2. measurement of physical quantities

1

2. Measurement of physical quantities2.1. Acquisition of information: active and passive information2.2. Units, systems of units, standards

2.2.1. Units2.2.1. Systems of units2.2.1. Standards

2.3. Primary standards2.3.1. Primary frequency standards2.3.2. Primary voltage standards2.3.3. Primary resistance standards2.3.4. Primary current standards2.3.5. Primary capacitance standards2.3.6. Primary inductance standards2.3.7. Primary temperature standards

LECTURE 2. Contents

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

2. MEASUREMENT OF PHYSICAL QUANTITIES

2.1. Acquisition of information

Reference xr

Active measurement object

Measurement object x1

Active information

Passive measurement object

Exciter

Measurement object

Reference

x1

xr

xe xe

Passive information

Ratio measuring system


y

y

3

AC magnetic field

v

B= f (R, fBV/Vref )

Measurement object

Reference

Measurement model

Example 1(a): Active measurement object


R

Instrumentation

v d[B cos(2f t) A]

d t


4

Example 1(b): Passive measurement object


DC magnetic field

B= f (R, fexcV/Vref )

Exciter

Measurement object

Reference

Measurement modelV

Rf

Instrumentation

v d[B cos(2f t) A]

d t


5

Example 2: (a) Passive measurement object


Measurement object

RVR Ratio

measuring system

Exciter IRatio

measuring system

V or I references

(b) Active measurement object

R

Measurement object

Rvn T0ºK

V reference

Ratio measuring systemR

62. 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 to which we refer the measurement is called (ערך פיזיקאלי)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]

72. 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]


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).


QUANTITY SYMBOL DEFINITION (STANDARDS)

1. Length m L Equal to 1,650,763.73 wavelengths in vacuum of the orange-red line of the krypton-86 spectra.

2. Mass 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.)

3. Time s T Time for 9,192,631,770 cycles of resonance vibration of the cesium-133 atom.

4. Temperature K K Absolute zero is defined as 0 kelvin. 0 degrees Celsius equals 273.16 kelvins.

5. Luminosity 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.

6. Electric current 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.

7. Amount of substance mol Number of elementary entities of a substance

equal to the number of atoms in 0.012 kg of carbon 12.

DIMENSION

*Angle rad The angle subtended at the center of a circle by an arc that is of the same length as the radius.

*Solid angle sr The solid angle subtended at the center of a sphere by an area on its surface equal to the square of its radius.

SYSTÈME INTERNATIONAL D’UNITÈS (SI): base and additional* units

UNIT

mole

radian

steradian

meter

kilogram

second

kelvin

candela

ampere

10

DEFINITION


Acceleration

Area

Volume

Force

Charge

Energy

Power

Resistance

Frequency

Pressure

Velocity

Potential (emf)

SYSTÈME INTERNATIONAL D’UNITÈS (SI): some derived units

meter/s/s

m s-2

ML-2

Rate of change of velocity of 1 meter per 1 second per one second. square

meter

m2

M2

Multiplication of two orthogonal (right-angle) lengths in meters cubic

meter

m3

M3

Multiplication of three mutually orthogonal (right-angle) lengths in meters.

newton

N

MLT-2

The force required to accelerate a 1 kilogram mass 1 meter / second / second.

coulomb

C

IT

Quantity of electricity carried by a current of 1 ampere for 1 second.

joule

J

ML2T-2

Work done by a force of 1 newton moving through a distance of 1 meter in the direction of the force. watt

W

ML2T-3

Energy expenditure at a rate of 1 joule per 1 second.

ohm

ML2T-3I-2

Resistance that produces a 1 volt drop with a 1 ampere current.

hertz

Hz

T-1

Number of cycles in 1 second.

pascal

Pa

ML-1T-2

Pressure due a a force of 1 newton applied over an area of 1 square meter.

meter/s

m s-1

LT-1

Rate of movement in a direction of 1 meter in 1 second.

volt

V

ML2T-3I-1

The potential when 1 joule of work is done in making 1 coulomb of electricity flow.

DEFINITIONQUANTITY SYMBOL DIMENSIONUNIT

11

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:

2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Standards

an artifact (prototype, מכשיר);

a natural phenomenon (atomic processes, etc.);

a standardized procedure of measurement using standardized measurement methods and equipment.

2.2.3. Standards

Reference: [1]

12

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 primary and secondary standards.

Primary standards are preserved and improved in a national institute of standards and technology.

Reference: [1]

13


Illustration: The hierarchy of standards

Primarystandard

Secondarystandard

Measuring instrument

Deviceunder test

Absolute accuracy

Relative accuracy

14

Defacto internationalstandards

Industrystandards

Standards users

Internationalstandards

Nationalstandards


Illustration: Measurement standards

International Electrotechnical

Commission (IEC)

International Organization for Standards (ISO)

Internationalstandards

Nationalstandards

Israeli Standards Institute

(SII)

British Standards Institute

(BSI)

Other national standards

associations

American NationalStandard Institute

(ANSI)

AmericanSociety for

Quality)ASQ (

AmericanSociety forTesting and Materials

)ASTM (

Institute of Electrical and

ElectronicEngineers

)IEEE (

Other member societies

American NationalStandard Institute

)ANSI(

15

Illustration: A primary standard of mass (the kilogram)


Swedish National Testing and Research Institute, www.sp.se

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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

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2.3.1. Primary frequency standard

2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.6. Primary frequency standards

Measurement uncertainty: ±11012 s (± 106 ppm).

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 standard Q=210.)

2.3. Primary standards

E

f 0= E/h e

18

Michelson interferometer (1887)


Measurement uncertainty: up to 1 nm.

http://en.wikipedia.org/wiki/Michelson-Morley_experiment http://eosweb.larc.nasa.gov/EDDOCS/Wavelengths_for_Colors.html

192. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.1. Primary voltage standards

2.3.2. Primary voltage standard

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.

V f0h2 q

A Josephson junction at ~4 K

AC Josephson effect (1962)

Laboratoire National de Métrologie et d'Essais. www.lne.fr/en/r_and_d/electrical_metrology/josephson_effect_ej.shtml

202. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.1. Primary voltage standards

A chip with N=19,000 series junctions enables the measurement of V = 10 V ± 110 10 (±10

4 ppm). 1 ppm=10 6

The standard volt is defined as the voltage required to produce a frequency of f0 483,597.9 GHz.

V f0h2 q

Laboratoire National de Métrologie et d'Essais. www.lne.fr/en/r_and_d/electrical_metrology/josephson_effect_ej.shtml

212. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.2. Primary current standards

2.3.3. Primary current standard: watt balance

V I m g v

Bureau International des Poids et Mesures. www.bipm.fr/en/scientific/elec/watt_balance/wb_principle.html

mg I dd z

V vdd z

VI

222. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.2. Primary current standards

Measurement uncertainty: I = 1 A ± 1106 (± 1 ppm).

National Institute of Standards and Technology. www.aip.org/png/html/planck.htm

NIST: National Institute of Standards and Technology (USA).

232. 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)

www.lne.fr/en/r_and_d/electrical_metrology/josephson_effect_ej.shtml http://www.warwick.ac.uk/%7Ephsbm/qhe.htm

Thin semiconductor at ~1.5 K

R hq2

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Example: Measurement uncertainty(Swedish National Testing and Research Institute)

2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.3. Primary resistance standards

Measurements are performed at

6,5 k and 12,9 k. 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 1 . The yearly drift of the

group is within ±0,01 ppm. T

µ µ

m m

m

k k

kM MM G

G G

T T

10 100

1 10

100 1

10100

1 10

1001

10 100

1 10

100 1

10 100

±20 ±7 ±4 ±2 ±0,5 ±0,5 ±0,5 ±0,5 ±0,5 ±0,5 ±2 ±4 ±5 ±7 ±15 ±50 ±0,01 ±0,03

±0,1 ±0,05

ppm ppm ppm ppm ppm ppm ppm ppm ppm ppm ppm ppm ppm ppm ppm ppm % % %

%


Traceability map

25

L

2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.4. Primary capacitance standards

2.3.5. Primary capacitance standard

The achieved uncertainty: 1 nF ± 510 6 (2 ppm).

Thompson-Lampard theorem and cross-capacitors (1956)

C 0 L L 1.9pF/m ln 2

L

C1 C2

262. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.4. Primary capacitance standards

ppm

ppm

ppm

ppm

ppm

ppm

ppm

1

10

100

1

10

100

1

10

pF

pF

pF

nF

nF

nF

µF

µF

±10

±5

±5

±5

±20

±50

±100

±500 ppm


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.


Traceability map

27

2.3.6. Primary inductance standard

2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.5. Primary inductance standards

Currently available standards of inductance have an inaccuracy of about 10 5 (10 ppm).

Reference: [1]

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.


Reference: [1]

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).

Z Z1 Z3 Z5

Z2 Z4 Z1

Z4

Z2

Z3

Z5

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1

10

100

1

10

100

1

10

µH

µH

µH

mH

mH

mH

H

H

±5000

±700

±100

±100

±100

±100

±100

±500

ppm

ppm

ppm

ppm

ppm

ppm

ppm

ppm

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 .




Traceability map

30

2.3.7. Primary temperature standard


Reference: [4]

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 0.0098C and 4.58 mmHg pressure.

The kelvin is defined as 273.16 of the triple point temperature.

Measurement uncertainty: ±2.5104 (± 250 ppm).



Concluding Table: measurement uncertainties

QUANTITY APPROXIMATE UNCERTAINTYUNIT

Temperature kelvin 250 ppm

Voltage volt 10 4 ppm

Electric current ampere 0.1 ppm

Resistance ohm 0.05 ppm

Capacitance farad 1 ppm

Inductance henry 2 ppm

Frequency hertz 10 7 ppm

Length meter 310 5 ppm

Mass kilogram 510 3 ppm

Luminosity candela 1.5 %

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2. measurement of physical quantities

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