution 23 (A) (B) Fig. 2.7
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2.16 Dynamic Characteristics 25 2.1
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2.16 Dynamic Characteristics 27 Sub
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2.17 Environmental Factors 29 2.17
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2.18 Reliability 31 guide. For inst
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2.20 Uncertainty 33 • Thermal sho
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Table 2.2. Uncertainty Budget for T
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3 Physical Principles of Sensing
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3.1 Electric Charges, Fields, and P
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3.2 Capacitance 45 The capacitor ma
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3.2 Capacitance 47 (A) (B) Fig. 3.6
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3.2 Capacitance 49 h 0 (A) (B) Fig.
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3.3 Magnetism 51 N S S N (A) (B) Fi
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3.3 Magnetism 53 electric charge ca
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3.3 Magnetism 55 3.3.3 Toroid Anoth
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3.4 Induction 57 • Changing the o
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3.5 Resistance 59 Fig. 3.16. Voltag
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3.5 Resistance 61 For pure resistan
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3.5 Resistance 63 resistor) and the
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3.5 Resistance 65 Fig. 3.19. Strain
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3.6 Piezoelectric Effect 67 (A) (B)
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3.6 Piezoelectric Effect 69 Another
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3.6 Piezoelectric Effect 71 Another
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3.6 Piezoelectric Effect 73 absorpt
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3.6 Piezoelectric Effect 75 that en
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3.7 Pyroelectric Effect 77 circuit
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3.7 Pyroelectric Effect 79 through
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3.7 Pyroelectric Effect 81 Fig. 3.2
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3.8 Hall Effect 83 Fig. 3.30. Hall
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Table 3.2. Typical Characteristics
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3.9 Seebeck and Peltier Effects 87
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3.10 Sound Waves 93 If we consider
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3.11 Temperature and Thermal Proper
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3.11 Temperature and Thermal Proper
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3.12 Heat Transfer 99 to about 35
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3.12 Heat Transfer 101 (A) (B) Fig.
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3.12 Heat Transfer 103 Fig. 3.41. S
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3.12 Heat Transfer 105 Fig. 3.42. S
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3.12 Heat Transfer 107 Fig. 3.44. W
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3.12 Heat Transfer 109 (A) (B) Fig.
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3.13 Light 111 [38] whose emissivit
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3.14 Dynamic Models of Sensor Eleme
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References 119 specified and three
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References 121 34. Thomson, W. On t
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124 4 Optical Components of Sensors
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Page 164 and 165: 146 4 Optical Components of Sensors
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Page 168 and 169: 150 Optical Components of Sensors 1
Page 170 and 171: 5 Interface Electronic Circuits 5.1
Page 172 and 173: 5.1 Input Characteristics of Interf
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Page 176 and 177: 5.2 Amplifiers 157 (A) (B) Fig. 5.5
Page 178 and 179: 5.2 Amplifiers 159 Fig. 5.7. Voltag
Page 180 and 181: 5.2 Amplifiers 161 (A) (B) Fig. 5.9
Page 182 and 183: 5.2 Amplifiers 163 Fig. 5.11. An eq
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Page 186 and 187: 5.3 Excitation Circuits 167 (A) (B)
Page 188 and 189: 5.3 Excitation Circuits 169 Fig. 5.
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Page 192 and 193: 5.3 Excitation Circuits 173 (A) (B)
Page 194 and 195: 5.4 Analog-to-Digital Converters 17
Page 196 and 197: Table 5.2. Binary Bit Weights and R
Page 206 and 207: 5.5 Direct Digitization and Process
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Page 210 and 211: 5.6 Ratiometric Circuits 191 (A) (B
Page 212 and 213: 5.7 Bridge Circuits 193 determine t
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Page 218 and 219: It can be solved for the temperatur
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Page 224 and 225: 5.9 Noise in Sensors and Circuits 2
Page 242 and 243: 5.10 Batteries for Low Power Sensor
Page 244 and 245: References 225 nickel-metal hydrate
Page 246 and 247: 6 Occupancy and Motion Detectors Se
Page 248 and 249: 6.2 Microwave Motion Detectors 229
Page 250 and 251: 6.2 Microwave Motion Detectors 231
Page 252 and 253: 6.3 Capacitive Occupancy Detectors
Page 254 and 255: 6.3 Capacitive Occupancy Detectors
Page 256 and 257: 6.4 Triboelectric Detectors 237 6.4
Page 258 and 259: 6.5 Optoelectronic Motion Detectors
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6.5 Optoelectronic Motion Detectors
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References 251 Fig. 6.17. Calculate
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7 Position, Displacement, and Level
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7.1 Potentiometric Sensors 255 (A)
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7.2 Gravitational Sensors 257 (A) (
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7.3 Capacitive Sensors 259 (A) (B)
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7.3 Capacitive Sensors 261 Fig. 7.7
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7.4 Inductive and Magnetic Sensors
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7.5 Optical Sensors 275 Therefore,
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7.5 Optical Sensors 277 (A) (B) (C)
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7.5 Optical Sensors 279 (A) (B) Fig
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7.5 Optical Sensors 281 Fig. 7.32.
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7.5 Optical Sensors 283 (A) (B) (C)
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7.5 Optical Sensors 285 is proporti
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7.6 Ultrasonic Sensors 287 (A) (B)
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7.7 Radar Sensors 289 (A) (B) Fig.
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7.7 Radar Sensors 291 (A) (B) Fig.
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7.8 Thickness and Level Sensors 293
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References 299 8. Dakin, J. P., Wad
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8 Velocity and Acceleration Acceler
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8.1 Accelerometer Characteristics 3
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8.2 Capacitive Accelerometers 305 a
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8.3 Piezoresistive Accelerometers 3
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8.5 Thermal Accelerometers 309 Fig.
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8.5 Thermal Accelerometers 311 forc
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8.6 Gyroscopes 313 8.6 Gyroscopes N
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8.6 Gyroscopes 315 (A) (B) Fig. 8.1
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8.6 Gyroscopes 317 Products Company
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8.7 Piezoelectric Cables 319 (A) (B
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References 321 (A) (B) Fig. 8.16.Ap
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9 Force, Strain, and Tactile Sensor
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9.1 Strain Gauges 325 (A) (B) Fig.
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9.2 Tactile Sensors 327 9.2 Tactile
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9.2 Tactile Sensors 329 (A) (B) Fig
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9.2 Tactile Sensors 331 Fig. 9.7. P
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9.2 Tactile Sensors 333 Fig. 9.9. T
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9.3 Piezoelectric Force Sensors 335
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References 337 14. Karrer, E. and L
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10 Pressure Sensors “To learn som
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10.3 Mercury Pressure Sensor 341 1
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10.4 Bellows, Membranes, and Thin P
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10.5 Piezoresistive Sensors 345 Fig
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10.5 Piezoresistive Sensors 347 bri
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10.6 Capacitive Sensors 349 (A) (B)
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10.7 VRP Sensors 351 (A) (B) Fig. 1
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10.8 Optoelectronic Sensors 353 Fig
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10.9 Vacuum Sensors 355 (A) (B) Fig
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References 357 (A) (B) (C) Fig. 10.
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11 Flow Sensors It’s a simple tas
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11.2 Pressure Gradient Technique 36
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11.3 Thermal Transport Sensors 363
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11.3 Thermal Transport Sensors 365
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11.4 Ultrasonic Sensors 367 A senso
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11.4 Ultrasonic Sensors 369 Fig. 11
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induced in the liquid. The magnitud
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11.6 Microflow Sensors 373 (A) (B)
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11.7 Breeze Sensor 375 (A) (B) Fig.
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11.9 Drag Force Flow Sensors 377 Wi
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References 379 11. Philip-Chandy, R
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12 Acoustic Sensors “Your ears wi
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12.3 Fiber-Optic Microphone 383 (A)
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12.4 Piezoelectric Microphones 385
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12.5 Electret Microphones 387 Fig.
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12.6 Solid-State Acoustic Detectors
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References 391 References 1. Hohm,
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13 Humidity and Moisture Sensors 13
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13.1 Concept of Humidity 395 Table
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13.2 Capacitive Sensors 397 Fig. 13
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13.3 Electrical Conductivity Sensor
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13.4 Thermal Conductivity Sensor 40
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13.6 Oscillating Hygrometer 403 chi
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References 405 9. Jachowicz, R. S.
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14 Light Detectors “There is noth
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14.1 Introduction 409 Table 14.1. B
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14.2 Photodiodes 411 Maximum revers
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14.2 Photodiodes 413 when i = 0), w
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14.2 Photodiodes 415 (A) (B) (C) Fi
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14.2 Photodiodes 417 Fig. 14.9. Res
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14.3 Phototransistor 419 Fig. 14.12
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14.4 Photoresistors 421 (A) (B) Fig
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14.5 Cooled Detectors 423 (A) (B) F
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14.6 Thermal Detectors 425 Table 14
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14.6 Thermal Detectors 427 Fig. 14.
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Table 14.3. Typical Specifications
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14.6 Thermal Detectors 431 A dual e
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14.6 Thermal Detectors 433 Fig. 14.
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14.6 Thermal Detectors 435 (A) (B)
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14.6 Thermal Detectors 437 Section
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14.7 Gas Flame Detectors 439 P = V
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References 441 housing assures wide
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15 Radiation Detectors Figure 3.41
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15.1 Scintillating Detectors 445 Fi
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15.2 Ionization Detectors 447 emitt
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15.2 Ionization Detectors 449 Fig.
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15.2 Ionization Detectors 451 parti
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15.2 Ionization Detectors 453 There
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References 455 the pure intrinsic t
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16 Temperature Sensors When a scien
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16 Temperature Sensors 459 from whi
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16.1 Thermoresistive Sensors 461 2.
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16.1 Thermoresistive Sensors 463 Ta
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16.1 Thermoresistive Sensors 465 Fi
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16.1 Thermoresistive Sensors 467 pr
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16.1 Thermoresistive Sensors 475 (m
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16.2 Thermoelectric Contact Sensors
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16.3 Semiconductor P-N Junction Sen
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16.4 Optical Temperature Sensors 49
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16.4 Optical Temperature Sensors 49
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16.5 Acoustic Temperature Sensor 49
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References 497 plate—the so-calle
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17 Chemical Sensors 1 Chemical sens
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17.3 Classification of Chemical-Sen
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17.4 Direct Sensors 503 17.4 Direct
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17.4 Direct Sensors 505 voltage e.
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17.4 Direct Sensors 507 This reacti
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17.4 Direct Sensors 509 (A) (B) Fig
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17.4 Direct Sensors 511 µm thick a
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17.5 Complex Sensors 513 Fig. 17.11
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17.5 Complex Sensors 515 Fig. 17.12
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17.5 Complex Sensors 517 frequency
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Table 17.1. SAW Chemical Sensors 17
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17.6 Chemical Sensors Versus Instru
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References 531 13. LaCourse, W.R. P
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18 Sensor Materials and Technologie
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18.1 Materials 535 etching is a key
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18.1 Materials 537 Fig. 18.3. The a
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18.1 Materials 539 The following is
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18.1 Materials 541 should be consid
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18.2 Surface Processing 543 sensor
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18.2 Surface Processing 545 On a co
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18.3 Nano-Technology 547 6000-Å la
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18.3 Nano-Technology 549 exposed to
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18.3 Nano-Technology 551 Fig. 18.10
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18.3 Nano-Technology 553 (A) (B) Fi
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References 555 Fig. 18.17. Bonding
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Appendix Table A.1. Chemical Symbol
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Table A.4. SI Conversion Multiples
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Table A.4 Continued Light cd/in. 2
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Table A.4 Continued Cup 2.36588 ×
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Appendix 565 Table A.7. Some Materi
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Appendix 567 Table A.11. Thermoelec
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Table A.14. Mechanical Properties o
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Appendix 571 Table A.18. Typical Em
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Table A.20. Characteristics of C-Zn
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Table A.23 Continued Manufacturer P
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Table A.25. Properties of Glasses S
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Index α-particles, 443 A/D, 175, 1
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Index 581 Coulomb’s law, 40 cross
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Index 583 H 2 O, 108 Hall, 82 Hall
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Index 585 occupancy sensors, 227 od
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Index 587 SAW, 75, 388, 404, 496, 5
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Index 589 velocity sensor, 302 vert
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