Measurement
Characteristics
Meelis Sildoja
Introduction

Measurement is the experimental process of acquiring
any quantitative information. When doing a
measurement, we compare the measurable quantity –
measurand - with another same type of quantity. This
other quantity is called measurement unit

Measurand – a physical quantity, property, or
condition which is measured
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Measurements

Can be divided into direct or indirect measurements

Direct measurement – measured quantity is registered directly from the
instruments display.
 Measuring voltage vith voltmeter
 Measuring length with ruler

Indirect measurement – result is calculated (using formula) from the values
obtained from direct measurements
 Finding work done by current:




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U – voltmeter
I – ammeter
t – clock
A=U*I*t
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Classification of physical quantites

Can be divided for quantities which value

is determined uniquely and does not depend on the zero
level



mass
can only be determined as a reference to some fixed zero
level

potential energy (zero level can be ground floor or 3d
floor and result depends on that)

Time
but time interval and change in potential energy belong to the
upper class
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Measurements main equation

The value of the measured quantity can be expressed as
Y  y [Y ]

where [Y] is the measurement unit and y is the
number, which shows how many times the measurable
quantity differs from the unit
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What is instrument

Instrument is a device that transforms a physical variable of
interest (the measurand ) into a form that is suitable for
recording (the measurement)

An example is ruler


the measurand is the length of
some object

the measurement is the number of
units (meters, inches, etc.) that
represent the length
In order for the measurement to have consistent meaning, it is necessary to
employ a standard system of units
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Simple Instrument Model
Physical
Measurement
Variable
Measurement
SENSOR
Measurand
X
Physical Process
Signal
Variable
S
M
Display

The key functional element of the instrument model is the sensor, which has
the function of converting the physical variable input into a signal variable output

Due to the property that signal variables can be manipulated in a transmission
system, such as an electrical or mechanical circuit, they can be transmitted to a
remote output or recording device

In electrical circuits, voltage is a common signal variable
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Simple Instrument Model
Common physical variables
Typical signal variables
• Force
• Voltage
• Length
• Current
• Temperature
• Displacement – spring of newtonmeter
• Acceleration
• Light – change in intensity
• Velocity
• Pressure
• Frequency
• Capacity
• Resistance
• Time
•…
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Simple Instrument Model

If the signal from Sensor output is small, it is needed to be
amplified. In many cases it is also necessary for the instrument to
provide a digital signal output for connection with a computerbased data acquisition systems.
Physical
Measurement
Variable
Measurand
Analog Signal
Variable
AMPLIFIER
SENSOR
X
Analog Signal
Variable
Digital Signal
Variable
A/D
Converter
S
Physical Process
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Computer
Memory
Output
9
Sensors

Sensor - the part of a
measurement system that
responds directly to the
physical variable being
measured

Sensors can be categorized
into two broad classes

Passive sensors

Active sensors
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Passive Sensors

Passive sensors do not add energy
as part of the measurement
process, but may remove energy
in their operation, ie energy is
converted to measurable
quantity

One example of a passive sensor is
a thermocouple, which converts
a physical temperature into a
voltage signal
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Active Sensors

Active sensors add energy to the
measurement environment as
part of the measurement
process

An example of an active sensor
is a radar or sonar, where
actively out-sended radio (radar)
or acoustic (sonar) waves reflect
off of some object and thus
measures its range from the
sensor
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Arecibo Observatory in Puerto Rico
Besides being most powerful radio telescopes
and the largest single unit telescope in the world,
it is also a radar  probably the world biggest
active sensor though
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Sensor Fusion (uniting of sensors)

Sensor fusion - in this case, two or more sensors are used to observe the
environment and their output signals are combined in some manner (typically
in a processor) to provide a single enhanced measurement
Instruments
X1
SENSOR
1
S1
X2
SENSOR
2
S2
X3
SENSOR
3
S3
Physical Process
SENSOR
FUSION
Examples:
1. Sensor output relation to the ambient temp is taken account during the measurements
2. Image synthesis where radar, optical, and infrared images can be combined into a
single enhanced image
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Operational Modes of Instrumentation
I
(Null instrument)

Null Instrument - A
measuring device that
balances the measurand
against a known value, thus
achieving a null condition.
Two inputs are essential to
the null instrument.
Null measurement devices usually consist of
1. automatic or manual feedback system that allows the comparison of known standard value,
2. an iterative balancing operation using some type of comparator
3. and a null deflection at parity
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Null instrument

Advantages:
 Minimizes measurement loading errors (i.e. alter
the value of the measured signal). Effective when
the measurand is a very small value.
 minimizes interaction between the measuring
system and the measurand, by balancing the
unknown input against a known standard input
 Achieving perfect parity (zero condition) is
limited only by the state of the art of the circuit
or scheme being employed

Disatvantages:
 Slow - an iterative balancing operation requires
more time to execute than simply measuring
sensor input. Not suitable for fast
measurements i.e. only for static measurements
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Null instrument - example

An equal arm balance scale
with manual balance feedback

Potetntiometer
AB is the potentiometer wire with resistance R1.
The EMF of a standard DC source is e volts.
The rheostat resistance is R . If the null point
is obtained at point C, then the EMF of e and e1
are equal
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Operational Modes of Instrumentation II
(Deflection instrument)

Deflection instrument - a measuring device whose output deflects (deviates)
proportional to the magnitude of the measurand

Deflection instruments are the most common measuring instruments

Advantages:
 high dynamic response i.e. can be used for fast measurements
 can be designed for either static or dynamic measurements or both

Disadvantages:
 by deriving its energy from the measurand, the act of measurement will
influence the measurand and change the value of the variable being
measured. This change is called a loading error.
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Deflection isnstrument - example
Spring scale as a deflection instrument. Scale has to be calibrated.
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Flow chart of a deflection
instrument
(e.g.multiplication of deflection
signal due to amplification )
The logic flow chart for a deflection instrument is straightforward

Examples of signal conditioning are to multiply the deflection
signal by some scaler magnitude, such as in amplification or
filtering, or to transform the signal by some arithmetic function
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Analog and Digital Sensors

Analog sensors - provide a signal that is continuous in
both its magnitude and its temporal (time) or spatial
(space) content

Digital sensors - provide a signal that is a direct digital
representation of the measurand. Digital sensors are
basically binary (“on” or “off ”) devices. Essentially, a
digital signal exists at only discrete values of time (or
space)
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Analog sensor

The defining word for analog is “continuous” i.e. if a sensor
provides a continuous output signal that is directly proportional
to the input signal, then it is analog
Thermocouple as an analog sensor
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Digital sensor

A common representation of digital signal is the discrete
sampled signal, which represents a sensor output in a form that
is discrete both in time or space and in magnitude.
Data can be sent either in
serial or parallel format
A rotating shaft with a revolution counter. Each revolution generates a spike.
In this example, the continuous rotation of the shaft is analog but the revolution count
is digital. The amplitude of the voltage spike is set to activate the counter and is
not related to the shaft rotational speed.
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Analog Readout Instruments

An analog readout instrument
provides an output indication that
is continuous and directly
analogous to the behavior of the
measurand

For example

deflection of a pointer or an
ink trace on a graduated scale

the intensity of a light beam
or a sound wave
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Digital Readout Instruments

A digital readout instrument provides an output indication that is discrete

Many digital devices combine features of an analog sensor with a digital
readout or, in general, convert an analog signal to a discrete signal. In such
situations, an analog to digital converter (ADC) is required.
 HP3458A digital multimeter, most widely used device in MRI
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E2
P
Z
Input Impedance

In the ideal case, the act of measurement should
not alter the value of the measured signal. Any
such alteration is a loading error

Loading errors can be minimized by impedance
matching of the source with the measuring
instrument – reduce the power needed for
measurement

The power loss through the measuring instrument
 where Z(W) is the input impedance of the
measuring instrument, and E(V) is the source
voltage potential being measured

To minimize the power loss, the input impedance
should be large
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E
P
Z
25
Input impedance - connecting
instruments
An equivalent circuit is formed by applying a measuring instrument
(device 2) to the output terminals of an instrument (device 1).

The potential actually sensed by device 2 will be

The difference between the actual potential E1 and the measured potential E2
is a loading error. High input impedance Z2 relative to Z1 minimizes this
error.

A general rule is for the input impedance to be at least 100 times the source
impedance to reduce the loading error to 1%.
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E 2  E1
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1  Z1 / Z 2
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Calibration

Calibration is the relationship between
the physical measurement variable
(input) and the signal variable (output)
for a specific sensor

Calibration curve – graph that
characterizes sensor or instrument
response to a physical input

Sensitivity of the device is determined
by the slope of the calibration curve.

Dynamic range - the difference between
the smallest and largest physical inputs
that can reliably be measured by an
instrument

Saturation - increasing the physical
input value to the level where there is
no change in output signal
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dynamic range
Saturation region
Calibration curve example.
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Error types and sources
Systematic errors (bias) –
measured values have similar
deviation from correct value
Systematic error
(bias)
Random
error
(precision)
Random errors (noise)–
measured values deviate
randomly around mean value.
Noise describes the precison
of measurements
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Correct terms

Measurement is described by its discrimination , its precision , and its
accuracy

These are too often used interchangeably, but they cover
different concepts:


Discrimination - the smallest increment that can be discerned. Term
resolution is used as a synonym, but according to the “book", it is
now officially decleared as incorrect!
Precision - the spread of values obtained during the measurements.
Two terms that should be used here are:



repeatability - variation for a set of measurements made in a very short
period
reproducibility – same concept, but for measurements made over a long
period
Accuracy - is the closeness of a measurement to the value defined to
be the true value
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Discrimination, precision and accuracy
Two sets of arrow
shots fired into a target
to understand the
measurement concepts
of
discrimination,
precision, and
accuracy
thickness of the hole
decides the discrimination
Better precision i.e. better
repeatability
Better accuracy
i.e. Mean value
closer to bullseye
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Systematic error sources

If measurements are made at
temperature other than the sensor was
calibrated it introduces systematic error.
If systematic error source is known, it
can be corrected for by the use of
compensation methods

Aging of the components will change
the sensor response and hence the
calibration

Damage or abuse of the sensor can also
change the calibration
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
Invasiveness - the measurement process
itself changes the intended measurand.
This is key concern in many
measurement problems.

Reading measurements by human
observer – common error source is
parallax i.e. reading dial from nonnormal angle

NB! Interaction between
measurand and measurement
device is always present
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Invasivness - example

Reducing invasivness


to use high impedance
electronic devices to
measure voltage
Extreme invasiveness

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large warm thermometer to
measure the temperature of
a small volume of cold fluid
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Periodical calibration

In order to prevent systematic errors,
sensors should be
periodically recalibrated
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Random error sources
Environmental
Noise
Transmission
Noise
N3
Sensor
Noise
N2
N1
X
AMPLIFIER
SENSOR
Physical Process

An example for N1 would be
background noise received by a
microphone

The noise will be amplified along with
the signal as it passes through the
amplifier

An example of N2 would be thermal
noise within a sensitive transducer, such
as an infrared sensor

Noise is presented as signal to noise ratio
(SNR).

A common example of N3 is 50 Hz
interference from the electric power grid

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SNR(dB)=10*log(Psignal/Pnoise)
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Random noise

What if Psignal < Pnoise ?

If some identifying characteristics of that signal are
known and sufficient signal processing power is
available, then the signal can be interpreted.

Example of such signal processing is the human ability
to hear a voice in a loud noise environment
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Estimating the measurement
accuracy

Error is defined as the difference between the measured value
and the true value of the measurand

E =(measured) - (true)

where


E = the measurement error

(measured) = the value obtained by a measurement

(true) = the true value of the measurand
Error can almost not be ever known, becuse we don’t know the
(true) value, error can only be estimated.
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What is uncertainty?

Uncertainty of measurement is a parameter that
describes the distribution of the (thinkable) measured
values

The word ‘uncertainty’ expresses the boubt to the
exactness of the result of the measurement

Measurement result is the measurement value with its
uncertainty
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Classification of uncertainties

Standard uncertainty – uncertainty of a measurement expressed as a standard
deviation

Standard uncertainty consists of many components which are divided into two
categories
 type A uncertainty which is estimated using statistical methods


uA(x), where x denotes the measured value for which the uncertainty is given
type B uncertainty which is estimated using means other than statistical
analysis

uB(x)

Combined standard uncertainty -

Expanded uncertainty –
Where k is the coverage factor, typically in range 2-3
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How to estimate uncertainties?
Type A – when taking multiple
values the distribution of these
values corresponds to normal or
Gaussian distribution
0.9
0.8
0.7
-1

Where the sx describes the
broadness of the curve and its
square is called variance

s  standard deviation

s2
_
x
1
f (x) [mm ]

_
x - sx
0.6
0.5
0.4
0.3
_
x - 2sx
0.2
0.1
_
x + 2sx
_
x + 3sx
_
x - 3sx
0
75.2 75.5 75.7 75.9 76.2 76.4 76.7 76.9 77.1 77.4 77.6 77.9
x [mm]
 variance
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_
x + sx
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How to estimate uncertainties II?

Standard deviation

Where xt is the true value

Since we don’t know the true value, we use

Where
is the mean value and sx experimental standard
deviation

and
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How to estimate uncertainties III?

If you take e.g. 100 measurements and divide them to 10 series
each consisting 10 values and then calculate the mean to each
series, you can show that the Stdev of the mean of the series is
related to the Stdev of one series as follows

Number n under the square-root, is the number of
measurements in one series
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