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12. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information
Passive measurement object
2. MEASUREMENT OF PHYSICAL QUANTITIES
2.1. Acquisition of information
ExciterExciter
Measurement objectMeasurement object
ReferenceReference
Ratio measuring system
Ratio measuring system
x1
x3
s x2y
Active measurement object
Measurement objectMeasurement object
ReferenceReference
Ratio measuring system
Ratio measuring system
x1
x3
y
2
Example: Passive measurement object
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information
Static magnetic field
B= f (R, V/Vref )
ExciterExciter
Measurement objectMeasurement object Ratio measuring system
Ratio measuring system
ReferenceReference
Measurement modelV
R
Instrumentation
3
AC magnetic field
v
B= f (R, fBV/Vref )
Measurement objectMeasurement object Ratio measuring system
Ratio measuring system
ReferenceReference
Measurement model
Example: Active measurement object
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information
R
Instrumentation
4
Example: Passive measurement object
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information
Measurement objectMeasurement object
RV
Ratio measuring system
ExciterExciter I
V and I referencesV and I references
Ratio measuring system
Ratio measuring system
Active measurement object
R
Measurement objectMeasurement object
Rv T0ºK
V referenceV reference
Ratio measuring system
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 nk 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]
72. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Systems of units
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
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Systems of units
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.
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards . 2.2.2. Standards
There are primary and 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
Primarystandard
Secondarystandard
Measuring instrument
Deviceunder test
Absolute accuracy
Relative accuracy
12
Defacto internationalstandards
Industrystandards
Standards users
Internationalstandards
Nationalstandards
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards . 2.2.2. Standards
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)
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Standards
Swedish National Testing and Research Institute, www.sp.se
14
Example: Preservation of the standard
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Standards
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.
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
162. 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)
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
172. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.1. Primary voltage standards
AC Josephson effect (1962)
V = f0 h/2q
V
i=I cos(2f0 t)Superconductor
Josephson junction (~1 nm)
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 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
=f(geometry)
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
Example: Measurement uncertainty(Swedish National Testing and Research Institute)
23
2.3.5. Primary inductance standard
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.5. Primary inductance standards
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]
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).
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
Example: Measurement uncertainty(Swedish National Testing and Research Institute)
25
2.3.6. Primary frequency standard
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.6. Primary frequency standards
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.)
Measurement uncertainty: ±11012 s (± 106 ppm).
E
f 0= E/h e
26
2.3.7. Primary temperature standard
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.6. Primary frequency standards
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).
27
Concluding Table: measurement uncertainties of base SI units
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.6. Primary frequency standards
Reference: [4]
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 %
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