1. EET204 MEASUREMENT and instrumentation
Prof Syed Idris Syed Hassan

2. Classification of instruments
Analog instrument
The measured parameter value displays in analog form such as moveable pointer and continuously measured. Error due to parallax.
Digital instrument
The measured parameter value display in digital form. Error due to conversion such quantization of signal level.

3. Characteristic of instruments
Generalize model of simple instrument
SENSOR X
Physical measurement
Variable
Measurand
Display S
Signal
variable M
Physical
Process
Measurand is represented by observable physical variable X, e.g weight.
Physical measurement variable such as force that can be detected by sensor
Sensor 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 system
Display the signal variable into either analoq or digital. The Observed output is measurement M

4. LIST THE FOLLOWING (QUIZ)
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

5. Example of physical variables
Common Physical variable
Typical signal variable
Force
Voltage
Length
Displacement
Temperature
Current
Acceleration
Velocity
Pressure
Light
Frequency
Capacity
Resistance
Time ……

6. Basic characteristic
There are two basic characteristic for selecting instrument for specific measuring:-
Static characteristic- measure unvarying process
Dynamic characteristic- measure varying process

7. Term of static characteristic
Instrument-A device used to determine the present value of a quantity under observe
Measurement-The process of determine the amount, capacity comparison with standard unit system
Accuracy-The degree of exactness (closeness) of measurement compared to the expected value.

8. Con’t
Resolution- The smallest change in a measured variable to which instrument response. (threshold)
Precision- A measure of consistency or repeatability of measurement.
Expected value-The design value that calculations indicate one should expect to measure

9. Con’t
Hysterisis-the different between loading and unloading curve due to magnetic hysterisis of the iron. Eg. In moving iron voltmeter.
Dead Zone/band-Total range of possible values for instrument will not giving a reading even there is a change in measured parameter.
Nominal value- input and output that had been stated by the manufacturer for user manual.

10. Con’t
Bias- A constant error that occur to instrument when the pointer not starting from zero scale.
Range-A minimum and maximum range for instrument to operate as stated by manufacturer
Sensitivity-The ratio of the change in output of the instrument to a change of input or measured variable

11. Dynamic characteristic
Dynamic characteristic are only concerned with the measurement of quentutues that vary with time

12. Process of Measurement
The step taken before measure
Procedure of measurement- identify the parameter or variable to be measured. How to record the result.
Characteristic of parameter : should know the parameter that to be measured. e,.d ac, dc, frequency etc
Quality : time and cost of equipment , instrument ability, measurement knowledge and suitable result.
Instrument : Choose a suitable equipment,e.g multimeter, voltmeter, oscilloscope etc.

13. Con’t During Measurement
Quality : Make sure the chosen instrument is the best, the right position when taken the result, frequency of measurement.
Safety first : Electrical shock, overload effect, limitation of instrument.
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

14. Con’t The step taken after measurement
Every data recorded must be analyzed, statically, mathematically and the result must be accurately and complete

15. Units and accuracy
In all experiment, analysis and reporting, it is essential to perform the work reliably, use appropriate units of measurement, and record the values accurately

16. Units 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

17. Units of measurement 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

18. Con’t 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

19. SI units
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

20. Physical constant Constant value symbol Speed of light (celeritus)
x 108 m/s c
Boltmann’s constant
1.38 x J/K k
Electron charge
1.609 x C
Permittivity of free space
8.85 x F/m o
Permeability of free space
4 x H/m o
Plank’s constant
6.626 x J.s h
Newton’s universal gravitation constant
6.67 x m3.s2 kg-1 G

21. Measurement categories
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.

22. Significant figures
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 o 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.

23. Relevant factors
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

24. Error in measurement
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)

25. Mathematical formulation of error
Absolute error where Percentage error Relative accuracy Percentage relative accuracy

26. Example 1
The expected value of the voltage across a resistor is 90V. However , the measurement gives a value of 89V. Calculate
Absolute error
Percentage error
Relative accuracy
Percentage of accuracy
Solution
Yn =90V and Xn =89V

27. Con’t
Percentage error Relative accuracy Percentage of accuracy

28. Type of error Errors categories under 3 major heading
Gross Errors- fault by the user reading the data such incorrect reading or incorrect use of instrument(human mistake).
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))
Random Errors- accumulation of large number of small effects and concern for high degree of accuracy. Can be analyzed using statistic . Eg manufacturing tolerances.

29. Other types of error
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

30. Statistical analysis of error in measurement
Arithmetic mean
where xi = i th reading taken
n = total number of readings

31. Con’t
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

32. Con’t Standard deviation
*** For small readings (n< 30), the denominator is n-1

33. Example 2 For the following given data , calculate Arithmetic mean
Deviation of each value
Algebraic sum of deviations
The average deviation
The standard deviation
Given
x1= 49.7
x2= 50.1
x3= 50.2
x4= 49.6
x5= 49.7

34. Arithmetic mean Deviation each value
solution
Arithmetic mean Deviation each value

35. Con’t
The algebraic sum of the deviation is Average deviation Standard deviation

36. Limiting Error
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.

37. Measurement error combination
If reading taking from many instruments and each instrument has its own error, thus when summing the quantities eg

38. Con’t
Difference of quantities

39. Con’t I Product of quantities Eg- Power = IV Total error
Quotient of quantities
Eg – R= V/I

40. Con’t 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

41. Example 3
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. Solution Magnitude of Limiting error is 0.02 x 600=12V Limiting error 250V is

42. Example 4 (EXERCISE)
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.