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2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information
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2. MEASUREMENT OF PHYSICAL QUANTITIES
2.1. Acquisition of information
Active measurement object
Active information
x1
Measurement object
xr
Reference
Passive measurement object
Exciter
xe
Measurement object
Reference
Ratio
measuring system
y
Passive information
xe
x1
xr
Ratio
measuring system
y
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information
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Example 1(a): Active measurement object
Measurement object
Ratio
measuring system
AC magnetic field
B= f (R, fB, V/Vref )
R
v
Measurement
model
Instrumentation
Reference
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information
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Example 1(b): Passive measurement object
Measurement object
Ratio
measuring system
DC magnetic field
B= f (R, w, V/Vref )
R
w
V
Measurement
model
Instrumentation
Exciter
Reference
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1. Acquisition of information
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Example 2: Passive measurement object
Measurement object
Exciter
V or I references
I
R
VR
Ratio
Ratio
measuring
measuring system
system
R
Active measurement object
Measurement object
T0ºK
R
vn
V reference
Ratio
measuring system
R
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.1. Units
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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]
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Systems of units
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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]
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
Length
meter
m
DIMENSION
DEFINITION
L
Equal to 1,650,763.73 wavelengths in vacuum of the
orange-red line of the krypton-86 spectra.
Mass
kilogram
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
second
s
T
Time for 9,192,631,770 cycles of resonance vibration
of the cesium-133 atom.
Temperature
kelvin
K
K
Absolute zero is defined as 0 kelvin.
0 degrees Celsius equals 273.16 kelvins.
C
Intensity of a light source (frequency 5.40x1014 Hz) that
gives a radiant intensity of 1/683 watts / steradian in a
given direction.
Luminosity
candela
C
Electric
current
ampere
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
mole
mol
-
Number of elementary entities of a substance
equal to the number of atoms in 0.012 kg of carbon 12.
*Angle
radian
rad
-
The angle subtended at the center of a circle by an arc that
is of the same length as the radius.
*Solid angle
steradian
sr
-
The solid angle subtended at the center of a sphere by an
area on its surface equal to the square of its radius.
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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
Acceleration
meter/s/s
m s-2
ML-2
Rate of change of velocity of 1 meter per 1 second per one
second.
Area
square
meter
m2
M2
Multiplication of two orthogonal (right-angle) lengths in
meters
Volume
cubic
meter
m3
M3
Multiplication of three mutually orthogonal (right-angle)
lengths in meters.
Force
newton
N
MLT-2
The force required to accelerate a 1 kilogram mass 1 meter
/ second / second.
Charge
coulomb
C
IT
Quantity of electricity carried by a current of 1 ampere for 1
second.
Energy
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.
Power
watt
W
ML2T-3
Energy expenditure at a rate of 1 joule per 1 second.
Resistance
ohm
W
ML2T-3I-2
Resistance that produces a 1 volt drop with a 1 ampere
current.
Frequency
hertz
Hz
T-1
Number of cycles in 1 second.
Pressure
pascal
Pa
ML-1T-2
Pressure due a a force of 1 newton applied over an area of
1 square meter.
Velocity
meter/s
m s-1
LT-1
Rate of movement in a direction of 1 meter in 1 second.
Potential
(emf)
volt
V
ML2T-3I-1
The potential when 1 joule of work is done in making 1
coulomb of electricity flow.
SYMBOL
DIMENSION
DEFINITION
DEFINITION
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2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Standards
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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]
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Standards
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There are primary and secondary standards.
Primary standards are preserved and improved in a national
institute of standards and technology.
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.
Reference: [1]
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
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2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Standards
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Illustration: Measurement standards
Standards users
International
standards
Defacto
international
standards
International
Organization for
Standards (ISO)
International
Electrotechnical
Commission (IEC)
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
National
standards
Industry
standards
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Standards
Illustration: A primary standard of mass (the kilogram)
Swedish National Testing and Research Institute, www.sp.se
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2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2. Units, systems of units, standards. 2.2.2. Standards
Example:
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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
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.1. Primary voltage standards
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2.3. Primary standards
2.3.1. Primary voltage standard
Josephson effect (1962)
i
i
1 nm
Lead oxide
B, f0
v
VJ 2VJ 3VJ
Lead
f0  10 GHz at 4 K
VJ = f0 h/2q
v
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.1. Primary voltage standards
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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
VJ = f0 h/2q
Reference: IEEE Trans. Magn., vol. 41, p. 3760, 2005.
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.1. Primary voltage standards
AC Josephson effect (1962)
Josephson junction (~1 nm)
Superconductor
i=I cos(2pf0 t)
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 of V = 10 V ± 110 -10 (± 10 -4 ppm).
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2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.2. Primary current standards
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2.3.2. Primary current standard
I
R/2
Fixed Helmholtz coils
I
F = m·g
I
R
All the coils are connected in series
M is the mutual induction between
the coils.
F = I 2 dM/dx
Measurement uncertainty: I = 1 A ± 310-6 (± 3 ppm).
R/2
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.3. Primary resistance standards
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2.3.3. Primary resistance standard
Quantum Hall effect (1980)
Thin semiconductor
at 1K
B 9 T
V
I
2VH
V
VH
B
R = VH /I=h/q2
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.3. Primary resistance standards
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Example: Measurement uncertainty
(Swedish National Testing and Research Institute)
Measurements are performed at 6,5
kW and 12,9 kW. 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 W. The yearly drift of the group is
within ±0,01 ppm.
10
µW
± 20 ppm
100
µW
± 7 ppm
1 mW
± 4 ppm
10 m W
± 2 ppm
100 mW
± 0,5 ppm
1
W
± 0,5 ppm
10
W
± 0,5 ppm
100
W
± 0,5 ppm
1
kW
± 0,5 ppm
10
kW
± 0,5 ppm
100
kW
± 2 ppm
1 MW
± 4 ppm
10 M W
± 5 ppm
100
MW
± 7 ppm
1
GW
± 15 ppm
10
GW
± 50 ppm
100
GW ± 0,01
%
1
TW ± 0,03
%
10
TW ± 0,05
%
%
100
TW
± 0,1
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)
C1
C2
L
C = e0 L ln(2)/p
C=(C1+C2)/2 = e0 L ln(2)/p 1.9 pF/m
The achieved inaccuracy: 1 nF ± 510 -6 (5 ppm).
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2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.4. Primary capacitance standards
Example: Measurement uncertainty
(Swedish National Testing and Research Institute)
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
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2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.5. Primary inductance standards
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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]
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.5. Primary inductance standards
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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.
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. 2.3.6. Primary frequency standards
2.3.6. Primary frequency standard
DE
e
f 0= DE/h
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=2107.)
Measurement uncertainty: ±110-12 s (± 10-6 ppm).
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2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.6. Primary frequency standards
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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]
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3. Primary standards. 2.3.6. Primary frequency standards
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Concluding Table: measurement uncertainties of base SI units
QUANTITY
UNIT
Time
second
110-13
10-7 ppm
Length
meter
310-11
10-5 ppm
Mass
kilogram
510-9
10-3 ppm
Electric current
ampere
110-6
1 ppm
Temperature
kelvin
2.510-4
250 ppm
Luminosity
candela
1.510-2
1.5 %
Amount of substance
mole
APPROXIMATE UNCERTAINTY
TBD
Reference: [4]
Next lecture
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