1 LECTURE 3. Contents 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

2 With the deflection method ( שיטת ההסחה ), the result of the measurement is entirely determined by the readout of the measurement device. 3. MEASUREMENT METHODS Deflection, difference, and null methods 3.MEASUREMENT METHODS 3.1. Deflection, difference, and null methods Reference: [1] 10 0 The linearity of the entire scale is important. A

3 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. 3. MEASUREMENT METHODS Deflection, difference, and null methods Reference: [1] Reference The linearity of a part of the scale is important. R A A  R = ? R

4 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. 3. MEASUREMENT METHODS Deflection, difference, and null methods Reference: [1] Reference The linearity of the scale is not important. A =  R ? R A R

5 00 (b) 1 mm ±1  m Reference 99 mm ±10  5 00 (c) 0 mm ±1  m 100 mm ±10  5 Inaccuracy: Example A: (a) deflection, (b) difference, and (c) null measurements (a) Null method: linearity is not important; sensitivity and zero drift are important. 3. MEASUREMENT METHODS Deflection, difference, and null methods 0 ±1  m 100 mm ±0.1 mm 100 mm Inaccuracy: ±0.1 mm Uncertainty: 1 ±1  m Reference

6 Example B: (a) deflection, (b) difference, and (c) null measurements 3. MEASUREMENT METHODS Deflection, difference, and null methods 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]

7 Example B: (a) deflection, (b) difference, and (c) null measurements 3. MEASUREMENT METHODS Deflection, difference, and null methods Sensor Non-electrical signal, x Electrical signal, y Input transducer (sensor) y x

8 Example B: (a) deflection, (b) difference, and (c) null measurements 3. MEASUREMENT METHODS Deflection, difference, and null methods Electrical signal, z Non-electrical signal, x Output transducer (actuator) x z Actuator

9 Example B: (a) deflection, (b) difference, and (c) null measurements 3. MEASUREMENT METHODS Deflection, difference, and null methods Measurement system interface Non-electrical signals Measurement System Sensor Actuator

10 Example B: (a) deflection, (b) difference, and (c) null measurements 3. MEASUREMENT METHODS Deflection, difference, and null methods Our aim in this example is to eliminate temperature drift in the sensitivity of a sensor with the help of a linear, temperature- insensitive reciprocal actuator. y x T1T1 T2T2 Sensor xy x z Actuator xz T1T1 T2T2

11 Example C: Difference measurements 3. MEASUREMENT METHODS Deflection, difference, and null methods Measurand, X m Measurement, Z m Amplifier YmYm Measurement model: T 1 T 2 x y Gain, S Input Transducer XmXm X m  YmYm ZmZm. G S G

12 Example C: Difference measurements 3. MEASUREMENT METHODS Deflection, difference, and null methods Measurand, X m Measurement, Z m Actuator G x z Amplifier ZmZm X cmp ZmZm YmYm Gain, A Measurement model: ZmZm XmXm... A T 1 T 2 x y X cmp Gain, S Input Transducer X m -X cmp S G 1  G S ZmZm XmXm. A.. 1  G S YmYm Ym Ym ...  0 A 1  G S X m S  

13 Example B: Null measurements 3. MEASUREMENT METHODS Deflection, difference, and null methods Measurand, X m Measurement, Z m Actuator x z Amplifier ZmZm X cmp ZmZm Ym0Ym0 Gain, A Measurement model: ZmZm XmXm.. G A T>>1 1 A. A.. XmXm =AZmZm. T 1 T 2 x y X cmp XmXm  Gain, S Input Transducer X m  X cmp Ym Ym ...  0 A 1  G S X m S S G 1  G S G   

Interchange method and substitution method According to the interchange method, two almost equal quantities are exchanged in the second measurement m2m2 m1m1 This method can determine both the difference between the two quantities and and the offset of the measuring system. Reference: [1] 3. MEASUREMENT METHODS Interchange method and substitution method A  m  m 1  m 2  OFF   = m 1  m 2  OFF

Interchange method and substitution method m1m1 m2m Reference: [1] MEASUREMENT METHODS 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.  = m 1  m 2  OFF   = m 2  m 1   OFF B A  m  A  B) OFF  A  B)

16 m1m1 m2m Interchange method and substitution method Reference: [1] 3. MEASUREMENT METHODS 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.  m  2  1)    1.5 OFF  2  1)    0.5 B A  m  A  B) OFF  A  B)

17 V o '  AV off  A  V a  V b ) Example A: Interchange method. VaVa VbVb VoVo V off 3. MEASUREMENT METHODS Interchange method and substitution method A V o  AV off  A  V a  V b ) VoVo VaVbVaVb VV AV off V o '  AV off  A  V a  V b ) V off = ? V a  V b = ?

18 V o '  AV off  A  V a  V b ) V off = ? V a  V b = ? V o '  AV off  A  V a  V b ) V o "  AV off  A  V a  V b ) V off = ? V a  V b = ? 3. MEASUREMENT METHODS Interchange method and substitution method VaVa VbVb VoVo V off A V o  AV off  A  V a  V b ) VoVo VaVbVaVb VV AV off V o "  AV off  A  V a  V b ) V o '  AV off  A  V a  V b ) Example A: Interchange method. V o '  V o " 2   A·V off V o '  V o " 2   A(V a  V b )

19 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 Reference: [1] 3. MEASUREMENT METHODS Interchange method and substitution method m?m? 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.

20 2 m Reference: [1] 3. MEASUREMENT METHODS Interchange method and substitution method The characteristics of the measurement system should therefore not influence the measurement. Only the time stability and the resolution of the system are important. 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. m?m?

21 m Reference: [1] 3. MEASUREMENT METHODS Interchange method and substitution method 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? 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.

m m=Bm=B Reference: [1] 3. MEASUREMENT METHODS Interchange method and substitution method 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RmR R 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.

23 3. MEASUREMENT METHODS 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 m m=Bm=B Reference: [1] Calibration: mRmR B

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

25 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]

26 3. MEASUREMENT METHODS Compensation method and bridge method Example: Measurement of voltage by compensation method. Vx?Vx? V ref  R (1  ) R Null voltage detector V x  V ref Reference: [1] Adjustable reference 0

27 3. MEASUREMENT METHODS 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 Partial compensationComplete compensationNo compensation Reference: [1] Reference

28 3. MEASUREMENT METHODS Compensation method and bridge method Bridge method (Christie, 1833, Wheatstone, 1843) V ref  R (1  ) R V ref  Null voltage 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, on the circuits internal impedance, or on the internal impedance of the null detector. Note that the bridge method requires a single power source.  R RR RxRx Reference: [1] V x  V ref 0 0 R RxRx

29 3. MEASUREMENT METHODS 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.

30 3. MEASUREMENT METHODS 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 Unreliable Valid Reliable Reference: [1]

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