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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
Dr.LsTeo/Ykleong 1/18
Chapter 1: Instrumentation system and measurement
Objectives of chapter
Introduction to general element of measurement system
Explaining some criteria in defining measurement errors
Describing of limiting error and its derivation/combination
Explaining type of errors that could be involved in a measurement system
Chapter contents and outline
1.0 Introduction to measurement system
1.1 Terms
1.2 Elements of a generalized measurement system
1.3 Functions of instrument
2.0 Measurement errors
2.1 Terms
2.2 Limiting and guarantee errors
2.3 Type of errors
3.0 Measurement Standard
3.1 Terms
3.2 Fundamental and secondary units
3.3 Symbols and notation (refer attachment)
3.4 Equation and numbering
3.5 Dimension analysis
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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1.0 Instrumentation system
A measurement system converts the unknown quantity of a energy to a numerical unit
using an instrument (result: number + measured unit, e.g.: 6.8 Kg/(ms)2.
1.1 Terms
Measurement comparison between an unknown quality and a predefined standard
Measurand the unknown quality to be measured.
Instrument physical device uses to determined measurand numerically.
1.2 Elements of a generalized measurement system
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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1. Transducer
a) a device which converts energy from one form to another
b) input transducer (sensor); output transducer (actuator)
2. Sensor
a) a device which senses and detects the physical quantity of measurand
b) mechanical, e.g. Bourdon tube pressure meter, advt: reliable for static & stable
condition, disavdt: not for fast transient measurement
c) electrical, e.g. voltmeter & ammeter, advt: more rapid condition
c) electronic, e.g. digital meter, advt: fast & higher precision
3. Variable conversion element e.g. ADC or DAC
4. Variable manipulation element
a) to manipulate the signal presented to it while preserving the original
information.
b) e.g. : signal amplifier.
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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5. Signal conditioning
a) operation performed on the signal to bring it to the desired form.
b) includes variable conversion and variable manipulation.
6. Telemetry
a) transmission of data from remote sources to serve specific purposes.
7. data presentation element (also output transducer)
a) to convey the measured quantity for further action: display, recording and
control.
b) E.g. CRT, printer, magnetic tapes, LCD.
1.3 Functions of instrument
a) Indicating function: meter display (in a car or voltmeter), digital display.
b) Recording function: data keeping, e.g. record volume of production
c) Controlling function: temperature, position, speed, liquid level, flow control
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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2.0 Measurement Error
2.1 Terms
1. True value -- Almost impossible to obtain in practice
2. Measured value value indicated by an instrument
It should follow by its uncertainty in measurement.
Exp:
l = (1.5 0.1) cm
3. Norminal value value of the quality specified by the manufacturer
It normally follows by tolerence
Exp:
R= 10 k 10 %
4. Static error
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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The difference between the measured value and the true value of the quantity
tm AAAtruevalueluemeasuredvaerror
=
5. Relative static error
tr A
A =
6. Accuracy
Closeness with which an instrument reading approaches the true value
7. Precision
Is a measure of the reproducibility of the measurement
It composed of 2 characteristics : conformity & number of significant figures
E.g.:
At = 1.51 mm
After measured:
System 1 gives; Am1 = 1.478mm (more precise)
System 2 gives; Am2 = 1.5mm (more accurate)
8. Sensitivity
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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the ratio of the magnitude of the output signal or response to the magnitude of
input signal
9. Hysterisis
A phenomenon which depicts different output effects when loading and unloading
10. Reliability
The period for an instrument which can maintain its accuracy and precision.
11. Resolution or discrimination
The smallest increment in input which can be detected with certainty by an
instrument
12. Response time
Time period for an instrument from sensing till it reached to a steady state
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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13. Frequency response
A minimum time that an instrument can sense an instantaneous signal changed.
14. Switching time
Normally for all digital circuits (including microprocessor devices)
Minimum time that can perform well in on-off switching
15. Bandwidth
The range of frequency that gives satisfactory output response.
2.2 Limiting or Guarantee Errors
1. What is guarantee error?
a) To ensure the customer the quality of the instrument, the manufacturer guarantees a
certain accuracy of their product.
b) The manufacturers specify the deviations from the nominal value of a particular
quantity.
c) The limits of these deviations from the specified value are defined as limiting errors or
guarantee errors.
d) Actual value Aa= AS A where AS is the nominal value & A is the limiting error.
A a satisfies: AS - A AV AS + A
e) Relative limiting error,
S
r AA
=
f) % Relative accuracy = (1- r )x 100%
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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g) E.g.: the value of capacitance of a capacitor is specified as 1 F 5% by the
manufacturer.
A = rAS = 0.05 X 1F = 0.05F
0.95F Aa 1.05F
2. Combination of limiting error
a) Sum of quantities
Let y be the final result which is the sum of measured quantities x1, x2,, xn.
y = x1 + x2 + xn
dy= dx1 + dx2 + dxn
If the errors in the component quantities, dxi , are represented by x1, x2, , xn,
limiting error y in y is given by :
y = x1 + x2 + xn
b) Difference of 2 quantities
y = u v
dy = du - dv
If the errors in u and v are u and v respectively, consider worst case, i.e., when the
error in u is +u and error in v is -v and vice versa,
y = ( u + v)
In general,
y = x1 x2 xn
y = (x1 + x2 ++ xn)
c) Product of n components
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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y=x1x2xn
ln y = lnx1 + lnx2 + +lnxn
differentiating:
n
n
xdx
xdx
xdx
ydy
+++= ...2
2
1
1
Limiting error:
=
=n
i i
i
xx
yy
1
d) Quotient of more then 2 quantities
nxxxy
...1
21
=
ln y = -lnx1 - lnx2 - -lnxn
Than limiting error
=
=n
i i
i
xx
yy
1
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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e) Power of a factor
y = x1m1x2m2xnmn
ln y = m1 ln x1 + m2 ln x2 ++ mn ln xn
limiting error:
=
=n
i i
ii xxm
yy
1
f) E.g.:
Given 3 resistors with values R1 =37 5% , R2 = 75 10%, R3 =50 5%.
Determine the magnitude and limiting error in ohm and in percent of the resistance of
a) these resistors which are connected in series.
b) These resistor which are connected in parallel
Solution :
In series
R1 = (37 1.85) R2 = (75 7.5) R3 = (50 2.5)
R = R1 + R2 +R3
R= R1 + R2 +R3
R = (1.62 11.85) or 162 7%
In parallel
1/R = 1/R1 + 1/R2 + 1/R3
R/R2 = R1 /R12 + R2/R22 + R3/R32
R= (16.56 1.01) or R= 16.56 6.1%
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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g) Known error
If error of a quantity is known exactly, the effect of error can be taken into a/c as in
combining limiting error. The only difference is that the sign of the error must be
preserved in all calculations.
2.3 Type of Errors
1. Gross Errors
Refer to errors due to human mistake in reading instruments and recording and
calculating measurement results.
E.g. 1: read the temperature as 31.5C while the actual reading may be 21.5C
E.g. 2: read 25.8C and record as 28.5C
Prevention: read and record carefully, and taking the average of several reading
2. Systematic Errors
a) Instrumental errors
i) due to inherent shortcoming in the instrument
Inherent due to their mechanical structure.
They may be due to construction, calibration or operation of the.
E.g.: If the spring (use for producing controlling torque) of a permanent magnet
instrument has become weak, the device will always read high.
Overcome methods
- re-calibrated carefully
- apply correction factors after determining the instrumental errors
ii) due to misuse of instrument
E.g. 1: failure to adjust the zero of instruments
E.g. 2: using leads of too high resistance (when measure low R value)
iii) due to loading effect of instruments
E.g.:
A voltmeter having a sensitivity of 1000/V reads 100V on its 150V scale
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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when connected across an unknown resistor in series with a milliammeter.
The milliammeter reads 5mA.
Think of the loading effect introduces by voltmeter or ammeter, and what is the
characteristic of ideal voltmeter and ideal ammeter?
A) calculate apparent resistance of the unknown resistor
Total resistance,
=== kxIE
RT
TT 20105
1003
Neglecting the effect of voltmeter,
unknown resistor, Rx =20k.
B) calculate actual resistance of the unknown resistor
Resistance of voltmeter,
Rx = 150k.
RT= Rx//RV
kkXRRRR
RVX
VXT 65.1720150
15020=
+=
+=
C) calculate % of error due to loading effect of voltmeter
% of error = (17.65-20)/17.65 = -0.133 or 13.3%
Accuracy = 100% - |%loading error| = 100-|-13.33| = 86.67%
i.e. loading effect cause inaccuracy of measurement.
This can be avoided by using appropriate instrument or using them intelligently (use
instrument in proper arrangement).
E.g.: using high voltmeter which have high resistance in relative to the load
resistance
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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2 (b) Environmental Errors
E.g.: effects of temperature, pressure, humidity, dust, vibrations or external magnetic or
electrostatic fields.
i) Keeping the conditions as nearly as constant as possible.
E.g.: temperature can be kept constant by keeping the equipment in a temperature
controlled enclosure.
ii) use equipment which is immune to these effects
E.g.: variations of resistance with temperature can be minimized by using resistance
materials which have a very low resistance temperature co-efficient
iii) employ techniques which eliminate the effects of disturbances
E.g.: effect of humidity & dust can be entirely eliminated by hermetically sealing the
equipment
iv) apply computed correction
2 (c) Observational Errors
i) Parallax error
ii) Reaction time
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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3.0 Measurement standard ~ before we can measure something, we must define its dimension and provide some standard, or reference unit, in terms of which the quantity can be expressed numerically. (Lord Kelvin)
3.1 Terms
Dimension- Defines some physical characteristics. Eg. Length, volume, velocity,
heat and etc.
Unit is a standard or reference by which a dimension can be expressed numerically
SI unit The international system of units
3.2 Fundamental and secondary units
There are five fundamental units or base units
a) Meter (m), L
b) Kilogram (Kg), M
c) Second (s), t
d) Ampere (A), I
e) Kelvin (K), T
Secondary units are the product of fundamental units
For eg : Area ( L2)- m2, Newton, Kgms-2 and etc
3.3 Symbols and notation (refer attachment)
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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3.4 Equation and numbering It is important to have a right concept to write an equation. For an example:
Y=MX + C
Where M and C are the constants. X and Y are the variables.
X is always refers as the input/ changes to the system. (Always put at the right side of
the equation.)
Whereas,
Y is always refers as the result/effect that cause by the changing of the X. (Always
put at the left side of the equation and also always as a single term)
For instant; Instantaneous Force induced that cause by the changing of the current
with a finite length L and constant magnetic flux B is given by
F=BIL
Where B and L are the constant.
I is the cause and F is the result.
But if an instantaneous force is applied to the finite length conductor which cut a
constant magnetic flux. A current is induced.
The equation is rather written as follow
I= F/BL
F is the cause and I is the result.
Although they look exactly the same but in the view for scientists or engineers, it is
totally different.
# The same principles that apply to plot a scientific graph. X axis is always refer as
cause and Y axis is always refer as result.
Question:
How should we write an equation that consists more than one input but just
one output?
And how should we write an equation that only has one input but multiple
output?
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EPM 1016: Instrumentation and measurement techniques Chapter 1: Instrumentation system and measurement
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3.5 Dimension analysis
It is necessary condition for correctness that every equation be balanced dimensionally.
For example:
Newton, F(N) = mass M(kg) X acceleration LS-2 (ms-2)
Example 1:
The unit of voltage is always expressed as volt (V), try to express this dimension with
only base units expression.
Solution
From definition: electric potential V is expressed either Joules per coulomb or in volts.
Then:
Volts = joules / coulomb
V = FL/Q
= MLS-2 X L / IS
= ML2S-3 I-1
Answer: V= kgm2s-3 A-1
Exercise 1: What is the dimension of electrical resistance? Expressed with base units
only.
Exercise 2: Electrical force expressed as follow:
2
2
rQkF =
What is the dimension of k? Expressed with only base unit only.