1 2. measurement of physical quantities. 2.1. acquisition of information 2. measurement of physical...

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

2. MEASUREMENT OF PHYSICAL QUANTITIES

2.1. Acquisition of information

ReferenceReference xr

Active measurement object

Measurement objectMeasurement object

Ratio measuring system


x1 y

Active information

Passive measurement object

ExciterExciter


ReferenceReference



x1

xr

xe xey

Passive information

2

AC magnetic field

v

B= f (R, fBV/Vref )

Measurement objectMeasurement object Ratio measuring system


ReferenceReference

Measurement model

Example 1(a): Active measurement object


R

Instrumentation

3

Example 1(b): Passive measurement object


DC magnetic field

B= f (R, V/Vref )

ExciterExciter

Measurement objectMeasurement object Ratio measuring system


ReferenceReference

Measurement modelV

R

Instrumentation

4

Example 2: Passive measurement object



RVR


ExciterExciter IRatio

measuring system


V or I referencesV or I references

Active measurement object

R


Rvn T0ºK

V referenceV reference


Ratio measuring systemR

52. 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]

62. 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]


QUANTITY SYMBOL DEFINITION

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

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.)

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

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

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.

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.

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

8

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

9

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

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.).

2.2.3. Standards

Reference: [1]

10

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]

11


Illustration: The hierarchy of standards

Primarystandard

Secondarystandard

Measuring instrument

Deviceunder test

Absolute accuracy

Relative accuracy

12

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(

13

Illustration: A primary standard of mass (the kilogram)


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

14

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

152. 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

vVJ 2VJ 3VJ

VJ = f0 h/2q

1 nm

Lead

Lead oxide

v

i

B, f0

f0 10 GHz at 4 K


2.3. Primary standards

2.3.1. Primary voltage standard

Josephson effect (1962)

VJ = f0 h/2q

1 nm

Lead

Lead oxide

v

i

B, f0

f0 10 GHz at 4 K

Reference: IEEE Trans. Magn., vol. 41, p. 3760, 2005.

עופרת

17

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


AC Josephson effect (1962)

V = f0 h/2q

V

i=I cos(2f0 t)Superconductor

Josephson junction (~1 nm)

A chip with N=19000 series junctions enables the measurement of V = 10 V ± 110 10 (± 10 4 ppm).

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

2.3.2. Primary current standard

Measurement uncertainty: I = 1 A ± 3106 (± 3 ppm).

R

R/2

R/2

F = m·g

Fixed Helmholtz coils

I

I I

All the coils are connected in series

F = I 2 dM/dxM is the mutual induction between the coils.

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

2.3.3. Primary resistance standard

R = VH /I=h/q2

V

B 9 T

I

Quantum Hall effect (1980)

Thin semiconductor at 1K

V

B

VH

2VH

20

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

10

100

1

10

100

1

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

%

%

%

%

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

2.3.4. Primary capacitance standard

The achieved inaccuracy: 1 nF ± 510 6 (5 ppm).

Thompson-Lampard theorem and cross-capacitors (1956)

C=(C1+C2)/2 = 0 L ln(2)/pF/m

L

C1 C2

C = 0 L ln(2)/

222. 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


23

2.3.5. 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]

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).

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.

24

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 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 .

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


25

2.3.6. Primary frequency standard

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

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

E

f 0= E/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 standard Q=210.)

26

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).


Reference: [4]

Concluding Table: measurement uncertainties of base SI units

QUANTITY APPROXIMATE UNCERTAINTYUNIT

Length meter 31011

Mass kilogram 5109

Time second 11013

Temperature kelvin 2.5104

Luminosity candela 1.5102

Electric current

ampere 1106

Amount of substance mole TBD

107 ppm

105 ppm

103 ppm

1 ppm

250 ppm

1.5 %

28Next lecture

Next lecture: LabView (in the computer class)

1 2. measurement of physical quantities. 2.1. acquisition of information 2. measurement of physical...

Documents