1. Ch 02 Basic Sensors and Principles

3. 2.1 Displacement measurements
2.2 Resistive (2.2)
2.4 Inductive (2.4)
2.5 Capacitive (2.5)
2.6 piezoelectric (2.6)
2.7 Temperature measurements
* 2.8 Thermocouples
* 2.9 Thermistors
* 2.10 Radiation thermometry
* 2.11 Fiber-optic temperature

4. 2.1 Displacement Measurements

5. 2.2 Resistive Sensors

6. Potentiometric devices for measuring displacements
Translational displacement measurement
Rotational displacement measurement

7. Strain Gages
Nanometer

8. Piezoresistive effect
Gage factor: G
Poisson’s ratio
Dimensional effect
Piezoresistive effect
(due to strain-induced change in the lattice structure of the material)

9. c
Diaphragm R2 R1 Rx A ui b a B Ry R3 R4
Armature d C D Ri
D uo
(a)
Strain-gage wires
(b)
Figure 2.2 (a) Unbonded strain-gage pressure sensor. The diaphragm is directly coupled by an armature to an unbonded strain-gage system. With increasing pressure, the strain on gage pair B and C is increased, while that on gage pair A and D is decreased. (b) Wheatstone bridge with four active elements. R1 = A, R2 = B, R3 = D, and R4 = C when the unbonded strain gage is connected for translation motion. Resistor Ry and potentiometer Rx are used to initially balance the bridge. vi is the applied voltage and Dv0 is the output voltage on a voltmeter or similar device with an internal resistance of Ri.

10. Figure 2. 3 Typical bonded strain-gage units (a) Resistance-wire type
Figure 2.3 Typical bonded strain-gage units (a) Resistance-wire type. (b) Foil type. (c) Helical-wire type. Arrows above units show direction of maximal sensitivity to strain.[Parts (a) and (b) are modified from Instrumentation in Scientific Research, by K. S. Lion. Copyright  1959 by McGraw-Hill, Inc. Used with permission of McGraw-Hill Book Co.] 

11. Semiconductor strain gages
Good or Bad?
Higher gage factor
G B
Greater resistivity-temperature coefficient
Higher nonlinearity

12. Semiconductor strain-gage units
(a) Unbonded, uniformly doped.
(b) Diffused p-type gage.
Pressure 1
Pressure 2
(d) Integrated cantilever-beam force sensor.
c) Integrated pressure sensor.

13. Semiconductor strain-gage units (cont.)
Pressure 1
Pressure 2
High sensitivity
Good temperature compensation
c) Integrated pressure sensor.

15. Figure 2.5 Mercury-in-rubber strain-gage plethysmography (a) Four-lead gage applied to human calf. (b) Bridge output for venous-occlusion plethysmography. (c) Bridge output for arterial-pulse plethysmography. [Part (a) is based on D. E. Hokanson, D. S. Sumner, and D. E. Strandness, Jr., "An electrically calibrated plethysmograph for direct measurement of limb blood flow." 1975, BME-22, 25-29; used with permission of IEEE Trans. Biomed. Eng., 1975, New York.]

16. vo = R/R0  vi , where R0 = R1 = R2 = R3 = R4 2.3 Bridge Circuitsa R4
D uo ui R3 R2 Ry Ri Rx R1 c
R2  R
R1 + R Rx ui b a Ry
R2 + R
R4  R d Ri
D uo
vo = R/R0  vi
, where R0 = R1 = R2 = R3 = R4
Figure 2.2 (b) Wheatstone bridge
vi  the applied voltage; Dv0  the output voltage on a voltmeter ; Ri  the internal resistance of the voltmeter ; Resistor Ry and potentiometer Rx  to initially balance the bridge.
Rx > 10 Rk, k = 1,2, 3, or 4.
Ry > 25 Rk, k = 1,2, 3, or 4.

17. 2.4 Inductive Displacement Sensors
L = n2Gµ
N: number of turns
G: geometric form factor
u: effective permeability
Inductive Displacement Sensors
Advantage:
not affected by the dielectric properties of the environment
Disadvantage:
affected by external magnetic field
Fig. 2.7(a) Self-inductance
Principle
Changing the geometric form factor or moving a magnetic core within the coil  alteration in self-inductance
Property
Change of inductance vs displacement： not linear
Advantage:
1. Low power requirement
2. produces large variations in inductance
Applications:
radiotelemetry

18. Fig. 2.7(b) Mutual-inductance
Principle：
Induced voltage in the secondary coil is a function of ：
coil geometry (seperation and axial alignment), numbers of primary and secondary turns, frequency and amplitude of the excitation voltage,
Property：
Induced voltage in the 2nd coil vs coil seperation: nonlinear
Trick：
To maximize the output signal ： choose the resonance frequency of the secondary coil
Applications:
Cardiac dimension, infant respiration, arterial diameter

19. Fig. 2.7(C) LVDT (Linear variable differential transformer)
To measure:
Pressure, displacement, force
Principle：
Motion of a high permeability alloy slug between the two secondary coils  Change the coupling between them
Trick：
To widen the region of linearity： connect the two coils in opposition
Property：
Linearity over a large range, a change of phase by 180 (when the core passes through the central position), saturation on the end
How good？
(0.5 to 2 mV)/(0.01 mm/V), displacement 0.1 to 250 mm, 0.25% linearity
Advantage:
A much higher sensitivity than that of a strain gage
Disadvantage:
More complex signal processing
(needs a phase-sensitive demodulator to determine the direction of displacement)

20. a a c c c b a b c c d b d d d d e
(a)
(b)
(c)
Figure 2.6 Inductive displacement sensors (a) Self-inductance. (b) Mutual inductance. (c) Differential transformer.

21. V: a phase-sensitive demodulator
X: Rectifier
V: a phase-sensitive demodulator a b e d c a b e d c
Figure 2.7 (a) As x moves through the null position, the phase changes 180 , while the magnitude of vo is proportional to the magnitude of x. (b) An ordinary rectifier-demodulator cannot distinguish between (a) and (b), so a phase-sensitive demodulator is required.

22. 2.5 Capacitive Sensors

23. Capacitive microphone
Figure 2.8 Capacitance sensor for measuring dynamic displacement changes

24. Biomedical applications: ?

25. 2.6 Piezoelectric Sensors
Distortion of asymmetrical crystal lattice
 charge reorientation
 relative displacement of + & - charges
 surface charges of opposite polarity on opposite sides

26. Source: http://newenergyandfuel

27. Piezoelectric effect
Tension = A force tending to stretch or elongate something
Source:

28. The direct piezoelectric effect is seen as a produced voltage when the material is under tension or compression stress.  Each of these two types of stress generate opposite polarity voltages in the crystal.  The inverted effect also occurs - this is when a potential difference is applied across the crystal and causes it to deform.
The deformation of the material brings the polarised dipoles closer into line, so that the positive and negative ends come closer together.  As this happens the electric dipoles have a cumulative effect and a potential difference is set up over the whole crystal.  The potential difference set up causes a positive charge at one end and a negative charge at the other end of the material.
The indirect or inverse piezoelectric occurs by exactly the opposite mechanism.  A potential difference is placed across the material and at a great enough difference the electric field within the material will then create a large enough force on the dipoles to move them into alignment to lower the energy of the arrangement.  The voltage needed to cause this effect is greater than the potential used for the initial poling process.  This effect is also impermanent - there is an elastic relaxation to the original shape when the potential difference is removed, whereas a poled material remains poled even when the field is removed.

29. q = k f (k: piezoelectric constant, C/N, coulomb/newton) (2.13)
Cv = k f
v = k f / C = k f / (0 r A / x) = k f x / (0 r A) (2.14)
q = Cv
v = voltage change
f : applied force
x: deflection
k: piezoelectric constant, coulomb/newton (C/N)

30. Equivalent circuit Rs = sensor leakage resistance
x: deflection
Amplifier
Cable e
Crystal x
q: generated charge
K: proportionality constant, C/m
x: deflection
Amplifier
(a)
Charge
generator
q = Kx Rs Cs Cc Ca +
iAmplifier = 0 uo  Ra
Rs = sensor leakage resistance
Cs = sensor capacitance
Cc = cable capacitance Ca = amplifier input capacitance Ra = amplifier input resistance
(b)
R = Ra Rs /(Ra+ Rs ) » Ra
C = Cs + Cc + Ca
Current
generator
is = Kdx/dt is C R iC iR +
ia= 0 uo 

31. Equivalent circuit LPF? HPF? Ks = K/C = (q/x)/C = Cq/x = V/x Unit: V/m
(b)
R = Ra Rs /(Ra+ Rs ) » Ra
C = Cs + Cc + Ca
Current
generator
is = Kdx/dt is C R iC iR +
ia= 0 uo 
LPF?
HPF?
Ks = K/C = (q/x)/C = Cq/x = V/x
Unit: V/m
Ks (= K/C): sensitivity, V/m
 (= RC): time constant, s

32. Example 2.2 Amplifier (a) Charge generator q = Kx Rs Cs Cc Ca +
iAmplifier = 0 uo  Ra
Example 2.2 A piezoelectric sensor has C = 500 pF. The sensor leakage resistance is 10 G. The amplifier input impedance is 5 M. What is the low corner frequency?
Ans:

33. Figure Sensor response to a step displacement (From Measurement Systems: Application and Design, by E. O. Doebelin. Copyright  1990 by McGraw-Hill, Inc. Used with permission of McGraw-Hill Book Co.)

34. High-frequency circuit model
Mechanical
resonance
Output voltage
Input force Lm Cm Cs Rt Rm
Usable
range
f c
Frequency
(a)
(b)

35. Mechanical
resonance
Output voltage
Input force Lm Cm Cs Rt Rm
Usable
range
f c
Frequency
(a)
(b)
Figure (a) High-frequency circuit model for piezoelectric senor. Rs is the sensor leakage resistance and Cs the capacitance. Lm, Cm, and Rm represent the mechanical system. (b) Piezoelectric sensor frequency response. (From Transducers for Biomedical Measurements: Application and Design, by R. S. C. Cobbold. Copyright  1974, John Wiley and Sons, Inc. Used by permission of John Wiley and Sons, Inc.)

36. Biomedical applications: ?

37. 2.7 Temperature Measurements
* 2.8 Thermocouples
* 2.9 Thermistors
* 2.10 Radiation thermometry
* 2.11 Fiber-optic temperature

39. 2.8 Thermocouples
Thermocouple:
Advantages:
Fast response time (Tc: 1 ms)
Small size (Diameter: 12 um)
Long-term stability
Ease of fabrication
Disadvantages:
Small output voltage
low sensitivity
Need for a reference temperature

40. Thermoelectric thermometry
Seebeck (1821) discovered an emf (electromotive force) across a junction of two dissimilar metals
Peltier emf: an emf due solely to the contact of two unlike metals and the junction temperature
Net Peltier emf  (T1 – T2)
Thomson (Lord Kelvin) emf: an emf due to the temperature gradient along each single conductor
Net Thomson emf  (T1 – T2)^2
Seebeck voltage: (By empirical calibration))
E = a T + (1/2) b T^2 + …

41. Empirical thermocouple laws
Homogeneous circuits
Intermediate metals
Intermediate (or successive) temperature
In a circuit composed of a single homogeneous metal, one cannot maintain an electric current by the application of heat alone
Same emf
Lead wires may be attached to the thermocouple without affecting the accuracy of the measured emf
The net emf in a circuit consisting of an interconnection of a number of unlike metals, maintained at the same temperature, is zero.
Calibration curves derived for a given reference-junction temperature can be used to determine the calibration curves for another reference temperature.

42. Cold Junction
Source:
Source:

43. Thermocouple Cold Junction Compensator
An electrically simulated cold junction

44. 2.9 Thermistors
Thermistors:
ceramic semiconductor with negative temperature coefficient
Advantages:
small size (0.5 mm)
large sensitivity (-3 to -5 %/C)
long-term stability (0.2% of nominal resistance value per year)
Disadvantages:

47. zero-power resistance
Thermistor temperature > ambient temperature.
Thermal destruction may occur！
0.001
0.01
0.1 1 10
100
1000
Temperature, ° C
(a)
Resistance ratio, R/R25º C 
zero-power resistance
Ohm’s law applies.
Thermistor temperature = ambient temperature.
Various materials
0.1
1.0 10
100
0.10
Water
Air
0.1 mW
1 mW
10 mW
100 mW
1 W
100 W
1 kW
10 kW
100 k W
1 M W A C B
Current, mA
(b)
10.0
100.0
Figure (a) Typical thermistor zero-power resistance ratio-temperature characteristics for various materials. (b) Thermistor voltage-versus-current characteristic for a thermistor in air and water. The diagonal lines with a positive slope give linear resistance values and show the degree of thermistor linearity at low cerrents. The intersection of the thermistor curves and the diagonal lines with the negative slope give the device power dissipation. Point A is the maximal current value for no appreciable self-heat. Point B is the peak voltage. Point C is the maximal safe continuous current in air. [Part (b) is from Thermistor Manual, EMC-6,  1974, Fenwal Electronics, Framinham, MA; used by permission.]

48. 2.10 Radiation Thermometry
Known relationship
Surface temperature of an object
Radiant power of the object
 Contactless measurement of body temperature
Every body above absolute zero radiates electromagnetic power.
Blackbody: an ideal thermal radiator; absorbs all incident radiation and emits the maximal possible thermal radiation

50. Visible light 390 to 750 nm (400 to790 THz)
0.001
0.002
0.003 10
(a)
Wavelength, mm 15 20
T = 300 K
m= mm 25 40 60 80
100%
% Total power
Spectral radient emittance, W-cm-2·mm-1
Visible light 390 to 750 nm (400 to790 THz) 1 10 50
100
(b)
Fused silica
Sapphire
Arsenic trisulfide
Thallium
bromide
iodine
Wavelength, mm 1 2 3
Wavelength, mm
(c)
Indium antimonide (InSb)
(photovoltaic)
Lead sulfide (PbS)
All thermal detectors 20 60
100 4 5 6 7 8
Figure (a) Spectral radiant emittance versus wavelength for a blackbody at 300 K on the left vertical axis; percentage of total energy on the right vertical axis. (b) Spectral transmission for a number of optical materials. (c) Spectral sensitivity of photon and thermal detectors.

51. A chopper amplifier is a system that transforms signals coming through direct current systems into alternating currents in order to efficiently boost the signal gain. While it is possible to boost the gain on a direct current system, these modifications often increase signal noise and decrease the stability of the signal. The most likely place to come across a chopper amplifier is in high-end electronic signal equipment and heavy machinery that rely on precisely-timed movements. Chopper circuits, the parts that turn a standard amplifier into a chopper amplifier, are also found in a number of other devices. [
将微弱的直流转换为交流, 然后放大
Chopper Amplifier is a device which convert low level signal or frequncy into high level frequncy.ac & d.c both
These are DC amplifiers. Some types of signal that need amplifying can be so small that an incredibly high gain is required, but very high gain DC amplifiers are much harder to build with low offset and 1/f noise, and reasonable stability and bandwidth. It's much easier to build an AC amplifier instead. A chopper circuit is used to break up the input signal so that it can be processed as if it were an AC signal, then integrated back to a DC signal at the output. In this way, extremely small DC signals can be amplified. This approach is often used in electronic instrumentation where stability and accuracy are essential; for example, it is possible using these techniques to construct pico-voltmeters and Hall sensors. [

52. Stationary chopped-beam radiation thermometer
Figure 2.17 Stationary chopped-beam radiation thermometer

53. Ear thermometer (耳溫槍)
Purpose： to determine the internal or core body temperature
What is measured：
Infrared radiation emitted from
Tympanic membrane (耳膜) and surrounding ear canal
Hypothalamus： body’s main thermostat regulating the core body temperature

54. Ear thermometer (耳溫槍) (cont.)
Mercury thermometer
Thermocouple
Thermistor
Measure the temperature of the sensor
In contact with the subject
Infrared thermometer
Detects the emitted energy ( proportional to the actual temperature)
Response time ~ 0.1 s
Accuracy ~ 0.1 C

55. Infrared detectors Infrared detector Thermal detector Low sensitivity
All wavelength responsive
Photon detector
(Quantum detector)
* Limited wavelength band 1 2 3
Wavelength, mm
(c)
Indium antimonide (InSb)
(photovoltaic)
Lead sulfide (PbS)
All thermal detectors 20 60
100 4 5 6 7 8

57. Figure 2.16 Details of the fiber/sensor arrangement for the GaAs semiconductor temperature probe.

58. Figure 2. 17 (a) General block diagram of an optical instrument
Figure 2.17 (a) General block diagram of an optical instrument. (b) Highest efficiency is obtained by using an intense lamp, lenses to gather and focus the light on the sample in the cuvette, and a sensitive detector. (c) Solid-state lamps and detectors may simplify the system.

59. Figure 2.18 Spectral characteristics of sources, filters, detectors, and combinations thereof (a) Light sources, Tungsten (W) at 3000 K has a broad spectral output. At 2000 K, output is lower at all wavelengths and peak output shifts to longer wavelengths. Light-emitting diodes yield a narrow spectral output with GaAs in the infrared, GaP in the red, and GaAsP in the green. Monochromatic outputs from common lasers are shown by dashed lines: Ar, 515 nm; HeNe, 633 nm; ruby, 693 nm; Nd, 1064 nm; CO2 (notshown), nm. (b) Filters. A Corning 5-65 glass filter passes a blue wavelength band. A Kodak 87 gelatin filter passes infrared and blocks visible wavelengths. Germanium lenses pass long wavelengths that cannot be passed by glass. Hemoglobin Hb and oxyhemoglobin HbO pass equally at 805 nm and have maximal difference at 660 nm. (c) Detectors. The S4 response is a typical phototube response. The eye has a relatively narrow response, with colors indicated by VBGYOR. CdS plus a filter has a response that closely matches that of the eye. Si p-n junctions are widely used. PbS is a sensitive infrared detector. InSb is useful in far infrared. Note: These are only relative responses. Peak responses of different detectors differ by 107. (d) Combination. Indicated curves from (a), (b), and (c) are multiplied at each wavelength to yield (d), which shows how well source, filter, and detector are matched. (e) Photon energy: If it is less than 1 eV, it is too weak to cause current flow in Si p-n junctions.

60. Figure 2. 19 Forward characteristics for p-n junctions
Figure 2.19 Forward characteristics for p-n junctions. Ordinary silicon diodes have a band gap of 1.1 eV and are inefficient radiators in the near-infrared. GaAs has a band gap of 1.44 eV and radiates at 900 nm. GaP has a band gap of 2.26 eV and radiates at 700 nm.

61. Coating n2
Air
n = 1.0 2
ic
Fiber 1 4 3 n1
Figure 2.20 Fiber optics. The solid line shows refraction of rays that escape through the wall of the fiber. The dashed line shows total internal reflection within a fiber.

62. 2.16 Radiation Sensors Radiation sensor Thermal sensor
Receives radiation  transforms into heat  Rise of sensor’s temperature
Thermistor, thermocouple, pyroelectric (焦電) sensor
Quantum sensor
Absorbs energy from individual photons  releases electrons from sensor material
Eyes, phototube, photodiode, photographic emulsion (感光乳劑 )

63. Figure 2.21 Photomultiplier An incoming photon strikes the photocathode and liberates an electron. This electron is accelerated toward the first dynode, which is 100 V more positive than the cathode. The impact liberates several electrons by secondary emission. They are accelerated toward the second dynode, which is 100 V more positive than the first dynode, This electron multiplication continues until it reaches the anode, where currents of about 1 mA flow through RL.

64. Figure 2.22 Voltage-current characteristics of irradiated silicon p-n junction. For 0 irradiance, both forward and reverse characteristics are normal. For 1 mW/cm2, open-circuit voltage is 600 mV and short-circuit current is 8 mA.