LECTURE 3. Contents
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3. Measurement methods
3.1. Deflection, difference, and null methods
3.2. Interchange method and substitution method
3.3. Compensation method and bridge method
3.4. Analogy method
3.5. Repetition method
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3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
3. MEASUREMENT METHODS
3.1. Deflection, difference, and null methods
With the deflection method (‫)שיטת ההסחה‬, the result of the
measurement is entirely determined by the readout of the
measurement device.
10
A
0
The linearity of the entire scale is important.
Reference: [1]
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3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
The difference method (‫)שיטת הפרש‬, 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.
A- R= ?
10
10
R
A
R
Reference
0
0
The linearity of a part of the scale is important.
Reference: [1]
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3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
With the null method (‫)שיטת אפס‬, 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.
A = R?
10
10
R
R
A
Reference
0
0
The linearity of the scale is not important.
Reference: [1]
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3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Example A: (a) deflection, (b) difference, and (c) null measurements
1 mm ±1 mm
0
100 mm ±0.1 mm
0 mm ±1 mm
0
0
0
Uncertainty:
Inaccuracy:
±0.1 mm
(b)
1 ±1 mm
(c)
Reference
99 mm ±10-5
Reference
(a)
Reference
100 mm
100 mm ±10-5
0 ±1 mm
Null method: linearity is not important;
sensitivity and zero drift are important.
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3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Example B: (a) deflection, (b) difference, and (c) null measurements
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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3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Example B: (a) deflection, (b) difference, and (c) null measurements
Input transducer (sensor)
Non-electrical signal, x
Sensor
Electrical signal, y
y
x
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3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Example B: (a) deflection, (b) difference, and (c) null measurements
Output transducer (actuator)
Electrical signal, z
Actuator
Non-electrical signal, x
x
z
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3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Example B: (a) deflection, (b) difference, and (c) null measurements
Sensor
Actuator
Measurement System
Sensor
Actuator
Non-electrical signals
Non-electrical signals
Measurement system interface
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3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Example B: (a) deflection, (b) difference, and (c) null measurements
Our aim in this example is to eliminate temperature drift in the
sensitivity of a sensor with the help of a linear, temperatureinsensitive reciprocal actuator.
x
y
z
Sensor
x
Actuator
y
x
T1
T1
T2
T2
x
z
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3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Example C: Difference measurements
Input Transducer
T1
y
Ym
T2
Measurand, Xm
Ym
Xm
x
G
Measurement, Zm
Amplifier
Gain, S
Measurement model:
Xm =
Zm
S. G
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3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Example C: Difference measurements
Ym =
Input Transducer
T1
y
Xm . S
1 + G . A .S
=0
T2
Measurand, Xm
Ym
+
Ym
Xm-Xcmp x
Measurement, Zm
G
Amplifier
Gain, S
-
Xcmp
z
Zm
Zm
Xcmp x
Zm
Xm
Gain, A
Actuator
S.G
1 + G .A . S
Measurement model:
1 + G.A. S
Xm Zm
S.G
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3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods
Example B: Null measurements
Xm . S
1 + G . A .S
Ym =
Input Transducer
T1
y
=0
G 
T2
Ym0
Measurand, Xm
+
Xm-Xcmp x
Measurement, Zm
G
Amplifier
Gain, S
-
X cmp Xm
z
Zm
Zm
Xcmp x
Zm
Xm
S .G
1 + G .A .S
Gain, A
Actuator
G. A. T>>1
Measurement model:
X = A. Z
m
m
1
A
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3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
3.2. Interchange method and substitution method
According to the interchange method, two almost equal
quantities are exchanged in the second measurement.
This method can determine both the difference between the
two quantities and and the offset of the measuring system.
A= m1-m2 + OFF
A
-3
m2
-2 -1 0 1 2
Dm = m1-m2 =?
3
OFF = ?
m1
Reference: [1]
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3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
3.2. Interchange method and substitution method
According to the interchange method, two almost equal
quantities are exchanged in the second measurement.
This method can determine both the difference between the
two quantities and and the offset of the measuring system.
A
-3
A= m1-m2 + OFF
B
-2 -1 0 1 2
B = m2 -m1+ OFF
3
Dm =0.5(A-B)
m1
m2
OFF = 0.5(A+B)
Reference: [1]
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3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
3.2. Interchange method and substitution method
According to the interchange method, two almost equal
quantities are exchanged in the second measurement.
This method can determine both the difference between the
two quantities and and the offset of the measuring system.
Dm =0.5(A-B)
A
-3
B
-2 -1 0 1 2
OFF = 0.5(A+B)
3
D m =0.5(-2-1) = -1.5
OFF = 0.5 (-2+1) = -0.5
m2
m1
Reference: [1]
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3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
Example A: Interchange method.
Vo
Vo = AVoff +A(Va-Vb)
Voff
Vo' = AVoff +A(Va-Vb)
A
AVoff
Vo
Va-Vb
Va
Vb
Vo' = AVoff +A(Va-Vb)
Voff = ?
Va-Vb = ?
Ve
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3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
Example A: Interchange method.
Vo
Vo = AVoff -A(Va-Vb)
Voff
Vo' = AVoff +A(Va-Vb)
A
AVoff
Vo
Va
Vb
Va-Vb
Vo" = AVoff -A(Va-Vb)
Vo' = AVoff +A(Va-Vb)
Vo" = AV
-A(V
Voff =
? a-Vb)
=?
off
Vo' +VaV-V
o" b
______
= A·V
V
=?
2 -V = ?
V
a
b
off
Vo' - Vo"
______
= A(V -V )
2
a
b
Ve
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3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
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 an
adjustable reference, 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.
m=?
m
2
1
0.5
0.2
Reference: [1]
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3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
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 an
adjustable reference, 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.
m=?
m
2
1
0.5
0.2
Reference: [1]
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3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
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 an
adjustable reference, 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.
m=?
2
m
1
0.5
0.2
Reference: [1]
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3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
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 an
adjustable reference, 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.
m=R
R
m=B
2
2
m
0.5
0.5
1
1
1
0.5
0.2
Reference: [1]
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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 (reference or standard). An unknown quantity
can then be measured accurately if its magnitude coincides
with the calibrating points.
Calibration: m=R
B
m=B
2
2
m
0.5
0.5
1
1
1
0.5
0.2
Reference: [1]
3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method
Examples: Substitution method.
Two next measurement methods, compensation and bridge
methods, are, in fact, applications of the substitution method.
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3. 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]
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3. MEASUREMENT METHODS. 3.3. Compensation method and bridge method
Example: Measurement of voltage by compensation method.
Adjustable reference
Null voltage detector
0
Vx=?
Vx = aVref
(1-a) R
Vref
aR
Reference: [1]
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3. 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.
0
0
Reference
0
Reference
0
No compensation Partial compensation Complete compensation
Reference: [1]
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3. MEASUREMENT METHODS. 3.3. Compensation method and bridge method
Bridge method (Christie, 1833, Wheatstone, 1843)
Null voltage
detector
Rx
Vref
R
0
Vx = aVref
(1-a) R
aR
Rx
Vref
aR
0
Vref

R
R
Originally was called ‘the bridge’
It can be shown that the null condition does not depend on the
power delivered by the power supply, on the circuits internal
impedance, or on the internal impedance of the null detector.
Note that the bridge method requires a single power source.
Reference: [1]
3. MEASUREMENT METHODS. 3.4. Analogy method
3.4. Analogy method
Analogy method (simulations) 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.
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3. 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.
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Unreliable
Reliable
Valid
Reference: [1]
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