3. Measurement Methods 43
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Transcript of 3. Measurement Methods 43
1
With the deflection method, the result of the measurement is
entirely determined by the readout of the measurement device.
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
3. MEASUREMENT METHODS
3.1. Deflection, difference, and null methods
Reference: [1]
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0
The linearity of the entire scale is important.
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The difference method indicates only the difference between
the unknown quantity and the known, reference quantity.
Here, the result of the measurement is partially determined by
the readout of the measurement device and partially by the
reference quantity.
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Reference: [1]
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0
10
0
Reference
The linearity of a part of the scale is important.
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With the null method, the result is entirely determined by a
known reference quantity. The readout of the measurement
instrument is used only to adjust the reference quantity to
exactly the same value as the known quantity. The indication is
then zero and the instrument is used as a null detector.
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Reference: [1]
10
0
10
0
Reference
The linearity of the scale is not important.
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(a)
100 mm ±103
100 mm
Inaccuracy: ±100 m Inaccuracy:
Example A: )a( deflection, )b( difference, and )c( null measurements
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
5
00
(b)
1 mm ±103
Reference
99 mm ±105
Inaccuracy: ±100 m Inaccuracy:
Example A: )a( deflection, )b( difference, and )c( null measurements
(a)
100 mm ±103
100 mm
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
±1 ±1 m
6
00
(b)
1 mm ±103
Reference
99 mm ±105
00
(c)
0 mm ±103
Reference
100 mm ±105
Inaccuracy: ±100 m Inaccuracy: Inaccuracy: ±100 m ±1 ±1 m
Example A: )a( deflection, )b( difference, and )c( null measurements
(a)
100 mm ±103
100 mm
Null method: linearity is not important;sensitivity and zero drift are important.
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
±0 ±1 m
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Example B: Null measurements, C=0, P0=FA
C1 C2
Oil
Membrane
F = m·g
Null method: linearity is not important;sensitivity and zero drift are important.
Pressure, P0
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
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Example C: Difference measurements, P = P0 P, P C
C1 C2
Oil
Membrane
F = m·gPressure, P0 + P
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
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Example C: Difference measurements, P = P0 P, P C
C1 C2
Membrane
Oil
F = m·gPressure, P0
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
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Example C: Difference measurements, P = P0 P, P C
C1 C2
Pressure, P0 P
Oil
Membrane
Difference method: linearity is important.
F = m·g
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
113. MEASUREMENT METHODS. 3.3. Compensation method and bridge method
Bridge method )Christie, 1833, Wheatstone, 1843(
Vref
Vref
R
(1) R Vref
Null detector
Originally was called ‘the bridge’
It can be shown that the null condition does not depend on the
power delivered by the power supply, the circuits internal
impedance, or the internal impedance of the null detector.
Note that the bridge method requires a single power source.
R
RR
Rx
Reference: [1]
VxVref
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Example D: Null measurements
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Let us first define some new terms that describe the interface of
a measurement system:
transducer is any device that converts a physical signal
of one type into a physical signal of another type,
measurement transducer is the transducer that does not
destroy the information to be measured,
input transducer or sensor is the transducer that
converts non-electrical signals into electrical signals,
output transducer or actuator is the transducer that
converts electrical signals into non-electrical signals.
Reference: [1]
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Example D: Null measurements
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
SensorSensorNon-electrical signal Electrical signal
Input transducer )sensor(
ES
N-ES
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Example D: Null measurements
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Electrical signal Non-electrical signal
Output transducer )actuator(
N-ES
ES
ActuatorActuator
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Example D: Null measurements
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Measurement system interfaceN
on-e
lect
rical
sig
nals
Non
-ele
ctric
al s
igna
ls
Measurement SystemMeasurement System
SensorSensor
SensorSensor ActuatorActuator
ActuatorActuator
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Example D: Null measurements
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Our aim in this example is to eliminate temperature drift in the
sensitivity of a dc magnetic field sensor with the help of a linear
temperature-insensitive reciprocal actuator.
VS
Ha
T1
T2
SensorSensorHa VS
Hact
Vo
ActuatorActuatorHactVo
T1
T2
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Example D: Null measurements
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Any ideas?
SensorSensor
Hact
VS
Ha
AVo
Null detector
Reference (Helmholtz coils)
VS0
Io
Io
T1
T2
Vo
T2
The sensor temperature-drift errors and nonlinearity are not important
Vs HactHaT1
Vo 1Vo 2
Hact 1Hact 2
HHaHact
H1H2 0
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Example E: Difference measurements
3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
SensorSensor
Hact
VS
Ha
AVo
Reference (Helmholtz coils)
VS 0
Io
HHaHact
T1
T2
Vo
T2
The sensor temperature-drift errors and nonlinearity are important
VS Hact T1
VS
VS
HactHact
Vo 2 Vo 1
H1H2
G AOL
1+AOL HactHa
Io
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3.2. Interchange method and substitution method
According to the interchange method, two almost equal
quantities are exchanged in the second measurement.
0 1 2-1-23-3
m1 m2
This method can determine both the magnitude of the
difference between the two quantities and and the magnitude
of possible asymmetry in the measuring system.
Reference: [1]
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
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3.2. Interchange method and substitution method
According to the interchange method, two almost equal
quantities are exchanged in the second measurement.
m2 m1
0 1 2-13
This method can determine both the magnitude of the
difference between the two quantities and and the magnitude
of possible asymmetry in the measuring system.
Reference: [1]
-2-3
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
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m2m1
-23-3
m =[1)2(]/2
Offset =[1 )2(]/2
3.2. Interchange method and substitution method
According to the interchange method, two almost equal
quantities are exchanged in the second measurement.
0 1 2-1
This method can determine both the magnitude of the
difference between the two quantities and and the magnitude
of possible asymmetry in the measuring system.
Reference: [1]
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
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The characteristics of the measurement system should
therefore not influence the measurement. Only the time stability
and the resolution of the system are important.
2 1 0.5 0.2
m
According to the substitution method, the unknown quantity is
measured first, and the measurement system reading is
remembered. Then, the unknown quantity is replaced with a
known and adjustable quantity, which is adjusted to obtain the
remembered reading.
Reference: [1]
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
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2m
1 0.5 0.2
According to the substitution method, the unknown quantity is
measured first, and the measurement system reading is
remembered. Then, the unknown quantity is replaced with a
known and adjustable quantity, which is adjusted to obtain the
remembered reading.
The characteristics of the measurement system should
therefore not influence the measurement. Only the time stability
and the resolution of the system are important.
Reference: [1]
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
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m
2
1 0.5 0.2
According to the substitution method, the unknown quantity is
measured first, and the measurement system reading is
remembered. Then, the unknown quantity is replaced with a
known and adjustable quantity, which is adjusted to obtain the
remembered reading.
The characteristics of the measurement system should
therefore not influence the measurement. Only the time stability
and the resolution of the system are important.
Reference: [1]
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
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1 0.5
According to the substitution method, the unknown quantity is
measured first, and the measurement system reading is
remembered. Then, the unknown quantity is replaced with a
known and adjustable quantity, which is adjusted to obtain the
remembered reading.
1
m
2 0.5
0.2
m=3.5
12 0.5
The characteristics of the measurement system should
therefore not influence the measurement. Only the time stability
and the resolution of the system are important.
3.5
Calibration
Reference: [1]
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
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1 0.5
1
m
2 0.5
0.2
m=3.5
12 0.5
3.5
Calibration
Reference: [1]
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
Calibration of a measurement system is, in fact, an application
of the substitution method. First the system is calibrated with a
know quantity. An unknown quantity can then be measured
accurately if its magnitude coincides with the calibrating points.
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Vo' AVoff AVaVb)
Example A: Interchange method.
Va Vb
Vo
Voff
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
A
Vo AVoff AVaVb)Vo
VaVb V
AVoff
Vo' AVoff AVaVb)
Voff = ?
VaVb = ?
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Vo' AVoff AVaVb)
Voff = ?
VaVb = ?
Vo' AVoff AVaVb)
Vo"AVoff AVaVb)
Voff = ?
VaVb = ?
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
Va Vb
Vo
VoffA
Vo AVoff AVaVb)Vo
VaVb V
AVoff
Vo"AVoff AVaVb)
Vo' AVoff AVaVb)
Example A: Interchange method.
Vo' Vo"
2A·V off
Vo' Vo"
2A)VaVb(
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Voff
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
Example: Amplifiers with the controllable polarity of the gain.
10k ±1%
10k ±1%
10k ±1%
10k ±1%
5k
5k
5k
Voff
A
A
vin
vin
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A
A
±?
±?
±?
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
Example: Amplifiers with the controllable polarity of the gain.
10k ±1%
10k ±1%
10k ±1%
10k ±1%
5k
5k
5k
Voff
Voff
vin
vin
313. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
Example B: Interchange method.
1°
? =
Offset?=
msr
true
2
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1
1°
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
1°
2
true
msr
Offset = )2°1°= 0.5°
= )2°1° = 1.5°
Example B: Interchange method.
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1°
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
= 1.5°
Offset = 0.5°
Example B: Interchange method.
363. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
Two next measurement methods, compensation and bridge
methods, are, in fact, applications of the substitution method.
Examples: Substitution method.
373. MEASUREMENT METHODS. 3.3. Compensation method and bridge method
3.3. Compensation method and bridge method
Compensation method removes the effect of unknown quantity
on the measurement system by compensating it with the effect
of known quantity. The degree of compensation can be
determined with a null indicator.
If the unknown effect is compensated completely, no power is
supplied or withdrawn from the unknown quantity.
The compensation method requires an auxiliary power source
that can supply precisely the same power that otherwise would
have been withdrawn from the measured quantity.
Reference: [1]
383. MEASUREMENT METHODS. 3.3. Compensation method and bridge method
Example: Measurement of voltage with compensation method.
Vx
Vref
R
(1) R
Null detector
VxVref
Reference: [1]
393. MEASUREMENT METHODS. 3.3. Compensation method and bridge method
NB: Note that the difference method and the null method make
use of the compensation method. In the difference method,
the compensation is only partial, whereas in the null method
it is complete.
00 00
Reference
Partial compensation Complete compensationNo compensation
Reference: [1]
403. MEASUREMENT METHODS. 3.3. Compensation method and bridge method
Bridge method )Christie, 1833, Wheatstone, 1843(
Vref
Vref
R
(1) R Vref
Null detector
Originally was called ‘the bridge’
It can be shown that the null condition does not depend on the
power delivered by the power supply, the circuits internal
impedance, or the internal impedance of the null detector.
Note that the bridge method requires a single power source.
R
RR
Rx
Reference: [1]
VxVref
413. MEASUREMENT METHODS. 3.4. Analogy method
3.4. Analogy method
Analogy method makes use of a model of the object from which
we wish to obtain measurement information.
The following models can be used.
Mathematical models )simulations(.
Linear scale models )e.g., acoustics of large halls, etc.(.
Non-linear scale models )e.g., wind tunnel models, etc.(.
Analogy method also widely uses the analogy existing between
different physical phenomena, for example, equivalent
mechanical models are used to model electrical resonant
circuits, equivalent electrical models are used to model quartz
resonators, equivalent magnetic circuits are used to model
magnetic systems, etc.
423. MEASUREMENT METHODS. 3.5. Repetition method
3.5. Repetition method
Wit this method several measurements of the same unknown
quantity are conducted each according to a different procedure
to prevent the possibility of making the same )systematic(
errors, specific to a certain type of measurements. Different
)correctly applied( methods of measurements will provide
similar results, but the measurement errors in the results will be
independent of each other. This will yield an indication of the
reliability of measurements.
6789
10
9876
6 7 8 9 9 8 7 6
Unreliable Valid
6789
10
9876
6 7 8 9 9 8 7 6
6789
10
9876
6 7 8 9 9 8 7 6
Reliable
Reference: [1]
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