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.