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3. MEASUREMENT METHODS. 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.

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

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  1. 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. 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 used and partially by the reference quantity. 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 instrument is therefore used as a null detector. Reference: [1]

  2. 100 mm ±10-3 100 mm (a) Inaccuracy: ±100 mm 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods Example: (a) deflection, (b) difference, and (c) null measurements Inaccuracy:

  3. 1 mm ±10-3 0 0 (b) 99 mm Inaccuracy: ±100 mm Inaccuracy: ±100 mm ±1 ±1mm 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods Example: (a) deflection, (b) difference, and (c) null measurements 100 mm ±10-3 100 mm (a) Inaccuracy:

  4. 0 mm ±10-3 0 0 (c) Reference 100 mm ±10-5 Inaccuracy: ±100 mm Inaccuracy: ±100 mm ±1 ±1mm ±1mm Inaccuracy: ±100 mm ±1 ±1 mm Null method: linearity is not important; sensitivity and zero drift are important. 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods Example: (a) deflection, (b) difference, and (c) null measurements 1 mm ±10-3 0 0 100 mm ±10-3 100 mm (a) (b) 99 mm Inaccuracy:

  5. Null method: linearity is not important; sensitivity and zero drift are important. 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods Example: Null measurements, DC=0, P0=FA Pressure, P0 F = m·g Oil Membrane C1 C2

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

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

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

  9. 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. Example: 0 -1 1 -2 2 -3 3 m1 m2 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. Reference: [1]

  10. 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. 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. Example: 0 -1 1 -2 2 -3 3 m2 m1 Reference: [1]

  11. 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. 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. Example: Offset =[1+ (-2)]/2 0 -1 1 -2 2 -3 3 Dm =[1-(-2)]/2 m1 m2 Reference: [1]

  12. The characteristics of the measurement system should therefore not influence the measurement. Only the time stability and the resolution of the system are important. Example: m 2 1 0.5 0.2 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. Reference: [1]

  13. 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 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. Example: Reference: [1]

  14. 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 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. Example: Reference: [1]

  15. The characteristics of the measurement system should therefore not influence the measurement. Only the time stability and the resolution of the system are important. Calibration 3.5 2 1 0.5 m 2 1 1 0.5 0.5 0.2 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. Example: m=3.5 Reference: [1]

  16. A 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method Example: Interchange method. Linear differential amplifier with offset Vo Vo =+A(Voff+Ve) V'o Voff A·Voff V0 Ve Ve Va-Vb Va Vb Vo =+A(Voff+Va-Vb) Voff=?

  17. A(Va-Vb) A·Voff A Va-Vb V''o (V'o+V''o)/2=A·Voff (V'o+V''o)/2=A·Voff (V'o-V''o)/2=A(Va-Vb) (V'o-V''o)/2=A(Va-Vb) 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method Example: Interchange method. Linear differential amplifier with offset Vo Vo =-A(Voff+Ve) Vo =+A(Voff+Ve) V'o Voff V0 Ve A Ve Va Vb

  18. 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method Example: Amplifiers with the controllable polarity of the gain 10k ±1% 10k ±1% Voff 5k Vin 5k 10k ±1% 10k ±1% Voff Vin 5k

  19. ±? ±? ±? 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method Example: Amplifiers with the controllable polarity of the gain 10k ±1% 10k ±1% Voff 5k Vin 5k 10k ±1% 10k ±1% Voff Vin 5k

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

  21. Offset = (2°- 1°)/2 = 0.5° 1 D = (2°+ 1°)/2 = 1.5° 1° 1° 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method Example: Interchange method. Level measurement Dmsr 2 Dtrue D

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

  23. Two next measurement methods, compensation and bridge methods, are also, in fact, applications of the substitution method. 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method Example: 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. Reference: [1]

  24. 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. 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. Reference: [1]

  25. 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]

  26. 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. 3. MEASUREMENT METHODS. 3.3. Compensation method and bridge method 0 0 0 0 Reference No compensation Partial compensation Complete compensation Reference: [1]

  27. 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. 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 R R Vx = aVref Originally was called ‘the bridge’ Reference: [1]

  28. 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. 3.4. 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). • Scale models (e.g., acoustics of large halls, etc.). • Non-linear scale models (e.g., wind tunnel models, etc.).

  29. 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 6 6 6 7 7 7 8 8 8 9 9 9 9 9 9 8 8 8 7 7 7 6 6 6 9 9 9 8 8 8 7 7 7 6 6 6 Unreliable Reliable Valid 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. Reference: [1]

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