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2. Measurement of physical quantities

LECTURE 2. Contents. 2. Measurement of physical quantities 2.1. Acquisition of information: active and passive information 2.2. Units, systems of units, standards 2.2.1. Units 2.2.1. Systems of units 2.2.1. Standards 2.3. Primary standards

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2. Measurement of physical quantities

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  1. LECTURE 2. Contents 2. Measurement of physical quantities 2.1. Acquisition of information: active and passive information 2.2. Units, systems of units, standards 2.2.1. Units 2.2.1. Systems of units 2.2.1. Standards 2.3. Primary standards 2.3.1. Primary frequency standards 2.3.2. Primary voltage standards 2.3.3. Primary resistance standards 2.3.4. Primary current standards 2.3.5. Primary capacitance standards 2.3.6. Primary inductance standards 2.3.7. Primary temperature standards

  2. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information 2. MEASUREMENT OF PHYSICAL QUANTITIES 2.1. Acquisition of information • Active measurement object Active information Measurement object x1 y Ratio measuring system Reference xr • Passive measurement object Passive information Measurement object x1 y xe xe Ratio measuring system Exciter Reference xr

  3. Measurement object Reference 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information Example 1(a): Active measurement object Ratio measuring system AC magnetic field B=f(R, fB,V/Vref ) R Measurement model v Instrumentation d[Bcos(2pf t)A] dt v = -

  4. Measurement object Exciter 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information Example 1(b): Passive measurement object Ratio measuring system DC magnetic field B=f(R, fexc,V/Vref ) f R Measurement model V Instrumentation Reference d[Bcos(2pf t)A] dt v = -

  5. Measurement object V or I references Exciter Measurement object 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information Example 2: (a) Passive measurement object Ratio measuring system I R Ratio measuring system R VR (b)Active measurement object V reference R Ratio measuring system T0ºK vn R

  6. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.1. Units 2.2. Units, systems of units, standards 2.2.1. Units • The known magnitude (גודל) of the physical quantity (ערך פיזיקאלי) to which we refer the measurement is called the measure (מידה). • For absolute measurements, the measure is internationally standardized and for simplicity is set equal to unity. • Therefore, in the case of absolute measurements, unit is the standard measure. Reference: [1]

  7. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Systems of units 2.2.2. Systems of units • If • k is the number of independent physical equations that describe a particular area of physics and • n is the number of different quantities in the k equations (n > k), then • n - k quantities can be used freely as base quantities in a system of units suitable for that area of physics. • The other k quantities are derived quantities that follow from the base quantities and the k equations. Reference: [1]

  8. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Systems of units • SI obtains its international authority from the Meter Convention, signed in Paris by the delegates of 17 countries, including the United States, on 20 May 1875, and amended in 1921. Today 48 states are members. The treaty established the General Conference on Weights and Measures (CGPM) as the formal diplomatic body responsible for ratification of the new proposals related to metric units. The scientific decisions are made by the International Committee for Weights and Measures (CIPM). • The activities of the national standards laboratories are coordinated by the International Bureau of Weights and Measures (BIPM, Sèvres, France). • The SI was established by the 11th CGPM in 1960, when the metric unit definitions, symbols and terminology were extensively revised and simplified. Tarantola A. Probability and measurements (lecture notes, Paris, 2001).

  9. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Systems of units SYSTÈME INTERNATIONAL D’UNITÈS (SI): base and additional* units QUANTITY UNIT SYMBOL DEFINITION (STANDARDS) DIMENSION m L Equal to 1,650,763.73 wavelengths in vacuum of the orange-red line of the krypton-86 spectra. meter 1. Length kg M Cylinder of platinum-iridium alloy kept in France and a number of copies. (May be replaced by an atomic standard within the next ten years.) kilogram 2. Mass s T Time for 9,192,631,770 cycles of resonance vibration of the cesium-133 atom. second 3. Time Absolute zero is defined as 0 kelvin. 0 degrees Celsius equals 273.16 kelvins. K K kelvin 4. Temperature Intensity of a light source (frequency 5.40x1014 Hz) that gives a radiant intensity of 1/683 watts/steradian in a given direction. C C candela 5. Luminosity A I Current that produces a force of 2.10-7 newtons per meter between a pair of infinitely long parallel wires 1 meter apart in a vacuum. ampere 6. Electric current mole mol Number of elementary entities of a substance equal to the number of atoms in 0.012 kg of carbon 12. - 7. Amount of substance radian rad - The angle subtended at the center of a circle by an arc that is of the same length as the radius. *Angle - The solid angle subtended at the center of a sphere by an area on its surface equal to the square of its radius. *Solid angle sr steradian

  10. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Systems of units SYSTÈME INTERNATIONAL D’UNITÈS (SI): some derived units QUANTITY UNIT SYMBOL DEFINITION DIMENSION DEFINITION Acceleration Rate of change of velocity of 1 meter per 1 second per one second. meter/s/s m s-2 ML-2 Area Multiplication of two orthogonal (right-angle) lengths in meters square meter m2 M2 Multiplication of three mutually orthogonal (right-angle) lengths in meters. Volume cubic meter m3 M3 Force The force required to accelerate a 1 kilogram mass 1 meter / second / second. newton N MLT-2 Charge Quantity of electricity carried by a current of 1 ampere for 1 second. coulomb C IT Work done by a force of 1 newton moving through a distance of 1 meter in the direction of the force. Energy joule J ML2T-2 Energy expenditure at a rate of 1 joule per 1 second. Power watt W ML2T-3 Resistance that produces a 1 volt drop with a 1 ampere current. Resistance ohm W ML2T-3I-2 Number of cycles in 1 second. Frequency hertz Hz T-1 Pressure due a a force of 1 newton applied over an area of 1 square meter. Pressure pascal Pa ML-1T-2 Rate of movement in a direction of 1 meter in 1 second. Velocity meter/s m s-1 LT-1 The potential when 1 joule of work is done in making 1 coulomb of electricity flow. Potential (emf) volt V ML2T-3I-1

  11. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Standards 2.2.3. Standards • The terms unit and physical quantity are both abstract concepts. In order to use a unit as a measure, there must be a realization of the unit available: a physical standard. • A standard can be: • an artifact (prototype, מכשיר); • a natural phenomenon (atomic processes, etc.); • a standardized procedure of measurement using standardized measurement methods and equipment. Reference: [1]

  12. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Standards Measurements are usually based on secondary or lower order (working) standards. These are are calibrated to higher (primary or secondary) standards. An even lower order standard (reference) is present in every instrument that can perform an absolute measurement. Such instruments should also be calibrated regularly, since aging, drift, wear, etc., will cause the internal reference to become less accurate. Accuracy is defined here as an expression of the closeness of the value of the reference to the primary standard value. There are primaryand secondary standards. Primary standards are preserved and improved in a national institute of standards and technology. Reference: [1]

  13. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Standards Illustration: The hierarchy of standards Primary standard Secondary standard Relative accuracy Absolute accuracy Measuring instrument Device under test

  14. Standards users National standards National standards International standards International standards Defacto international standards Industry standards International Organization for Standards (ISO) International Electrotechnical Commission (IEC) American National Standard Institute (ANSI) American National Standard Institute (ANSI) British Standards Institute (BSI) Israeli Standards Institute (SII) Other national standards associations American Society for Quality (ASQ) American Society for Testing and Materials (ASTM) Institute of Electrical and Electronic Engineers (IEEE) Other member societies 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Standards Illustration: Measurement standards

  15. Swedish National Testing and Research Institute, www.sp.se 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Standards Illustration: A primary standard of mass (the kilogram)

  16. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Standards Example: Preservation of the standard Swedish national testing and research institute looks after its weight well! At the latest major international calibration of national kilogram prototypes, in 1991, the mass of the Swedish prototype was determined to 0.999 999 965 kg, with an uncertainty of measurement of ± 2.3 μg. It was found that, after more than a century, the mass of our national kilogram had changed by only 2 μg compared to that of the international prototype. No other national standard anywhere in the world has been better kept. Swedish National Testing and Research Institute. www.sp.se

  17. Measurement uncertainty: ±110-12 s (± 10-6 ppm). 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.6. Primary frequency standards 2.3. Primary standards 2.3.1. Primary frequency standard DE f0= DE/h e The atoms of Cesium-133 are selected with electrons jumping to a lower energy level and emitting photons at f 0= 9.19263177160 GHz. The unit of time, 1 s, is defined as the duration of exactly f0 cycles. A crystal oscillator in the feedback loop of the exciter is used to adjust the frequency of the standard to that frequency at which most transactions occur. (The quality factor of so tuned standardQ=2107.)

  18. Measurement uncertainty: up to 1 nm. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.6. Primary frequency standards Michelson interferometer (1887) http://en.wikipedia.org/wiki/Michelson-Morley_experiment http://eosweb.larc.nasa.gov/EDDOCS/Wavelengths_for_Colors.html

  19. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.1. Primary voltage standards 2.3.2. Primary voltage standard AC Josephson effect (1962) h 2q V= f0 A Josephson junction at ~4 K If a direct voltage is applied to the junction terminals, the current of the electron pairs crossing the junction oscillates at a frequency which depends solely on the applied voltage V and fundamental constants. Laboratoire National de Métrologie et d'Essais.www.lne.fr/en/r_and_d/electrical_metrology/josephson_effect_ej.shtml

  20. A chip with N=19,000 series junctions enables the measurement ofV = 10 V ± 110-10 (±10-4 ppm). 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.1. Primary voltage standards h 2q V= f0 The standard volt is defined as the voltage required to produce a frequency of f0 = 483,597.9 GHz. 1 ppm=10-6 Laboratoire National de Métrologie et d'Essais.www.lne.fr/en/r_and_d/electrical_metrology/josephson_effect_ej.shtml

  21. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.2. Primary current standards 2.3.3. Primary current standard: watt balance I V dF dz dF dz mg =- I V= - v VI= mgv Bureau International des Poids et Mesures.www.bipm.fr/en/scientific/elec/watt_balance/wb_principle.html

  22. Measurement uncertainty:I= 1 A ± 110-6 (± 1 ppm). 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.2. Primary current standards NIST: National Institute of Standards and Technology (USA). National Institute of Standards and Technology.www.aip.org/png/html/planck.htm

  23. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.3. Primary resistance standards 2.3.4. Primary resistance standard Quantum Hall effect (von Klitzing 1980) Thin semiconductor at ~1.5 K h q2 R= www.lne.fr/en/r_and_d/electrical_metrology/josephson_effect_ej.shtml http://www.warwick.ac.uk/%7Ephsbm/qhe.htm

  24. 10 µ W ppm 100 µ W ppm m 1 W ppm 10 m ppm 100 m W ppm 1 ppm 10 ppm 100 ppm 1 k W ppm 10 k W ppm 100 k W ppm 1 ppm 10 ppm 100 M W ppm 1 ppm 10 ppm 100 % 1 % 10 % 100 % 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.3. Primary resistance standards Example: Measurement uncertainty (Swedish National Testing and Research Institute) Traceability map Measurements are performed at 6,5kW and 12,9kW. These levels are converted to primary standards by using different types of dividers. Between the realizations, the resistance unit is maintained with a group of six primary standards at 1W. The yearly drift of the group is within ±0,01 ppm. ± 20 ± 7 ± 4 W ± 2 ± 0,5 W ± 0,5 W ± 0,5 W ± 0,5 ± 0,5 ± 0,5 ± 2 M W ± 4 M W ± 5 ± 7 G W ± 15 G W ± 50 ± 0,01 G W ± 0,03 T W ± 0,05 T W ± 0,1 T W Swedish National Testing and Research Institute. www.sp.se

  25. The achieved uncertainty: 1 nF± 510-6 (2 ppm). 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.4. Primary capacitance standards 2.3.5. Primary capacitance standard Thompson-Lampard theorem and cross-capacitors (1956) C1 C2 L L ln 2 p C= e0L  L 1.9pF/m

  26. 1 pF ±10 ppm 10 pF ±5 ppm 100 pF ±5 ppm 1 nF ±5 ppm 10 nF ±20 ppm 100 nF ±50 ppm 1 µF ±100 ppm 10 µF ±500 ppm 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.4. Primary capacitance standards Example: Measurement uncertainty (Swedish National Testing and Research Institute) Traceability map The capacitance unit maintained at SP consists of a group of six 100 pF standards. The measurements are executed with a capacitance bridge with which the unit under test can be directly compared with a reference standard. Swedish National Testing and Research Institute. www.sp.se

  27. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.5. Primary inductance standards 2.3.6. Primary inductance standard It is difficult to realize an accurate standard of inductance. This is caused by the relatively complex geometry of a coil, power losses, skin effect, proximity effect, etc. Currently available standards of inductance have an inaccuracy of about 10-5 (10 ppm). Reference: [1]

  28. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.5. Primary inductance standards An extremely pure inductance, with values ranging from mH to kH in the audio frequency range, can be obtained by means of active electronic circuits, e.g. generalized impedance converters (GIC). Z1 Z3 Z5 Z2 Z4 Z = Z1 Z2 Z3 Z4 Z5 Reference: [1]

  29. 1 µH ±5000 ppm 10 µH ±700 ppm 100 µH ±100 ppm 1 mH ±100 ppm 10 mH ±100 ppm 100 mH ±100 ppm 1 H ±100 ppm 10 H ±500 ppm 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.5. Primary inductance standards Example: Measurement uncertainty (Swedish National Testing and Research Institute) Traceability map The realization of inductance is made from frequency, resistance and capacitance. This realization is made every second year and comprises calibration of all primary standards. The most frequently used calibration method of inductance standards is substitution measurement. The unknown standard is compared with a known standard having the same nominal value as the unknown. Swedish National Testing and Research Institute. www.sp.se

  30. Measurement uncertainty: ±2.510-4 (± 250 ppm). 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.6. Primary frequency standards 2.3.7. Primary temperature standard The standard reference temperature is defined by the triple point of water, at which the pressure and temperature is adjusted so that ice, water, and water vapor exist simultaneously in a closed vessel. The triple point of pure water occurs at +0.0098C and 4.58 mmHg pressure. The kelvin is defined as 1/273.16 of the triple point temperature. Swedish National Testing and Research Institute. www.sp.se Reference: [4]

  31. 10-4 ppm volt Voltage 0.1 ppm Electric current ampere 0.05 ppm Resistance ohm Capacitance 1 ppm farad 10-7 ppm hertz Frequency 250 ppm Temperature kelvin 2 ppm Inductance henry 310-5 ppm Length meter 510-3 ppm Mass kilogram 1.5% candela Luminosity 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.6. Primary frequency standards Concluding Table: measurement uncertainties QUANTITY UNIT APPROXIMATE UNCERTAINTY

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