Measurement Theory Principles

1
LECTURE 2. Contents
2. Measurement of physical quantities 2.1. Ac
quisition of information active and passive
information 2.2. Units, systems of units,
standards 2.2.1. Units 2.2.1. Systems of
units 2.2.1. Standards 2.3. Primary
standards 2.3.1. Primary frequency
standards 2.3.2. Primary voltage
standards 2.3.3. Primary resistance
standards 2.3.4. Primary current
standards 2.3.5. Primary capacitance
standards 2.3.6. Primary inductance
standards 2.3.7. Primary temperature standards
2
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1.
Acquisition of information
2. MEASUREMENT OF PHYSICAL QUANTITIES 2.1.
Acquisition of information
Active measurement object
Active information
Measurement object
x1
y
Ratio measuring system
Reference
xr
Passive measurement object
Passive information
Measurement object
x1
y
xe
xe
Ratio measuring system
Exciter
Reference
xr
3
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1.
Acquisition of information
Example 1(a) Active measurement object
Ratio measuring system
AC magnetic field
B f (R, fB, V/Vref )
R
Measurement model
v
Instrumentation
dB cos(2pf t) A d t
v -
4
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1.
Acquisition of information
Example 1(b) Passive measurement object
Ratio measuring system
DC magnetic field
B f (R, fexc, V/Vref )
f
R
Measurement model
V
Instrumentation
Reference
dB cos(2pf t) A d t
v -
5
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.1.
Acquisition of information
Example 2 (a) Passive measurement object
Ratio measuring system
I
R
Ratio measuring system
VR
R
(b) Active measurement object
V reference
R
Ratio measuring system
T?0ºK
vn
R
6
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 physical
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,
unit is the standard measure.
Reference 1
7
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
equations that describe a particular area of
physics and n is the number of different
quantities in the k equations (n gt 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
8
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2.
Units, systems of units, standards. 2.2.2.
Systems of units
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).
9
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2.
Units, systems of units, standards. 2.2.2.
Systems of units
SYSTÈME INTERNATIONAL DUNITÈS (SI) base and
additional units
QUANTITY
UNIT
SYMBOL
DEFINITION (STANDARDS)
DIMENSION
m
L
Equal to 1,650,763.73 wavelengths in vacuum of
the orange-red line of the krypton-86 spectra.
meter
1. 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
2. Mass
s
T
Time for 9,192,631,770 cycles of resonance
vibration of the cesium-133 atom.
second
3. Time
Absolute zero is defined as 0 kelvin. 0 degrees
Celsius equals 273.16 kelvins.
K
K
kelvin
4. Temperature
Intensity of a light source (frequency 5.40x1014
Hz) that gives a radiant intensity of 1/683
watts/steradian in a given direction.
C
C
candela
5. 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
6. Electric current
mol
Number of elementary entities of a substance
equal to the number of atoms in 0.012 kg of
carbon 12.
mole
-
7. Amount of substance
rad
-
The angle subtended at the center of a circle by
an arc that is of the same length as the radius.
radian
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
10
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2.
Units, systems of units, standards. 2.2.2.
Systems of units
SYSTÈME INTERNATIONAL DUNITÈS (SI) some derived
units
QUANTITY
UNIT
DEFINITION
SYMBOL
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
square meter  
Multiplication of two orthogonal (right-angle)
lengths in meters  
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  
11
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

• an artifact (prototype, ?????)
• a natural phenomenon (atomic processes, etc.)
• a standardized procedure of measurement using
  standardized measurement methods and equipment.

Reference 1
12
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2.
Units, systems of units, standards. 2.2.2.
Standards
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
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
 
14
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2.
Units, systems of units, standards. 2.2.2.
Standards
Illustration Measurement standards
15
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.2.
Units, systems of units, standards. 2.2.2.
Standards
Illustration A primary standard of mass (the
kilogram)
16
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.
Swedish National Testing and Research Institute.
www.sp.se
17
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3.
Primary standards. 2.3.6. Primary frequency
standards
2.3. Primary standards
2.3.1. Primary frequency standard
DE
f 0 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 standard Q2?107.)
18
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3.
Primary standards. 2.3.6. Primary frequency
standards
Michelson interferometer (1887)
http//en.wikipedia.org/wiki/Michelson-Morley_expe
riment
http//eosweb.larc.nasa.gov/EDDOCS/Wavelengths_for
_Colors.html
19
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3.
Primary standards. 2.3.1. Primary voltage
standards
2.3.2. Primary voltage standard
AC Josephson effect (1962)
h 2 q
V f0
A Josephson junction at 4 K
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.
Laboratoire National de Métrologie et d'Essais.
www.lne.fr/en/r_and_d/electrical_metrology/josephs
on_effect_ej.shtml
20
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3.
Primary standards. 2.3.1. Primary voltage
standards
h 2 q
V f0
The standard volt is defined as the voltage
required to produce a frequency of f0 483,597.9
GHz.
1 ppm10 -6
Laboratoire National de Métrologie et d'Essais.
www.lne.fr/en/r_and_d/electrical_metrology/josephs
on_effect_ej.shtml
21
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3.
Primary standards. 2.3.2. Primary current
standards
2.3.3. Primary current standard watt balance
I
V
dF d z
dF d z
mg - I
V - v
V I m g v
Bureau International des Poids et Mesures.
www.bipm.fr/en/scientific/elec/watt_balance/wb_pri
nciple.html
22
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3.
Primary standards. 2.3.2. Primary current
standards
NIST National Institute of Standards and
Technology (USA).
National Institute of Standards and Technology.
www.aip.org/png/html/planck.htm
23
2. 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)
Thin semiconductor at 1.5 K
h q2
R
www.lne.fr/en/r_and_d/electrical_metrology/josephs
on_effect_ej.shtml
http//www.warwick.ac.uk/7Ephsbm/qhe.htm
24
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3.
Primary standards. 2.3.3. Primary resistance
standards
Example Measurement uncertainty (Swedish
National Testing and Research Institute)
Traceability map
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.

20


7

4
W
2

0,5
W

0,5

W

0,5

W

0,5

0,5

0,5


2
W
M

4
M
W
5

7
G
W

15
W
G

50
G
W

0,01
W
T

0,03
0,05
W
T


W
T

0,1
Swedish National Testing and Research Institute.
www.sp.se
25
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3.
Primary standards. 2.3.4. Primary capacitance
standards
2.3.5. Primary capacitance standard
Thompson-Lampard theorem and cross-capacitors
(1956)
C1
C2
L
L
ln 2 p
C e0 L ? L 1.9 pF/m
26
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3.
Primary standards. 2.3.4. Primary capacitance
standards
Example Measurement uncertainty (Swedish
National Testing and Research Institute)
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
Swedish National Testing and Research Institute.
www.sp.se
27
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3.
Primary standards. 2.3.5. Primary inductance
standards
2.3.6. 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).
Reference 1
28
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3.
Primary standards. 2.3.5. Primary inductance
standards
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).
Z1 Z3 Z5 Z2 Z4
Z
Z1
Z2
Z3
Z4
Z5
Reference 1
29
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3.
Primary standards. 2.3.5. Primary inductance
standards
Example Measurement uncertainty (Swedish
National Testing and Research Institute)
Traceability map
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.
Swedish National Testing and Research Institute.
www.sp.se
30
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.
Swedish National Testing and Research Institute.
www.sp.se
Reference 4
31
2. MEASUREMENT OF PHYSICAL QUANTITIES. 2.3.
Primary standards. 2.3.6. Primary frequency
standards
Concluding Table measurement uncertainties
QUANTITY
APPROXIMATE UNCERTAINTY
UNIT
32
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