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3.3 Magnetism 55 3.3.3 Toroid Another useful device that can produce a magnetic field is a toroid (Fig. 3.14B), which we can describe as a solenoid bent into the shape of a doughnut. A calculation of the magnetic field inside the toroid gives the following relationship: B = µ 0 i 0 N 2π r , (3.32) where N is the total number of turns and r is the radius of the inner circular line where the magnetic field is calculated. In contrast to a solenoid, B is not constant over the cross section of a toroid. Also, for an ideal case, the magnetic field is equal to zero outside a toroid. The density of a magnetic field, or the number of magnetic lines passing through a given surface, is defined as the magnetic flux B for that surface: ∫ B = B dS. (3.33) The integral is taken over the surface, and if the magnetic field is constant and is everywhere at a right angle to the surface, the solution of the integral is very simple: B = BA, where A is the surface area. Flux, or flow of the magnetic field, is analogous to the flux of electric field. The SI unit for magnetic flux, as follows from the above, is tesla meter 2 , to which is named weber. It is abbreviated as Wb: 1Wb = 1T m 2 . (3.34) 3.3.4 Permanent Magnets Permanent magnets are useful components for fabricating magnetic sensors for the detection of motion, displacement, position, and so forth. To select the magnet for any particular application, the following characteristics should be considered: • Residual inductance (B) in gauss—how strong the magnet is • Coercive force (H ) in oersteds—how well will the magnet resist external demagnetization forces • Maximum energy product, MEP, (BH ) is gauss oersteds times 10 6 . A strong magnet that is also very resistant to demagnetization forces has a high MEP. Magnets with a higher MEP are better, stronger, and more expensive. • The temperature coefficient in %/ ◦ C shows how much B changes with temperature. Magnets are produced from special alloys (see Table A.6). Examples are rare earth (e.g., samarium)–cobalt alloys. These are the best magnets; however, they are too hard for machining and must be ground if shaping is required. Their maximum MEP is about 16 × 10 6 . Another popular alloy is Alnico, which contains aluminum, nickel, cobalt, iron, and some additives. These magnets can be cast or sintered by
56 3 Physical Principles of Sensing pressing metal powders in a die and heating them. Sintered Alnico is well suited to mass production. Ceramic magnets contain barium or strontium ferrite (or another element from that group) in a matrix of a ceramic material that is compacted and sintered. They are poor conductors of heat and electricity, are chemically inert, and have a high value of H . Another alloy for the magnet fabrication is Cunife, which contains copper, nickel, and iron. It can be stamped, swaged, drawn, or rolled into final shape. Its MEP is about 1.4 × 10 6 . Iron–chromium magnets are soft enough to undergo machining before the final aging treatment hardens them. Their maximum MEP is 5.25 × 10 6 . Plastic and rubber magnets consist of barium or strontium ferrite in a plastic matrix material. They are very inexpensive and can be fabricated in many shapes. Their maximum MEP is about 1.2 × 10 6 . 3.4 Induction In 1831, Michael Faraday in England and Joseph Henry in the United States discovered one of the most fundamental effects of electromagnetism: an ability of a varying magnetic field to induce electric current in a wire. It is not important how the field is produced—either by a permanent magnet or by a solenoid—the effect is the same. Electric current is generated as long as the magnetic field changes. A stationary field produces no current. Faraday’s law of induction says that the induced voltage, or electromotive force (e.m.f.), is equal to the rate at which the magnetic flux through the circuit changes. If the rate of change is in webers per second, the e.m.f. (e) will be in volts: e =− d B . (3.35) dt The minus sign is an indication of the direction of the induced e.m.f. If varying magnetic flux is applied to a solenoid, the e.m.f. appears in every turn and all of these e.m.f.’s must be added. If a solenoid, or other coil, is wound in such a manner so that each turn has the same cross-sectional area, the flux through each turn will be the same, and then the induced voltage is V =−N d B , (3.36) dt where N is the number of turns. This equation may be rewritten in a form which is of interest to a sensor designer or an application engineer: V =−N d(BA) . (3.37) dt The equation means that the voltage in a pickup circuit can be produced by either changing the amplitude of the magnetic field (B) or area of the circuit (A). Thus, induced voltage depends on the following: • Moving the source of the magnetic field (magnet, coil, wire, etc.) • Varying the current in the coil or wire which produces the magnetic field
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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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Page 26 and 27: 1.2 Sensor Classification 7 oscillo
Page 28 and 29: 1.3 Units of Measurements 9 Table 1
Page 30 and 31: Table 1.7. SI Basic Units Reference
Page 32 and 33: 2 Sensor Characteristics “O, what
Page 34 and 35: 2.2 Span (Full-Scale Input) 15 Fig.
Page 36 and 37: 2.4 Accuracy 17 2.4 Accuracy Avery
Page 38 and 39: 2.6 Calibration Error 19 To compute
Page 40 and 41: 2.8 Nonlinearity 21 Fig. 2.4. Trans
Page 42 and 43: 2.12 Resolution 23 (A) (B) Fig. 2.7
Page 44 and 45: 2.16 Dynamic Characteristics 25 2.1
Page 46 and 47: 2.16 Dynamic Characteristics 27 Sub
Page 48 and 49: 2.17 Environmental Factors 29 2.17
Page 50 and 51: 2.18 Reliability 31 guide. For inst
Page 52 and 53: 2.20 Uncertainty 33 • Thermal sho
Page 54 and 55: Table 2.2. Uncertainty Budget for T
Page 56 and 57: 3 Physical Principles of Sensing
Page 58 and 59: 3.1 Electric Charges, Fields, and P
Page 64 and 65: 3.2 Capacitance 45 The capacitor ma
Page 66 and 67: 3.2 Capacitance 47 (A) (B) Fig. 3.6
Page 68 and 69: 3.2 Capacitance 49 h 0 (A) (B) Fig.
Page 70 and 71: 3.3 Magnetism 51 N S S N (A) (B) Fi
Page 72 and 73: 3.3 Magnetism 53 electric charge ca
Page 76 and 77: 3.4 Induction 57 • Changing the o
Page 78 and 79: 3.5 Resistance 59 Fig. 3.16. Voltag
Page 80 and 81: 3.5 Resistance 61 For pure resistan
Page 82 and 83: 3.5 Resistance 63 resistor) and the
Page 84 and 85: 3.5 Resistance 65 Fig. 3.19. Strain
Page 86 and 87: 3.6 Piezoelectric Effect 67 (A) (B)
Page 88 and 89: 3.6 Piezoelectric Effect 69 Another
Page 90 and 91: 3.6 Piezoelectric Effect 71 Another
Page 92 and 93: 3.6 Piezoelectric Effect 73 absorpt
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Page 96 and 97: 3.7 Pyroelectric Effect 77 circuit
Page 98 and 99: 3.7 Pyroelectric Effect 79 through
Page 100 and 101: 3.7 Pyroelectric Effect 81 Fig. 3.2
Page 102 and 103: 3.8 Hall Effect 83 Fig. 3.30. Hall
Page 104 and 105: Table 3.2. Typical Characteristics
Page 106 and 107: 3.9 Seebeck and Peltier Effects 87
Page 112 and 113: 3.10 Sound Waves 93 If we consider
Page 114 and 115: 3.11 Temperature and Thermal Proper
Page 116 and 117: 3.11 Temperature and Thermal Proper
Page 118 and 119: 3.12 Heat Transfer 99 to about 35
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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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150 Optical Components of Sensors 1
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5 Interface Electronic Circuits 5.1
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5.1 Input Characteristics of Interf
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5.1 Input Characteristics of Interf
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5.2 Amplifiers 157 (A) (B) Fig. 5.5
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5.2 Amplifiers 159 Fig. 5.7. Voltag
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5.2 Amplifiers 161 (A) (B) Fig. 5.9
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5.2 Amplifiers 163 Fig. 5.11. An eq
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5.3 Excitation Circuits 165 5.3.1 C
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5.3 Excitation Circuits 167 (A) (B)
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5.3 Excitation Circuits 169 Fig. 5.
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5.3 Excitation Circuits 171 atures.
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5.3 Excitation Circuits 173 (A) (B)
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5.4 Analog-to-Digital Converters 17
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Table 5.2. Binary Bit Weights and R
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5.5 Direct Digitization and Process
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5.5 Direct Digitization and Process
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5.6 Ratiometric Circuits 191 (A) (B
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5.7 Bridge Circuits 193 determine t
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5.7 Bridge Circuits 195 Fig. 5.38.
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5.7 Bridge Circuits 197 Fig. 5.39.
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It can be solved for the temperatur
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5.8 Data Transmission 201 (A) (B) (
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5.8 Data Transmission 203 wire meth
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5.9 Noise in Sensors and Circuits 2
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5.10 Batteries for Low Power Sensor
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References 225 nickel-metal hydrate
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6 Occupancy and Motion Detectors Se
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6.2 Microwave Motion Detectors 229
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6.2 Microwave Motion Detectors 231
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6.3 Capacitive Occupancy Detectors
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6.3 Capacitive Occupancy Detectors
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6.4 Triboelectric Detectors 237 6.4
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6.5 Optoelectronic Motion Detectors
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and the facet pitch is 6.5 Optoelec
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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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