chapter 1- basic concepts of instrumentation and measurement
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Prof Syed Idris Syed Hassan
Analog instrumentThe measured parameter value displays in analog form such as moveable pointer and continuously measured. Error due to parallax.
Digital instrumentThe measured parameter value display in digital form. Error due to conversion such quantization of signal level.
Generalize model of simple instrument
Measurand is represented by observable physical variable X, e.g weight.Physical measurement variable such as force that can be detected by sensorSensor convert the physical variable input into signal variable. Sensor can be in the form of electrical or mechanical.Signal variable can be manipulated in a transmission systemDisplay the signal variable into either analoq or digital. The Observed output is measurement M
SENSORX
Physical measurementVariable
MeasurandDisplay
S
Signalvariable
MPhysical Process
Measurant Physical Var
Sensor Signal Var
Instrument
Scale
Mass Down force Strain gauge
Pressure, voltage
Weighing machine
Kg, Ibs, kati
Time
Temperature
Pressure
Speed
Accelerator
Wind speed
Voltage
Common Physical variable Typical signal variable
Force Voltage
Length Displacement
Temperature Current
Acceleration Force
Velocity Pressure
Pressure Light
Frequency Frequency
Capacity
Resistance
Time……
There are two basic characteristic for selecting instrument for specific measuring:-
1.Static characteristic- measure unvarying process
2.Dynamic characteristic- measure varying process
1. Instrument-A device used to determine the present value of a quantity under observe
2. Measurement-The process of determine the amount, capacity comparison with standard unit system
3. Accuracy-The degree of exactness (closeness) of measurement compared to the expected value.
4. Resolution- The smallest change in a measured variable to which instrument response. (threshold)
5. Precision- A measure of consistency or repeatability of measurement.
6. Expected value-The design value that calculations indicate one should expect to measure
X
XXecision n
1PrvalueaverageX
valuemeasuredX n
7. Hysterisis-the different between loading and unloading curve due to magnetic hysterisis of the iron. Eg. In moving iron voltmeter.
8. Dead Zone/band-Total range of possible values for instrument will not giving a reading even there is a change in measured parameter.
9. Nominal value- input and output that had been stated by the manufacturer for user manual.
10. Bias- A constant error that occur to instrument when the pointer not starting from zero scale.
11. Range-A minimum and maximum range for instrument to operate as stated by manufacturer
12. Sensitivity-The ratio of the change in output of the instrument to a change of input or measured variable
input
outputS
Dynamic characteristic are only concerned with the measurement of quentutues that vary with time
The step taken before measure1. Procedure of measurement- identify the
parameter or variable to be measured. How to record the result.
2. Characteristic of parameter : should know the parameter that to be measured. e,.d ac, dc, frequency etc
3. Quality : time and cost of equipment , instrument ability, measurement knowledge and suitable result.
4. Instrument : Choose a suitable equipment,e.g multimeter, voltmeter, oscilloscope etc.
During Measurement1. Quality : Make sure the chosen instrument
is the best, the right position when taken the result, frequency of measurement.
2. Safety first : Electrical shock, overload effect, limitation of instrument.
3. Sampling : See the changing of parameter during measurement, which value should be taken when the parameter keep changing. Take enough sample and it is accepted
The step taken after measurement1. Every data recorded must be analyzed,
statically, mathematically and the result must be accurately and complete
In all experiment, analysis and reporting, it is essential to perform the work reliably, use appropriate units of measurement, and record the values accurately
Metric Prefix Name Power term
f femto 10-15
p pico 10-12
n nano 10-9
micro 10-6
m milli 10-3
c centi 10-2
d deci 10-1
da deca 101
h hecto 102
k kilo 103
M mega 106
G giga 109
T tera 1012
P peta 1015
Quantity Unit Symbol Value
Frequency Hertz Hz s-1
Velocity Meter/second ms-1
Acceleration Meter/sec square ms-2
Force newton N kg.m.s-2
Energy joule J N.m
Power watt W Js-1
Electric current
ampere A
Electric charge
coulomb C A.s
Voltage volt V J.C-1
Electric field Volt/meter V.m-1
Resistance ohm V.A-1
Conductance siemen S -1
capacitance farad F C.V-1
Quantity Unit Symbol Value
Resistivity Ohm.meter .m
Conductivity Siemen/meter
S.m-1
Magnetic flux linjage weber Wb V.s
Magnetic flux density tesla T Wb.m-2
Inductance henry H Wb.A-1
SI means International System Unit and mandated by ISO. These SI units are
Note SI unit for mass not gram but kilogram.Mole contains number of atom of 6 x 1023 so called Avogadro number. In carbon equivalent to 12 gram
Quantity Unit Symbol
Length meter m
Time second s
Mass kilogram kg
Current ampere A
Temperature kelvin K
Amount of matter mole mol
Luminous intensity candela cd
Constant value symbol
Speed of light (celeritus) 2.9979 x 108 m/s c
Boltmann’s constant 1.38 x 10-23 J/K k
Electron charge 1.609 x 10-19 C c
Permittivity of free space 8.85 x 10-12 F/m o
Permeability of free space 4 x 10-7 H/m o
Plank’s constant 6.626 x 10-34 J.s h
Newton’s universal gravitation constant
6.67 x 10-11 m3.s2 kg-1
G
Direct measurement-measuring the quantity “face to face”.
Indirect measurement-second quantity inferred from the first. Eg to determine surface temperature of sun by inferred from color of the sun.
Null- balancing the desired quantity by controlling the source.eg measuring resistor using Wheatstone bridge.
Should quote measured value in reasonable which specifically denote the accuracy. For example the thermometer has the small scale 0.1o C. That means the error will be + 0.05o C. If some one quote the reading 30.04o C. Is it reasonable or not? So this is doubtful !!!. Then the correct one is 30.0o C.
Error- difference between the reported value and the true one.
Validity-How well an instrument reflects what it is purported to measure
Robustness-the input of the instrument varies slightly, does its output stably reflect the changes . (does it unstable or chaotic?)
Reliability- whether the measurement is consistent when taken at very different time and condition.
Repeatability- when repeat, does it give the same value
Error is defined as the difference between the true value (expected value) of the measurand and the measured value indicated by the instrument. Express in absolute error or as percentage of error
Absolute errors are defined as the difference between the expected value of the variable and the measured value of the variable.
Relative error : Usually in percentage of absolute error to the expected value. (also called percentage error)
Absolute error
wherePercentage error
Relative accuracy
Percentage relative accuracy
nn XYeerrorAbsolute ,valueectedYn expvaluemeasuredX n
n
nn
Y
XYAaccuracylative
1,Re
100
n
nn
Y
XYerrorPercentage
%100
%100,
A
errorPercentageaaccuracyrelativePercentage
The expected value of the voltage across a resistor is 90V. However , the measurement gives a value of 89V. Calculatea)Absolute errorb)Percentage errorc)Relative accuracyd)Percentage of accuracy
SolutionYn =90V and Xn =89V VVeerrorAbsolute 18990,
Percentage error
Relative accuracy
Percentage of accuracy
%111.110090
8990100
n
nn
Y
XYerrorPercentage
9889.00111.01
90
899011,Re
n
nn
Y
XYAaccuracylative
%89.981009889.0
%100,
AaaccuracyrelativePercentage
Errors categories under 3 major heading1. Gross Errors- fault by the user reading the data
such incorrect reading or incorrect use of instrument(human mistake).
2. Systematic Errors-due to instrument errors (improper calibration, faulty instrument etc), environment errors (harsh condition such high temperature, humidity, pressure, EM field etc) and observation errors (such as parallax ,interpolation (between two point of scale) , last digit bobble(fluctuate))
3. Random Errors- accumulation of large number of small effects and concern for high degree of accuracy. Can be analyzed using statistic . Eg manufacturing tolerances.
Zero setting- the reading may read zero but actually is not zero.
Gain error- amplifiers are widely used in instrument. A carefully calibration is needed.
Processing error- in modern instruments contain complex processing devices usually related with A/D where introduce quantization error and processing program
Arithmetic mean
where xi = i th reading taken
n = total number of readings
n
i i
n
xn
n
xxxxxmeanArithmetic
1
321
1
......,
Deviation
Note: The algebraic sum of the deviation of a set numbers from their arithmetic mean is zero
The average deviation
Where |d1|, |d2 |, |d3 |, …..|dn|are absolute values of deviations
xxdDeviation nn ,
n
ddddDdeviationAverage n
.....
, 321
Standard deviation
*** For small readings (n< 30), the denominator is n-1
n
ddddSdeviationdardS n
223
22
21 .....
,tan
For the following given data , calculatea) Arithmetic meanb) Deviation of each valuec) Algebraic sum of deviationsd) The average deviatione) The standard deviationGiven x1= 49.7
x2= 50.1
x3= 50.2
x4= 49.6
x5= 49.7
Arithmetic mean
Deviation each value86.49
5
7.496.492.501.507.49
......321
n
xxxxx n
16.086.497.4911 xxd
34.086.492.5033 xxd
26.086.496.4944 xxd
16.086.497.4955 xxd
24.086.491.5022 xxd
The algebraic sum of the deviation is
Average deviation
Standard deviation
016.026.034.024.016.0 sumd
232.05
16.026.034.024.016.0
.....321
n
ddddD n
27.015
16.026.034.024.016.0
.....
22222
223
22
21
n
ddddS n
Most manufacturers state the instrument is accurate within percentage of full scale.
Example + 2% of full scale. So for instrument has full scale (eg. Voltmeter) 10V, then the accuracy is + 0.2V. Thus the expected value might be 9.8V or 10.2V.
If reading taking from many instruments and each instrument has its own error, thus when summing the quantities
eg
nn VVVVVVVVE ...... 321321
2121 VVVVE
Difference of quantities
2121 VVVVE
Product of quantitiesEg- Power = IVTotal error
Quotient of quantitiesEg – R= V/I
Total error
VinerrorIinerrorpowerinerror %%%
I
VinerrorIinerrorRinerror %%%
Quantity Raised to a Power.Eg Lets two quantities are A and B and
they are related by a formula AB , thus total error can be shown to be
AinerrorBAerror B %%
A 600V voltmeter is specified to be accurate within + 2% at full scale. Calculate the limiting error when the instrument is used to measured a voltage of 250V.SolutionMagnitude of Limiting error is 0.02 x 600=12VLimiting error 250V is %8.4%100
250
12% error
A voltmeter reading 70V on its 100V range and an ammeter reading 80mA on its 150mA range are used to determine the power dissipated in a resistor. Both instruments are having accuracy limitation of within + 1.5% at full scale deflection. Determine the limiting error of the power.
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