2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information

1. Active measurement object Measurement object x1 y Ratio measuring system Reference x3 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information 2. MEASUREMENT OF PHYSICAL QUANTITIES 2.1. Acquisition of information • Passive measurement object Measurement object x1 y s x2 Ratio measuring system Exciter Reference x3

2. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information Example: Passive measurement object Measurement object Ratio measuring system Static magnetic field B=f(R, w,V/Vref ) w R Measurement model V Instrumentation Exciter Reference

3. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information Example: Active measurement object Measurement object Ratio measuring system AC magnetic field B=f(R, fB,V/Vref ) R Measurement model v Instrumentation Reference

4. Active measurement object Measurement object V reference R Ratio measuring system T0ºK v 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information Example: Passive measurement object Measurement object V and I references Exciter Ratio measuring system I R Ratio measuring system R V R

5. 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 of the quantity to which we refer the measurement is called the measure. For absolute measurements the measure is internationally standardized and for simplicity is set equal to unity. Therefore, in the case of absolute measurements, the measure constitutes the unit of the quantity that is being measured, Reference: [1]

6. 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 quantity equations that describe a particular area of physics and n is the number of different quantities in the k equations, then n-k quantities can be used freely as base quantities in a system of units suitable for that area of physics. • The other quantities are derived quantities that follow from the base quantities and the k equations. Reference: [1]

7. 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 DIMENSION m L Equal to 1,650,763.73 wavelengths in vacuum of the orange-red line of the krypton-86 spectra. meter 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 Mass s T Time for 9,192,631,770 cycles of resonance vibration of the cesium-133 atom. second Time Absolute zero is defined as 0 kelvin. 0 degrees Celsius equals 273.16 kelvins. K K kelvin Temperature C C Intensity of a light source (frequency 5.40x1014 Hz) that gives a radiant intensity of 1/683 watts / steradian in a given direction. candela 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 Electric current mole mol Number of elementary entities of a substance equal to the number of atoms in 0.012 kg of carbon 12. - 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

8. 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

9. 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: • a tangible representation of the physical quantity, for example, in the case for the standard measure of mass: the kilogram; • a standardized procedure of measurement using standardized measurement methods and equipment; • a natural phenomenon (atomic processes, etc.). Reference: [1]

10. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards . 2.2.2. Standards Measurements are usually based on secondary or even 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]

11. 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

12. 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

13. 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)

14. 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.

15. VJ = f0h/2q 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.1. Primary voltage standards 2.3. Primary standards 2.3.1. Primary voltage standard Josephson effect (1962) i i 1 nm Lead oxide B, f0 v v VJ 2VJ 3VJ Lead f0 10 GHz at 4 K

16. VJ = f0h/2q 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.1. Primary voltage standards 2.3. Primary standards 2.3.1. Primary voltage standard Josephson effect (1962) i 1 nm Lead oxide B, f0 v Lead עופרת f0 10 GHz at 4 K Reference:IEEE Trans. Magn., vol. 41, p. 3760, 2005.

17. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.1. Primary voltage standards 2.3. Primary standards 2.3.1. Primary voltage standard AC Josephson effect (1962) Josephson junction (~1 nm) i=I cos(2pf0 t) Superconductor V= f0 h/2q V The standard volt is defined as the voltage required to produce a frequency of 483,597.9 GHz. A chip with N=19000 series junctions enables the measurement ofV = 10 V ± 110-10 (± 10-4 ppm).

18. F=I2 dM/dx 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.2. Primary current standards 2.3.2. Primary current standard I R/2 Fixed Helmholtz coils I I R/2 F = m·g R All the coils are connected in series M is the mutual induction between the coils = f(geometry) Measurement uncertainty:I= 1 A ± 310-6 (± 3 ppm).

19. R= VH /I=h/q2 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.3. Primary resistance standards 2.3.3. Primary resistance standard Quantum Hall effect (1980) Thin semiconductor at 1K B 9 T V I 2VH VH V B

20. 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) 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

21. C1 C2 L C=(C1+C2)/2=e0 L ln(2)/p 1.9 pF/m The achieved inaccuracy: 1 nF± 510-6 (5 ppm). 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.4. Primary capacitance standards 2.3.4. Primary capacitance standard Thompson-Lampard theorem and cross-capacitors (1956) C =e0 L ln(2)/p

22. 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)

23. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.5. Primary inductance standards 2.3.5. 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). 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). Reference: [1]

24. 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) The realization of inductance at 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.

25. 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.6. Primary frequency standards 2.3.6. 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.) Measurement uncertainty: ±110-12 s (± 10-6 ppm).

26. 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. Measurement uncertainty: ±2.510-4 (± 250 ppm). Reference: [4]

27. 310-11 Length meter 510-9 Mass kilogram 110-13 second Time 2.510-4 Temperature kelvin 1.510-2 candela Luminosity Electric current 110-6 ampere TBD Amount of substance mole 2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.6. Primary frequency standards Concluding Table: measurement uncertainties of base SI units QUANTITY UNIT APPROXIMATE UNCERTAINTY 10-7 ppm 10-5 ppm 10-3 ppm 1 ppm 250 ppm 1.5% Reference: [4]

28. Next lecture Next lecture: LabView (in the computer class)