3.1. Deflection, difference, and null methods 3. MEASUREMENT METHODS. 3.1. 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]

The linearity of a part of the scale is important. 3. MEASUREMENT METHODS. 3.1. 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]

The linearity of the scale is not important. 3. MEASUREMENT METHODS. 3.1. 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]

Example A: (a) deflection, (b) difference, and (c) null measurements 3. MEASUREMENT METHODS. 3.1. 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:

Example A: (a) deflection, (b) difference, and (c) null measurements 3. MEASUREMENT METHODS. 3.1. 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

Example A: (a) deflection, (b) difference, and (c) null measurements 3. MEASUREMENT METHODS. 3.1. 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.

Example B: Null measurements, DC=0, P0=FA 3. MEASUREMENT METHODS. 3.1. 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.

Example C: Difference measurements, P = P0 ± DP, DP  DC 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods Example C: Difference measurements, P = P0 ± DP, DP  DC F = m·g Pressure, P0 + DP Oil Membrane C1 C2

Example C: Difference measurements, P = P0 ± DP, DP  DC 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods Example C: Difference measurements, P = P0 ± DP, DP  DC Pressure, P0 F = m·g Oil Membrane C1 C2

Example C: Difference measurements, P = P0 ± DP, DP  DC 3. MEASUREMENT METHODS. 3.1. 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.

Originally was called ‘the bridge’ 3. MEASUREMENT METHODS. 3.3. 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]

Example D: Null measurements 3. MEASUREMENT METHODS. 3.1. 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]

Input transducer (sensor) 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods Example D: Null measurements Input transducer (sensor) Non-electrical signal Sensor Electrical signal ES N-ES

Output transducer (actuator) 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods Example D: Null measurements Output transducer (actuator) Electrical signal Actuator Non-electrical signal N-ES ES

Measurement system interface 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods Example D: Null measurements Measurement system interface Measurement System Sensor Actuator Non-electrical signals Non-electrical signals Sensor Actuator

Example D: Null measurements 3. MEASUREMENT METHODS. 3.1. 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

Example D: Null measurements 3. MEASUREMENT METHODS. 3.1. 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

Example E: Difference measurements 3. MEASUREMENT METHODS. 3.1. 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

3.2. Interchange method and substitution method 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 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]

3.2. Interchange method and substitution method 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 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]

3.2. Interchange method and substitution method 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 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]

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]

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]

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]

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]

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]

Example A: Interchange method. 3. MEASUREMENT METHODS. 3.2. 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 = ?

______ = A·V off ______ = A(Va-Vb) Example A: Interchange method. Vo 3. MEASUREMENT METHODS. 3.2. 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)

Example: Amplifiers with the controllable polarity of the gain. 3. MEASUREMENT METHODS. 3.2. 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

Example: Amplifiers with the controllable polarity of the gain. 3. MEASUREMENT METHODS. 3.2. 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

Example B: Interchange method. 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method Example B: Interchange method. Dmsr 2 D Dtrue D = ? Offset =? 1°

Example B: Interchange method. 3. MEASUREMENT METHODS. 3.2. 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°

Example B: Interchange method. 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method Example B: Interchange method. Offset = 0.5° 1° D = 1.5°

Compensation of Temperature-Drift Errors 3. MEASUREMENT METHODS. 3.2. 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

Compensation of the temperature-drift errors. 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method Compensation of the temperature-drift errors.

Examples: Substitution method. 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.

3.3. Compensation method and bridge method 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]

Example: Measurement of voltage with compensation method. 3. MEASUREMENT METHODS. 3.3. 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]

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]

Originally was called ‘the bridge’ 3. MEASUREMENT METHODS. 3.3. 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]

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.

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]

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