1. 3.1. Deflection, difference, and null methods
3. MEASUREMENT METHODS Deflection, difference, and null methods
3. MEASUREMENT METHODS
3.1. Deflection, difference, and null methods
With the deflection method, the result of the measurement is entirely determined by the readout of the measurement device. 10
The linearity of the entire scale is important.
Reference: [1]

2. The linearity of a part of the scale is important.
3. MEASUREMENT METHODS Deflection, difference, and null methods
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. 10 10
Reference
The linearity of a part of the scale is important.
Reference: [1]

3. The linearity of the scale is not important.
3. MEASUREMENT METHODS Deflection, difference, and null methods
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. 10 10
Reference
The linearity of the scale is not important.
Reference: [1]

4. Example A: (a) deflection, (b) difference, and (c) null measurements
3. MEASUREMENT METHODS Deflection, difference, and null methods
Example A: (a) deflection, (b) difference, and (c) null measurements
(a)
100 mm ±10-3
100 mm
Inaccuracy: ±100 mm
Inaccuracy:

5. Example A: (a) deflection, (b) difference, and (c) null measurements
3. MEASUREMENT METHODS Deflection, difference, and null methods
Example A: (a) deflection, (b) difference, and (c) null measurements
(b)
1 mm ±10-3
Reference
99 mm ±10-5
100 mm ±10-3
100 mm
(a)
Inaccuracy:
Inaccuracy: ±100 mm
±1 ±1 mm

6. Example A: (a) deflection, (b) difference, and (c) null measurements
3. MEASUREMENT METHODS Deflection, difference, and null methods
Example A: (a) deflection, (b) difference, and (c) null measurements
(b)
1 mm ±10-3
Reference
99 mm ±10-5
(c)
0 mm ±10-3
Reference
100 mm ±10-5
100 mm ±10-3
100 mm
(a)
Inaccuracy:
Inaccuracy: ±100 mm
Inaccuracy: ±100 mm ±1 ±1 mm
±0 ±1 mm
Null method: linearity is not important;
sensitivity and zero drift are important.

7. Example B: Null measurements, DC=0, P0=FA
3. MEASUREMENT METHODS Deflection, difference, and null methods
Example B: Null measurements, DC=0, P0=FA
Pressure, P0
F = m·g
Oil
Membrane C1 C2
Null method: linearity is not important;
sensitivity and zero drift are important.

8. Example C: Difference measurements, P = P0 ± DP, DP  DC
3. MEASUREMENT METHODS Deflection, difference, and null methods
Example C: Difference measurements, P = P0 ± DP, DP  DC
F = m·g
Pressure, P0 + DP
Oil
Membrane C1 C2

9. Example C: Difference measurements, P = P0 ± DP, DP  DC
3. MEASUREMENT METHODS Deflection, difference, and null methods
Example C: Difference measurements, P = P0 ± DP, DP  DC
Pressure, P0
F = m·g
Oil
Membrane C1 C2

10. Example C: Difference measurements, P = P0 ± DP, DP  DC
3. MEASUREMENT METHODS Deflection, difference, and null methods
Example C: Difference measurements, P = P0 ± DP, DP  DC
Pressure, P0 - DP
F = m·g
Oil
Membrane C1 C2
Difference method: linearity is important.

11. Originally was called ‘the bridge’
3. MEASUREMENT METHODS Compensation method and bridge method
Bridge method (Christie, 1833, Wheatstone, 1843)
Null detector Rx
a R
(1-a) R
Vref
Vref 
Vref
a R
Vx = aVref 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, the circuits internal impedance, or the internal impedance of the null detector.
Note that the bridge method requires a single power source.
Reference: [1]

12. Example D: Null measurements
3. MEASUREMENT METHODS Deflection, difference, and null methods
Example D: 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]

13. Input transducer (sensor)
3. MEASUREMENT METHODS Deflection, difference, and null methods
Example D: Null measurements
Input transducer (sensor)
Non-electrical signal
Sensor
Electrical signal ES
N-ES

14. Output transducer (actuator)
3. MEASUREMENT METHODS Deflection, difference, and null methods
Example D: Null measurements
Output transducer (actuator)
Electrical signal
Actuator
Non-electrical signal
N-ES ES

15. Measurement system interface
3. MEASUREMENT METHODS Deflection, difference, and null methods
Example D: Null measurements
Measurement system interface
Measurement System
Sensor
Actuator
Non-electrical signals
Non-electrical signals
Sensor
Actuator

16. Example D: Null measurements
3. MEASUREMENT METHODS Deflection, difference, and null methods
Example D: Null measurements
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. Ha VS Vo
Hact
Sensor
Actuator VS
Hact T1 T1 T2 T2 Ha Vo

17. Example D: Null measurements
3. MEASUREMENT METHODS Deflection, difference, and null methods
Example D: Null measurements
Sensor
Hact VS Ha
A= Vo
Null detector
Reference (Helmholtz coils)
VS  0 Io
Any ideas? T1 T2 Vo
The sensor temperature-drift errors and nonlinearity are not important Vs
Hact=Ha
Vo 1=Vo 2
Hact 1=Hact 2
DH=Ha -Hact
DH1=DH2 =0

18. Example E: Difference measurements
3. MEASUREMENT METHODS Deflection, difference, and null methods
Example E: Difference measurements
Reference (Helmholtz coils) Io
Hact
G AOL
1+AOL b VS
Hact = Ha _______
Sensor Vo Io
VS > 0
A< Ha VS
Hact T1
The sensor temperature-drift errors and nonlinearity are important T1 T2
Hact 1
VS 2 T2
Hact 2
VS 1
Vo 2
Vo 1
DH=Ha -Hact Vo
DH1 DH2

19. 3.2. Interchange method and substitution method
3. MEASUREMENT METHODS 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 magnitude of the difference between the two quantities and and the magnitude of possible asymmetry in the measuring system. 1 2 -1 -2 3 -3 m1 m2
Reference: [1]

20. 3.2. Interchange method and substitution method
3. MEASUREMENT METHODS 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 magnitude of the difference between the two quantities and and the magnitude of possible asymmetry in the measuring system. -1 -2 1 2 -3 3 m2 m1
Reference: [1]

21. 3.2. Interchange method and substitution method
3. MEASUREMENT METHODS 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 magnitude of the difference between the two quantities and and the magnitude of possible asymmetry in the measuring system.
Offset =[1+ (-2)]/2 -1 -2 1 2 -3 3
Dm =[1-(-2)]/2 m1 m2
Reference: [1]

22. 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 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. 2 1
0.5
0.2 m
Reference: [1]

23. 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 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. m 2 1
0.5
0.2
Reference: [1]

24. 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 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. 2 m 1
0.5
0.2
Reference: [1]

25. 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 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.
3.5
Calibration
m=3.5 1 2
0.5 2 1
0.5 m 1
0.5
0.2
Reference: [1]

26. 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.
3.5
Calibration
m=3.5 1 2
0.5 2 1
0.5 m 1
0.5
0.2
Reference: [1]

27. Example A: Interchange method.
3. MEASUREMENT METHODS Interchange method and substitution method
Example A: Interchange method. Vo
Vo = AVoff +A(Va-Vb)
Vo' = AVoff +A(Va-Vb)
Voff A
AVoff Vo
Va-Vb Ve Va Vb
Vo' = AVoff +A(Va-Vb)
Voff = ?
Va-Vb = ?

28. ______ = A·V off ______ = A(Va-Vb) Example A: Interchange method. Vo
3. MEASUREMENT METHODS Interchange method and substitution method
Example A: Interchange method. Vo
Vo = AVoff -A(Va-Vb)
Vo' = AVoff +A(Va-Vb)
Voff A
AVoff Vo
Va-Vb Ve
Vo" = AVoff -A(Va-Vb) Va Vb
Vo' = AVoff +A(Va-Vb)
Vo" = AVoff -A(Va-Vb)
Voff = ?
Va-Vb = ?
Vo' = AVoff +A(Va-Vb)
Voff = ?
Va-Vb = ?
Vo' + Vo" 2
______ = A·V off
Vo' - Vo" 2
______ = A(Va-Vb)

29. Example: Amplifiers with the controllable polarity of the gain.
3. MEASUREMENT METHODS Interchange method and substitution method
Example: Amplifiers with the controllable polarity of the gain.
10k ±1%
10k ±1%
Voff A
vin 5k 5k
10k ±1%
10k ±1%
Voff A
vin 5k

30. Example: Amplifiers with the controllable polarity of the gain.
3. MEASUREMENT METHODS Interchange method and substitution method
Example: Amplifiers with the controllable polarity of the gain.
10k ±1%
10k ±1%
Voff A
vin 5k ±? 5k
10k ±1%
10k ±1%
Voff A
vin 5k

31. Example B: Interchange method.
3. MEASUREMENT METHODS Interchange method and substitution method
Example B: Interchange method.
Dmsr 2 D
Dtrue
D = ?
Offset =? 1°

32. Example B: Interchange method.
3. MEASUREMENT METHODS Interchange method and substitution method
Example B: Interchange method.
Dmsr 2
Offset = (2° - 1°)/2 = 0.5°
D = (2° + 1°)/2 = 1.5° 1 D
Dtrue 1° 1°

33. Example B: Interchange method.
3. MEASUREMENT METHODS Interchange method and substitution method
Example B: Interchange method.
Offset = 0.5° 1°
D = 1.5°

34. Compensation of Temperature-Drift Errors
3. MEASUREMENT METHODS Interchange method and substitution method
Example: Interchange method.
Compensation of Temperature-Drift Errors
in Fundamental-Mode Orthogonal Fluxgates
Anton Plotkin, Eugene Paperno, Alexander Samohin,
and Ichiro Sasada
IEEE Instrumentation and Measurement Technology
Conference Sorrento, April 24-27, 2006
Prize for excellence:
graduate-student outstanding
research paper
Measurement object x1 xe
Ratio
measuring system xe y
Exciter -1

35. Compensation of the temperature-drift errors.
3. MEASUREMENT METHODS Interchange method and substitution method
Compensation of the temperature-drift errors.

36. Examples: Substitution method.
3. MEASUREMENT METHODS Interchange method and substitution method
Examples: Substitution method.
Two next measurement methods, compensation and bridge methods, are, in fact, applications of the substitution method.

37. 3.3. Compensation method and bridge method
3. MEASUREMENT METHODS 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]

38. Example: Measurement of voltage with compensation method.
3. MEASUREMENT METHODS Compensation method and bridge method
Example: Measurement of voltage with compensation method.
Null detector
(1-a) R
Vref Vx
a R
Vx = aVref
Reference: [1]

39. 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.
Reference
No compensation
Partial compensation
Complete compensation
Reference: [1]

40. Originally was called ‘the bridge’
3. MEASUREMENT METHODS Compensation method and bridge method
Bridge method (Christie, 1833, Wheatstone, 1843)
Null detector Rx
a R
(1-a) R
Vref
Vref 
Vref
a R
Vx = aVref 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, the circuits internal impedance, or the internal impedance of the null detector.
Note that the bridge method requires a single power source.
Reference: [1]

41. 3. MEASUREMENT METHODS. 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.

42. 3. MEASUREMENT METHODS. 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. 6 7 8 9 10
Unreliable 6 7 8 9 10
Reliable
Valid 6 7 8 9 10
Reference: [1]

43. Next lecture
Next lecture: