Acceleration measurement, 398
Accelerometers:
differential transformer, 253–269
effect
of damping ratio, 401
loading on test objects, 411
pressure-to-force type, 435
construction, 406
servo-accelerometer, 405
Accuracy, definition of, 77
of null-balance systems, 100, 107
of standards, 33
Aliasing (in sampling), 364
Amplifiers:
controlled-source model, 125–127
effect of feedback, 155
instrument amplifier, 319
preamplifier, 314–315, 319, 344
Amplitude modulation, 246–249, 255–258
frequency spectra of, 259
in strain measurement, 257
in temperature measurement, 255
Analog data corrections, 200–204
Analog-to-digital conversion (ADC), 345–349, 369
Anemometer, hot-wire/film, 491–495
Angular measurements, 250, 274
Averaging, signal, 159
Bandwidth, 685
Bernoulli’s equation, 477
Bimetallic thermometers, 511–512
Binary-coded decimal (BCD), 325
Binary numbering system, 325–326
Bourdon-tube pressure gage, 100, 430
Break frequency, 206
Bridge circuit(s), 134–137, 535–537
diode, 247
ideal voltage/current drives, 145
inductance, 269
mass-flow meter, 499
operational amplifier, 322
Calibration:
accelerometers, 413–415, 418–422
Capacitive transducers: applications, 293–298, 599–601
with operational amplifiers, 318
Carrier (auxiliary) input, 67–70
types of, 260
Carrier systems, 246, 255, 263
Characteristics, static, 48–51
of resistance thermometers, 534
of thermocouples, 516
Charge amplifiers, 316–318, 409
Chopping, in pyrometers, 255, 554–556
in strain gage amplifier, 257
Common mode, 102–103, 371, 531
rejection ratio, 103, 310, 320
Comparative measurements, 105
Compensation, series, 219–224, 675
Computer-based instruments, 374
Constant current drive, 143, 145, 164, 282
Constant voltage drive, 143, 145, 282
Controlled-source transducers, 125
Correction, for dynamic data, See Dynamic data correction
Cross-correlation function, 476
Cross-sensitivity, 6, 631, 641–645
Current divider, 697
using operational amplifier, 323
Damping ratio, 190
from system parameters, 192–194
measurement of, 192
D’Arsonval movement, 191, 205, 271
Data acquisition systems, 368–375
Data logging, 371
Data transmission, 371, 531, 553–554
Dead band (dead zone), 56
Decibel (dB), 207
Decoder, 340
Delay, transport, 184
Demodulation, phase sensitive, 249
DeMorgan theorem, 333
Dial gage, 389
Differential equations:
characteristic equation, 731
solutions of, 729
complementary function, 731–732
general solution, 731
particular solution, 734
Differential measurement, 102–104
in noise reduction, 164
multiple transformer circuits, 253
signal demodulation, 249
Differentiator, RC network, 214–215
operational transformer, 313
Digital storage oscilloscope, 359
signal (positive logic), 326
Digital-to-analog converter, 245–247
Dimension measurement, 388–394
Diode bridge rectifier, 247–249, 683
Discrete Fourier transform (DFT), 362
Displacement measurements:
Displacement transducers:
gage blocks, 388
types, capacitive, 293–294, 601
Doppler flowmeters:
Drag-force flowmeter, 487
Dual slope ADC, 348
Dynamic compensation:
feedback compensation, 225
in hot-wire anemometer, 493
series compensation, 219–220, 223
rise time, 204
using transfer function, 228
Dynamic range, 54
Dynamometer, absorption, 90, 422
eddy current, 267
transmission, 423
Eddy current devices, 266–267, 270
Electric circuit elements, 705–708
Electrolytic flowmeter, 464
Electromagnetic flowmeter, 471
Emissivity, 547
Energy model, See Transducer models
Energy, auxiliary, 70
English-to-SI, tables, 32, 458
Environment and transducer, 4–7, 42
EPUT meter, 353
maximum, 82
systematic and random, 79
uncertainty analysis of, 81–88
Experimentation, objectives of, 23–25
Extensometer, 253
Fast Fourier transform (FFT), 361–363
Feedback compensation, 225, 493
Feedback effect:
on input/output impedance, 155
on component nonlinearity, 151–152
on system performance, 153–155
Feedback system:
hot-wire anemometer, 493
operational amplifier, 310
recorder, 357
Filters, active, 321
characteristics of, 159
laboratory experiment, 684–690
in noise reduction, 157
ringing of, 204
statistical, 159
First-order instruments:
frequency response, 206, 209–211
laboratory experiment, 666–669
time constant evaluation, 651–653
laboratory experiment, 653–655
Flexures:
for force sensing, 251–252, 444
for strain gage applications, 283, 629–631
Flexures, cross-sensitivity of, 631, 641–645
Flexure, energy model, 121
Flip-flops:
D type, 336
latch type, 335
J-K type, 337
Flow measurement methods:
direct, 460
indirect, 476
Flowmeter:
drag-force, 487
positive displacement, 461
Flowmeter calibration, 460
Flow-rate measurement, mass, 495
by density and volume, 496
direct mass flowmeters, 497–499
Fluid density measurements, 495–497
Force measurement:
basic principles, 415
Force transducer:
dynamic calibration of, 418–422
platform scale, 444
tool dynanometer, 11
Fourier series, 57, 226, 361, 735
Fourier transform:
symmetrical rules, 742
discrete Fourier transform, 362
fast Fourier transform, 361
inverse transform, 233, 740–742
Frequency domain analysis, See Frequency response
Frequency measurement, 352–353
Frequency modulation, 260–262, 678
measurement of, 193
Frequency response, 179, 205, 662–664
elementary transfer
general transfer function, 216–219
Frequency standard, 33
Functional stages, 9–11, 610–616
Gage, dimensional, 251, 268–270
Ground, instrument, 160
Hot-wire/hot-film anemometer, 491
constant current, 494
constant temperature, 493
Hydraulic servo, 149
Impedance:
bridge, 136
definition of, 108
Impedance head, 417
Impulse function, 182
frequency content of, 234
Incremental model, 61–65, 72–74
one-port device, 62
two-port device, 73
self-inductance, 265
Induction potentiometer, 274
Inductive transducers:
applications, 266–275, 602–605
basic types, 265
Inherent insensitivity, 162–163
Initial state (operating point):
effect on linearization, 61–64
of transistor amplifier, 128–131
cross-sensitivity of, 6
primary and secondary, 70
“guard” input, 371
Input coupling (AC/DC), 581–586
feedback effect on, 154
of voltage follower, 415
Input test signals, 182
Input/output coupling, 6, 631, 641–645
Instrument, classification of, 181
zero and sensitivity drift, 54
Integrated circuit, 306, 308, 556
Integrator:
operational amplifier, 312
Interferometry:
dimensional measurement, 392–394
laser velocimeter, 471
flow visualization, 463
International Practical Temperature Scale (IPTS-68), 33, 510
Kirchhoff’s voltage and current laws, 699–710, 714
Laminar flowmeter, 473
Least squares method, 49–51, 53
implications of, 53
Linear model, 62
Linearity drift, 54
Linearity, independent and proportional, 52–53
Liquid-in-glass thermometer, 236, 237
Liquid level transducers:
bubblers, 434
differential transformer, 252
Load cell, 251–252, 288, 416, 608
Loading, effects, 6–7, 74, 75, 111
Loading, in current measurement, 116
in displacement measurement, 117
in static force measurement, 115
in voltage measurement, 112–114, 579–581
LVDT, See Differential transformer
Magnetic shield, 161
Mass cancellation, 416
Mass flowmeter, 497
thermal, 473
bridge circuit, 499
Mass standard, 30
potential sensors for, 13
Measurement:
physical laws for, 41
Measurement methods, 12, 97–98
comparative method, 105
comparison of methods, 105–108
Measuring system:
functional stages of, 9–10, 610–617
structure of, 97
Mercury-in-glass thermometer, 236, 237, 511
stem correction, 512
Microphone, capacitive, 295
Mistakes, in measurement, 78
Modeling, of linear systems, 178–179
Modulation: (see also Carrier input)
amplitude modulation (AM), 246–249, 255–258
laboratory demonstration, 680–684
frequency modulation (FM), 260, 679
Modulation, in noise reduction, 165
Multimeter, d’Arsonval, 36, 571
digital, 573
in data acquisition, 368
Mutual inductance, 119
Natural frequency, 190, 192–193
Noise:
definition of, 5
in differential measurement, 102
sensitivity, 43
effect of initial state, 44
Noise reduction methods:
statistical, 159
information conversion, 165–167
inherent insensitivity, 162–163
Nomenclature, 29
effect of feedback, 151
effect on output signal, 57–61
Nonself-generating transducers, 67, 70, 125, 243
Ohmmeter circuit, 36
One-port device, Thevenin’s equivalent, 112–117
Operating point, See Initial state
Operational amplifier (op amp):
in charge amplifier, 316–318, 409
in instrument amplifier, 319
laboratory experiment, 690–693
Optical pyrometer, 550–552, 556
Oscillator, 573
Oscilloscope:
input coupling (AC/DC), 581–586
storage oscilloscope, 359
Output signal, 6
primary and secondary, 70
effect of feedback, 154
Output storage device, 358
effect of damping ratio, 194
PC-based instruments, 374
Period measurement, 352
Periodic input, response to, 226–228
Phase angle measurement, 352
Physical laws for sensing, 12–13
first-order effects, 41–46, 592
signal-to-noise ratio, 42
Taylor series expansion, 41–42
Piezoelectric, transducers, 403
material, 405
Pitot static tube, 104, 482–484
compressible flow, 484
Potentiometer, induction, 274
function generator, 597
Preamplifier, 314–315, 319, 344
Precision, definition of, 77
Pressure measurement, 423
related physical laws, 433
Pressure transducers:
types, bourdon tube, 101, 252, 430
capacitance, 294
inductance, 269
manometer, 428
for high pressure, 429
Pressure-to-force conversion, 435
in accelerometer, 435
measurement uncertainty, 547–549
type, broad-band, 548, 552, 555
narrow-band, 547, 550–552, 556
two-color (ratio), 550
Radioisotope flowmeter, 464
Ramp function, 182
Random error, 79
Range, dynamic, 54
Readibility, scale, 54
Recorder, strip-chart, 355
Rejection ratio, common-mode, 103
Resistance:
in parallel, 697
in series, 696
error sources, 538
standards, 535
Resistance measurement, 370–372, 537
Resistance transducers, 593–599
Resolution, 55
Resolver, 271
Rise time, 203
Root-mean-square (rms) value, 573–576, 712–713
Root-sum-square (rss) error, 82–85
Rosette, strain gage, 276, 622
strain-to-stress, 278, 622–624
Rotary differential transformer, 250
RTD, See Resistance thermometer
Sample-and-hold circuit, 343–344
Second-order instruments:
laboratory experiment, 673–674
laboratory experiment, 660–662
settling time, 661
coefficient, 515
Seismic instrument, 190, 398–401
acceleration measurement, 401
displacement measurement, 399
velocity measurement, 399
Self-generating transducers, 67, 70
physical laws for, 41
Sensitivity, definition of, 42, 184
drift, 47
effect of initial condition, 43–44
null and unbalance methods, 105–108
Sensors: (see also Transducers)
initial-boundary conditions, 19–20
primary and secondary, 10–11, 283
Settling time, 661
Shock tube, 440
Signal:
averaging, 159
definition of, 6
digital, 326
periodic, 226
transient, 233
sensitivity, 42
waveform reproduction, 196–198
Signal analyzer, 360
Signal conditioning, 10, 305, 370, 674
Signal-to-noise ratio (S/N), 42–44
in differential measurement, 103
Standard deviation, 51
Stefan-Boltzmann law, 542, 546
Step function, 182
frequency content of, 234
laboratory experiments, 651, 655
Strain gage:
applications, 283–290, 617–648
Strain gage circuits: (see also Transducer circuits)
resistance of components, 164, 284–285, 289
Stress-strain, biaxial, 276, 278, 618–621, 645–647
Strip-chart recorder, 355
Stroboscope, 356–358, 396, 607
Synchro transducer, 274
Systematic error, 79
Switch, electronic, 327
Tape recorder, magnetic, 354
Temperature standard (IPTS-68), 510
Temperature measurement:
accuracy, 33
methods of, 509
Test signals, 181–184, 233–236
material tolerance, 540
resistance versus temperature, 541
Thermocouple:
dynamic compensation, 221, 675–677
error sources, 521–522, 527–530
hardware compensation, 524
software compensation, 521–523
series-parallel circuit, 530
Thermocouple potentiometer, 98, 596
Thermometer:
integrated circuit (IC), 556
stem correction, 512
pressure, 513
resistance, 532
Thevenin’s equivalent, 109, 702–705
Three-port, See Transducer model
Time constant:
dynamic compensation of, 219–222
effect of, 188, 201, 206, 666, 668
evaluation of, 187–188, 206, 652–653, 668
hot-wire anemometer, 494
thermocouple, 650
Time interval measurement, 352
Time response:
analog data correction, 200–204
definition of, 21
laboratory experiment, 648–662
limitation of, 204
test signals, 181–184, 233–236
Torque measurement, 287, 294, 422–425
Torr, 427
Transducers, definition of, 11
interaction with environment, 4–7, 19, 41–42, 81
Transducer circuits:
ballast circuit, 35, 141–144, 282
ideal power source, 143, 144–147
non-ideal power source, 144
controlled source (amplifier), 125–127
dynamic model, 177–179, 181, 205
one-port, 112
two-port, 118
three-port, 125
incremental model, 61–64, 72–74
null-balance method model, 99
unbalance method model, 102
self-/nonself-generating, 67, 70
Thevenin’s, 109
Bode plots, 206
Transients:
frequency contents of, 228–231
system response, 233
Transport delay, 184
True waveform reproduction, 196–198
Truth table, 329, 332, 336, 338
Turbine flow meter, 488–489, 498–499
Two-port device, 70–74, 117–118
Ultra-sonic flowmeter, 466–470
Uncertain analysis:
Uncertainty analysis, applications:
alternative test method, 86
estimation in design, 85
Uncertainty, in pryometry, 547–548
Units, definition of, 29
Velocity (motion) transducers:
miscellaneous, 397
stroboscope, 396
vibrating wedge, 396
Vernier caliper, 389
Viscosity, absolute (dynamic), 458
kinematic, 458
Viscosity meter, 436
Voltage follower, 314–315, 319, 344
Voltage divider, 696
Voltage measurement, 112–114, 579–581
Vortex-shedding flowmeter, 489–491
Waveform reproduction, 196–198
Wheatstone bridge, 135
Wien’s radiation law, 545
Window, sampling, 367
X-Y plotter, 356
Zero-order instrument, 184
demonstration,
frequency domain, 665
time domain, 650