Bài giảng Sensors and analytical devices - Part B: Sensors Characteristics - Nguyễn Công Phương
A car is equiped with altitude & temperature sensors & associated measurement
systems. It is traveling up a hill at a constant vertical speed of 3.6 km/h. The
temperature at the bottom of the hill is 20oC, Tx(x) = 20oC – 0.1x. The altitude
sensing system is a zero – order response. The temperature sensing system has a
first – order response with τ = 10s.
a) What are the temperature & height measurements at 10, 20, 30, & 40s?
b) What are the temperature measurements if τ = 1s?
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Nguyễn Công Phương
Sensors and Analytical Devices
Sensors Characteristics
Contents
A. Introduction
B. Sensors Characteristics
I. Static Characteristics
II. Dynamic Characteristics
C. Some Basic Measurement Methods
D. Measurement Systems
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Static Characteristics
1. Accuracy
2. Precision
3. Repeatability
4. Reproducibility
5. Stability
6. Error
7. Noise
8. Drift
9. Resolution
10. Minimum detectable signal
11. Calibration curve
12. Sensitivity
13. Linearity
14. Selectivity
15. Hysteresis
16. Measurement range
17. Response & recovery time
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Accuracy
• Accuracy: the correctness of a sensing system’s output
in comparison to the actual value of a measurand.
• To assess the accuracy:
– The system is benchmarked against a standard measurand,
or
– The output is compared with a measurement system with a
superior accuracy
More accurate
Less accurate
25_meter_precision_and_50_meter_pistol_target-svg/
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Precision
• Precision: the capacity of a sensing system to give
the same reading when repetively measuring the
same measurand under the same condition.
• It is a statistical parameter & can be assessed by
the standard deviation (variance) of a set of
readings of the system for similar inputs
Low precision High precision High precision
Low accuracy Low accuracy High accuracy
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Repeatability
• When all operating & environmental
conditions remain constant, repeatability is the
sensing system’s ability to produce the same
response for successive measurements.
• It is closely related to precision.
Temperature
The actual
temperature
10:00 10:02 20:00 20:02 Time
10:01 20:01
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Reproducibility
• The sensing system’s ability to produce the
same responses after measurement conditions
have been altered.
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Stability
• The sensing system’s ability to produce the
same output value when measuring the same
measurand over a period of time.
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Static Characteristics
1. Accuracy
2. Precision
3. Repeatability
4. Reproducibility
5. Stability
6. Error
7. Noise
8. Drift
9. Resolution
10. Minimum detectable signal
11. Calibration curve
12. Sensitivity
13. Linearity
14. Selectivity
15. Hysteresis
16. Measurement range
17. Response & recovery time
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Error
• Error is the difference between the actual
value of the measurand and the value produced
by the sensing system.
• It can be systematic or random.
Absolute error Output Truevalue
Output Truevalue
Relative error
Truevalue
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Noise
• Noise: the unwanted fluctuations in the output signal of the
sensing system, when the measurand is not changing.
• Electronic noise: thermal energy causes charge carriers to
move in random motion, which results in random variations
of current and/or voltage.
• Shot noise: the random fluctuations, which are caused by
the carriers’ random arrival time, produce shot noise.
• Generation – recombination noise: it is produced from the
generation & recombination of electrons & holes in
semiconductors
• Pink noise (or 1/f noise): in this type of noise the
components of the frequency spectrum of the interesting
signals are inversely proportional to the frequency.
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Drift
• It is observed when a gradual change in the
sensing system’s output is seen, while the
measurand actually remains constant.
• It is the undesired change that is unrelated to
the measurand.
Temperature
The actual
temperature
Time
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Resolution
• Resolution (sometimes discrimination): the
minimal change of the measurand that can
produce a detectable increment in the output
signal.
• It is strongly limited by any noise in the signal.
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Minimum Detectable Signal
• Minimum Detectable Signal (MDS) is the
minimum signal increment that can be
observed, when all interfering factors are taken
into account.
• When the increment is assessed from zero, the
value is generally referred to as threshold or
detection limit.
• If the interferences are large relative to the
input, it will be difficult to extract a clear
signal & small MDS can not be obtained.
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Static Characteristics
1. Accuracy
2. Precision
3. Repeatability
4. Reproducibility
5. Stability
6. Error
7. Noise
8. Drift
9. Resolution
10. Minimum detectable signal
11. Calibration curve
12. Sensitivity
13. Linearity
14. Selectivity
15. Hysteresis
16. Measurement range
17. Response & recovery time
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Calibration Curve
• Calibration curve: the relationship between the
measured variable x & the signal variable
generated by the system y.
• A sensing system has to be calibrated against a
known measurand to assure that the sensing
results in correct outputs.
y
x
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Sensitivity
• Sensitivity: the ratio of the incremental change
in the sensor’s output (Δy) to the incremental
change of the measurand in input (Δx).
• An ideal sensor has a large & preferably
constant sensitivity in its operating range.
y y
x
x
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Linearity
• Linearity: the closeness of the calibration
curve to a specified line.
• The degree of resemblance to a straight line
describes how linear a system is.
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Selectivity
• Selectivity: the sensing system’s ability to
measure a target measurand in the presence of
other interferences.
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Hysteresis
• Hysteresis: the difference between output
readings for the same measurand, depending
on the trajectory followed by the sensor.
• It may cause false & inaccurate readings.
y
x
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Measurement Range
• Measurement range (dynamic range or span):
the maximum & minimum values of the
measurand that can be measured with a
sensing system.
• All sensing systems are designed to perform
over a specified range.
• Signals outside of this range may be
unintelligible, cause unacceptably large
inaccuracies, & may even result in irreversible
damage to the sensor.
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Response and Recovery Time
• Response time: the time a sensing system
requires to reach a stable value when it is
exposed to a measurand.
• Recovery time: the time a sensing system
requires to reach a stable value when it is no
longer exposed to a measurand.
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Contents
A. Introduction
B. Sensors Characteristics
I. Static Characteristics
II. Dynamic Characteristics
C. Some Basic Measurement Methods
D. Measurement Systems
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Dynamic Characteristics (1)
• Applied to time – varying measurands.
• To describe the sensing system’s transient
properties.
• Can be used to define how accurately the
output signal is employed for the description
of a time – varying measurand.
• Deal with issues such as the rate at which the
output changes in response to a measurand
alteration, and how these changes occur.
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Dynamic Characteristics (2)
x() t Linear time invariant y() t
(LTI) system
dn y()()() t d n1 y t dy t
a a ... a a y ( t )
ndtn n1 dt n1 1 dt 0
dm1 x()()() t d m 2 x t dx t
b b ... b b x ( t ) b
mdtm1 m1 dt m 2 2 dt 1 0
x() t
t
dn y()()() t d n1 y t dy t
a a ... a a y ( t ) b
ndtn n1 dt n1 1 dt 0 1
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Dynamic Characteristics (3)
x() t Linear time invariant y() t
(LTI) system
b1
a0 y( t ) b 1 or y ( t ) K
a0
Zero – order system
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Dynamic Characteristics (4)
x() t Linear time invariant y() t
(LTI) system
dy() t
a a y() t b (First – order system)
1dt 0 1
a1 dy() t b 1
y() t 1
a0 dt a 0
dy() t 0.8
y(), t K 1
dt 0.6 K(1 1/ e ) 0.6321 K
a b y(t)
1; K 1
0.4
a0 a 0
t
0.2
y( t ) K (1 e )
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
t (s)
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Dynamic Characteristics (5)
Ex.
A car is equiped with altitude & temperature sensors & associated measurement
systems. It is traveling up a hill at a constant vertical speed of 3.6 km/h. The
o o
temperature at the bottom of the hill is 20 C, Tx(x) = 20 C – 0.1x. The altitude
sensing system is a zero – order response. The temperature sensing system has a
first – order response with τ = 10s.
a) What are the temperature & height measurements at 10, 20, 30, & 40s?
b) What are the temperature measurements if τ = 1s?
vx 3.6km/h 1m/s
x( t ) vx t 1 t t
x
dy() t
y()() t x t
dt
dTm () t
10Tm ( t ) T x ( t )
dt T() t T() t
x Linear time invariant m
20 0.1x
(LTI) system y() t
20 0.1t x() t
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Dynamic Characteristics (6)
Ex.
A car is equiped with altitude & temperature sensors & associated measurement
systems. It is traveling up a hill at a constant vertical speed of 3.6 km/h. The
o o
temperature at the bottom of the hill is 20 C, Tx(x) = 20 C – 0.1x. The altitude
sensing system is a zero – order response. The temperature sensing system has a
first – order response with τ = 10s.
a) What are the temperature & height measurements at 10, 20, 30, & 40s?
b) What are the temperature measurements if τ = 1s?
dT() t dT() t
10m T ( t ) 20 0.1 t m 0.1T ( t ) 2 0.01 t
dt m dt m
0.1dt
()t e e0.1t
e0.1t (2 0.01 t ) dt C 2e0.1t dt 0.01 te 0.1 t dt C
T() t
m e0.1t e0.1t
20e0.1t 0.1 tde 0.1 t C 20e0.1t 0.1 te 0.1 t e 0.1 t dt C
e0.1t e0.1t
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Dynamic Characteristics (7)
Ex.
A car is equiped with altitude & temperature sensors & associated measurement
systems. It is traveling up a hill at a constant vertical speed of 3.6 km/h. The
o o
temperature at the bottom of the hill is 20 C, Tx(x) = 20 C – 0.1x. The altitude
sensing system is a zero – order response. The temperature sensing system has a
first – order response with τ = 10s.
a) What are the temperature & height measurements at 10, 20, 30, & 40s?
b) What are the temperature measurements if τ = 1s?
20e0.1t 0.1 te 0.1 t e 0.1 t dt C 20e0.1t 0.1 te 0.1 t 10 e 0.1 t C
T() t
m e0.1t e0.1t
21 0.1t Ce0.1t
21 0.1 0 Ce0.1 0 20
o
Tm (0) 20 C
C 1
0.1t
Tm ( t ) 21 0.1 t e
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Dynamic Characteristics (8)
Ex.
A car is equiped with altitude & temperature sensors & associated measurement
systems. It is traveling up a hill at a constant vertical speed of 3.6 km/h. The
o o
temperature at the bottom of the hill is 20 C, Tx(x) = 20 C – 0.1x. The altitude
sensing system is a zero – order response. The temperature sensing system has a
first – order response with τ = 10s.
a) What are the temperature & height measurements at 10, 20, 30, & 40s?
b) What are the temperature measurements if τ = 1s?
o o 0.1t
Tx( x ) 20 C 0.1 t ; T m ( t ) 21 C 0.1 t e
Time (s) Altitude (m) Real temp (oC) Measured temp (oC) Temp error (oC)
0 0 20 20 0
10 10 19 19.6321 0.6321
20 20 18 18.8647 0.8647
30 30 17 17.9502 0.9502
40 40 16 16.9817 0.9817
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Dynamic Characteristics (9)
Ex.
o o 0.1t
Tx( x ) 20 C 0.1 t ; T m ( t ) 21 C 0.1 t e
20 Actual temperature
Measured temperature
C)
o 19
18
Temperature ( 17
16
0 5 10 15 20 25 30 35 40
Time (s)/Altitude (m)
1
C)
o
0.8
0.6
0.4
0.2
Temperature error (
0
0 5 10 15 20 25 30 35 40
Time (s)/Altitude (m)
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Dynamic Characteristics (10)
Ex.
A car is equiped with altitude & temperature sensors & associated measurement
systems. It is traveling up a hill at a constant vertical speed of 3.6 km/h. The
o o
temperature at the bottom of the hill is 20 C, Tx(x) = 20 C – 0.1x. The altitude
sensing system is a zero – order response. The temperature sensing system has a
first – order response with τ = 10s.
a) What are the temperature & height measurements at 10, 20, 30, & 40s?
b) What are the temperature measurements if τ = 1s?
o o 0.1t
Tx( x ) 20 C 0.1 t ; 10 T m ( t ) 21 C 0.1 t e
o o t
Tx( x ) 20 C 0.1 t ; 1 T m ( t ) 20.1 C 0.1 t 0.1 e
Time (s) Altitude (m) Real temp (oC) Measured temp (oC) Temp error (oC)
0 0 20 20 0
10 10 19 19.1 0.1
20 20 18 18.1 0.1
30 30 17 17.1 0.1
40 40 16 16.1 0.1
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Dynamic Characteristics (11)
= 10 = 1
20 Actual temperature 20 Actual temperature
Measured temperature Measured temperature
C) C)
o 19 o 19
18 18
Temperature ( 17 Temperature ( 17
16 16
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40
Time (s)/Altitude (m) Time (s)/Altitude (m)
C) 1 C) 1
o o
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
Temperature error ( Temperature error (
0 0
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40
Time (s)/Altitude (m) Time (s)/Altitude (m)
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Dynamic Characteristics (12)
x() t Linear time invariant y() t
(LTI) system
d2 y()() t dy t
a a a y() t b (Second – order system)
2dt2 1 dt 0 1
1d2 y ( t ) 2 dy ( t )
y() t K
2dt 2 dt
a
2 0 : the undamped naturalfrequency
a2
a
1 a a : thedampening ratio
2 0 2
b
K 1
a0
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Dynamic Characteristics (13)
1d2 y ( t ) 2 dy ( t )
y() t K
2dt 2 dt
2
1.8
1.6
1.4
1.2
1
y(t)/K
0.8
= 0
0.6 = 0.1
= 0.2
0.4 = 0.4
= 1.0
0.2 = 2.0
= 0.707
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time (s)
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Các file đính kèm theo tài liệu này:
- bai_giang_sensors_and_analytical_devices_part_b_sensors_char.pdf