1. 1 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. 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods 3.MEASUREMENT METHODS 3.1. Deflection, difference, and null methods Reference: [1]

2. 2 00 Example: (a) deflection, (b) difference, and (c) null measurements 00 (a)(b)(c) 100 mm ±10  3 1 mm ±10  3 0 mm ±10  3 Reference Inaccuracy: ±100  m ±1 ±1  m ±1  m 100 mm Null method: linearity is not important; sensitivity and zero drift are important. 99 mm100 mm ±10  5 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods

3. 3 Example: Null measurements,  C=0, P 0 =F  A C1C1 C2C2 Oil Membrane F = m·g Null method: linearity is not important; sensitivity and zero drift are important. Pressure, P 0 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods

4. 4 Example: Difference measurements, P = P 0   P,  P   C C1C1 C2C2 Oil Membrane F = m·g Pressure, P 0  P 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods

5. 5 Example: Difference measurements, P = P 0  P,  P   C C1C1 C2C2 Membrane Oil F = m·g Pressure, P 0 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods

6. 6 Example: Difference measurements, P = P 0 ±  P,  P   C C1C1 C2C2 Pressure, P 0  P Oil Membrane Difference method: linearity is important. F = m·g 3. MEASUREMENT METHODS. 3.1. Deflection, difference, and null methods

7. 7 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 -2 3 -3 m1m1 m2m2 Example: 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

8. 8 3.2. Interchange method and substitution method According to the interchange method, two almost equal quantities are exchanged in the second measurement. m2m2 m1m1 Example: 0 1 2 3 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

9. 9 m2m2 m1m1 -2 3 -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. Example: 0 1 2 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

10. 10 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 Example: 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

11. 11 2 m 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. Example: 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

12. 12 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. Example: 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

13. 13 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 Example: 1 2 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

14. 14 Example: Interchange method. Linear differential amplifier with offset VaVa VbVb VoVo V0V0 VaVbVaVb V' o VV V o =  A(V off  V a  V b ) V off =? V off A A·V off VV V o =  A(V off  V  ) 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method

15. 15 (V' o  V'' o )/2=A(V a  V b ) V o =  A(V off  V  ) A VV Example: Interchange method. Linear differential amplifier with offset VbVb A V0V0 V'' o VaVbVaVb VoVo V' o (V' o  V'' o )/2=A·V off VaVa A·V off (V' o  V'' o )/2=A(V a  V b ) A(VaVb)A(VaVb) V off VV V o =  A(V off  V  ) 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method

16. 16 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method Example: Amplifiers with the controllable polarity of the gain 10k ±1% 5k V in V off

17. 17 ±? 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method Example: Amplifiers with the controllable polarity of the gain 10k ±1% 5k V in V off

18. 18 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method Example: Interchange method. Level measurement 1°  = ? Offset =?  msr   true 22

19. 19 11  1° 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method Example: Interchange method. Level measurement 1° 22  true  msr Offset = (2°   1°  = 0.5°  = (2°   1°  = 1.5°

20. 20 1° 3. MEASUREMENT METHODS. 3.2. Interchange method and substitution method Example: Interchange method. Level measurement  = 1.5° Offset = 0.5°

21. 21 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. Two next measurement methods, compensation and bridge methods, are also, in fact, applications of the substitution method. Reference: [1]

22. 22 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]

23. 23 3. MEASUREMENT METHODS. 3.3. Compensation method and bridge method Example: Measurement of voltage with compensation method VxVx V ref VxVx  V ref  R (1  ) R Null detector = Reference: [1]

24. 24 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 0 0 Reference Partial compensationComplete compensationNo compensation Reference: [1]

25. 25 3. MEASUREMENT METHODS. 3.3. Compensation method and bridge method Bridge method (Christie, 1833, Wheatstone, 1843) V ref  R (1  ) R V ref  VxVx  V ref 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 RxRx Reference: [1]

26. 26 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.). 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.

27. 27 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. 6 7 8 9 10 9 8 7 6 67899876 Unreliable Valid 6 7 8 9 10 9 8 7 6 67899876 6 7 8 9 9 8 7 6 67899876 Reliable Reference: [1]

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