MEASUREMENTS AND

INSTRUMENTATIONEC2351

Prepared By

JhansiRani.R AP/ECE

UNIT 1BASIC MEASUREMENT CONCEPTS Measurement systems Static and dynamic characteristics Units and standards of measurements Error analysis Moving coil meters Moving iron meters Multimeters Bridge measurements

Maxwell Hay Schering Anderson Wien bridge.

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SIGNIFICANCE OF MEASUREMENT

Importance of Measurement is simply and eloquently expressed in the following statement of famous physicist Lord Kelvin:

“I often say that when you can measure what you are speaking about and can express it in numbers, you know something about it; when you cannot express in it numbers your knowledge is of meager and unsatisfactory kind”

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INTRODUCTION Measurement means, to monitor a process or a

operation and using an instrument, express the parameter, quantity or a variable in terms of meaningful numbers.

Measurement of a given parameter or quantity is the act or result of a quantitative comparison between a predefined standard and an unknown quantity to be measured.

There are 2 basic requirements: The comparison standard is accurately defined and

commonly accepted , and The procedure and the instrument used for obtaining

the comparison must be provable.

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EVOLUTION OF INSTRUMENTS.

a) Mechanical b) Electrical c) Electronic Instruments.

MECHANICAL: These instruments are very reliable

for static and stable conditions. But their disadvantage is that they are unable to respond rapidly to measurements of dynamic and transient conditions.

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CONTD

ELECTRICAL: It is faster than mechanical, indicating the

output are rapid than mechanical methods. But it depends on the mechanical movement of the meters. The response is 0.5 to 24 seconds.

ELECTRONIC: It is more reliable than other system. It uses

semiconductor devices and weak signal can also be detected.

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Measuring instrument: It is defined as the device for determining the value

or magnitude of a quantity or variable.

Electronic measurement: It is the one which is based on electronic or electrical

principles for its measurement function.

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ADVANTAGES OF ELECTRONIC MEASUREMENT Most of the quantities can be converted by

transducers into the electrical or electronic signals. Electronic signals can be amplified, filtered,

multiplexed, sampled and measured. Measured signals can be transmitted over long

distance through cables or radio links, without any loss of information.

Many measurements can be done simultaneously or in rapid succession.

Electronic circuits can measure the events of very short duration

Higher sensitivity, low power consumption and a higher degree of reliability are the important features of electronic instruments and measurements.

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FUNCTIONAL ELEMENTS OF AN INSTRUMENT

Primary Sensingelement

VariableConversion

element

Variablemanipulation

element

Data Transmission

element

Data presentation

element

Data Storage &playbackelement

Quantity To be measured

observer

Data conditioning element

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Primary Sensing Element: An element of an instrument which makes

first contact with the quantity to be measured. In most cases a Transducer follows primary sensing element which converts the measurand into a corresponding electrical signal.

Variable Conversion Element: output of the primary sensing element is in electrical form such as Voltage, Frequency….such an o/pt may not be suitable for the actual measurement system. (Ex: A/D converter)

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Variable Manipulation Element: The level of the o/pt from the previous stage may not be enough to drive the next stage. Thus variable manipulation element manipulates the signal, preserving the original nature of the signal.

Data Transmission Element: When the elements of the system are physically separated, it is necessary to transmit the data from one stage to other. This is achieved by the data transmission element.

Data Presentation Element: The data is monitored, for analyzing purpose

using data presentation element.(Ex: Visual display)

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EXAMPLE

Moving coil senses current Magnets & coil convert current in coil to force Force is transmitted to pointer through

mechanical links Pointer and scale presents the current value

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AMMETER

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PERFORMANCE CHARACTERISTICS

Static characteristics: The set of criteria defined for the instruments, which are used to measure the quantities which are slowly varying with time or mostly constant, ie., do not vary with time is called static characteristics

Dynamic characteristics: when the quantity under measurement changes rapidly with time, it is necessary to study the dynamic relations existing b/w i/pt and o/pt which is expressed as differential equations

The set of criteria defined based on such dynamic differential equation is called dynamic characteristics

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CALIBRATION

Calibration is the process of making an adjustment or making a scale so that the reading of an instrument agree with the accepted and certified standard.

Note: if the device is repaired, aged or modified then recalibration is carried out.

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STATIC CHARACTERSTICS

Accuracy Precision Resolution Error Sensitivity Threshold Reproducibility Zero drift Stability Linearity

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ACCURACY: DEGREE OF CLOSENESS WHICH THE INSTRUMENT READING APPROACHES THE TRUE VALUE OF THE QUANTITY TO BE MEASURED. IT INDICATES THE ABILITY OF AN INSTRUMENT TO INDICATE TRUE VALUE OF THE QUANTITY.

A) ACCURACY AS “% OF FULL SCALE READING”:IF THE INSTRUMENT HAVE UNIFORM SCALE, THEN ACCURACY IS EXPRESSED AS % OF FULL SCALE READING.

ACCURACY IS 0.1% FOR FULL SCALE OF 50 UNITS MEANS 0.05 UNITS ERROR IS PRESENT IN ANY MEASUREMENT.

ACCURACY IS 0.2% FOR FULL SCALE OF 25 UNITS MEANS 0.05 UNITS ERROR

THUS AS READING DECREASES ERROR IS MORE AND LEADS MISLEADING.

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B) ACCURACY AS “% OF TRUE VALUE”:

Best method for specifying accuracy. It is specified in terms of true value of the quantity being measured. Eg: ±0.1% of true value.

As the reading gets smaller error also gets reduced. Hence accuracy is better.

C) Accuracy as “% of scale span”:

Maximum point on scale -Minimum point on scale is scale span.

For range 25-225, Scale span is 200 If accuracy is 0.2% of span then, error is 0.4 units in

any measurement.

D) Point Accuracy It is specified at only one point of scale. R.JhansiRani AP/ECE

PRECISION:

It is the measure of consistency or repeatability of measurement.

It denotes the closeness with which individual measurements are departed or distributed about the average of numbers of measured values.

High precision may not have high accurate

Types: conformity Number of significant figures.

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Conformity:Error created due to limitation of scale reading is a

precision error.

Ex: resistor of value 2385692Ω is read as 2.4MΩ.

Significant figures:Precision is obtained from number of significant

figures.

Ex: 110 ohms can be specified as 109 or 111 thus 3 significant figures.

If it is specified as 110.0 then it may be 110.1 or 109.9

Thus there are 4 significant figures.

Greater the significant figure greater is the precision.

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Error:The algebraic difference between the indicated

value and the true value of the quantity to be measured is called an error.

Error of 1 ut is negligible when measure in order of 1000 ut

Error of 1 ut is significant when measure in order of 5 ut

e = At – Am , where

e – error (or) absolute errorAm – measured value of quantity At – true value of quantity

Note: instead of specifying absolute error, the relative or percentage of error is specified. R.JhansiRani AP/ECE

Relative error:

True value

absolute error

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Sensitivity:The ratio of the change in output of an

instrument to a change in the value of the quantity to be measured.

Note: if the calibration curve is linear, then sensitivity of the instrument is the slope of the calibration curve.

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For manufactures

Reciprocal of sensitivity is called inverse sensitivity or deflection factor.

unit: sensitivity – mm/µA, mm/Ω, counts/V etc; Deflection meter - µA/mm, Ω/mm, V/counts etc; Sensitivity should be high, to achieve this the range

of the instrument should not exceed the value to be measured.

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Resolution means smallest measurable input change.

Threshold:If the i/pt is slowly varied from zero, the o/pt does

not change until some minimum value of the i/pt is exceeded. This minimum value of the i/pt is called threshold.

Threshold is the smallest measurable i/pt.

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LINEARITYTHE CLOSENESS TO WHICH A CURVE APPROXIMATES

ASTRAIGHT LINE.

DEFINITION: IT IS DEFINED AS THE MAXIMUM DEVIATION OF THE ACTUAL CALIBRATION CURVE (O/PT) FROM THE IDEALIZED ST.LINE, EXPRESSED AS A % OF FULL SCALE READING OR A % OF THE ACTUAL READING.

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Zero drift:The deviation in the instrument output with time from its zero value, when the variable to be measured is a constant.

Reproducibility: It is the degree of closeness with which a

given value may be repeatedly measured.

Reproducibility and repeatability are a measure of the closeness with which a given i/pt may be measured again and again.

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Stability: Ability of an instrument to retain its

performance throughout its specified operating life and the storage life.

Tolerance: The maximum allowable error in the

measurement is specified interms of some value which is called tolerance.

Bias: The constant error which exists over

the full range of measurement of an instrument is called bias.

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Hysteresis If the i/pt to the instrument is increased from a negative value, the o/pt also increases : curve 1

If the curve is decreased steadily, the o/pt does not follow the same curve but lags by certain value: curve 2

Difference b/w two curves is called HYSTERESIS.

The noncoincidence of loadingand unloading curves

Dead space: Range of i/pt values were there is no change in o/pt is called dead space.

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DYNAMIC CHARACTERISTICS Speed of response Fidelity Lag Dynamic error

STANDARD VARIATIONS IN I/PT ARE

Sudden, instantaneous and finite change in the input.

i/pt -> Au(t)

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Linear change in i/pt. it changes at a constant rate wrt time.

i/pt -> At u(t)

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i/pt is proportional to the square of the time & hence represents constant acceleration

i/pt -> At2 u(t)

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It exist only at t=0 & zero otherwise Area under it is its magnitude and if its unity it is

called delta function δ(t)

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i/pt which changes in acco9rdance with a sinusoidal function of constant amplitude. Frequency is the independent variable in this case.

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Speed of response: It gives information about how fast the

system reacts to the changes in the input.

Fidelity: it is defined as the degree to which an instrument

indicates the changes in the measured variable without dynamic error.

Lag: Delay in the response of a system. retardation lag: response of the system begins

immediately after a change in the variable has occurred. time delay: response begins after some time called dead

time, after the application of input.

Dynamic error• Difference between the true value of the variable

to be measured changing with time and the value indicated by the measurement system assuming zero static error R.JhansiRani AP/ECE

UNITS

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UNITS The S.I system of units is divided into 3 categories

Fundamental units Supplementary units Derived units

Fundamental units: units which are independently chosen and

not dependent on any other units are called fundamental units or base units

Ex: meter (m), kilogram (Kg), second (s), Ampere (A)

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Supplementary units: Radian for the plane angle: (θ,Φ) Plane angle subtended by an arc of a circle equal in length to

the radius of the circle.

Steradian for the solid angle: (θs,Φs) Angle subtended at the center of the sphere by the surface

whose area is equal to the square of the radius of the sphere.

Derived units: These units are derived from fundamental and supplementary

unitsEx: velocity- m/s, acceleration- m/s2, force- Newton(N)

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MEASUREMENT STANDARDS A standard of measurement is a physical

representation of a unit of measurement.

A standard means known accurate measure of physical quantity.

ex: unit of mass: Kg

Kilogram is defined as the mass of cubic decimeter of water as its temperature of maximum density of 4 degree Celsius

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TYPES OF STANDARDSTYPES OF STANDARDS

1. International standards2. Primary standards3. Secondary standards4. Working standards

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INTERNATIONAL STANDARDS These standards are maintained at the

international bureau of weights and measures and are periodically evaluated and checked by absolute measurements.

These standards are not available for ordinary users for calibration.

For accuracy they are replaced by absolute units which are more accurate than international standards.

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PRIMARY STANDARDS They are maintained at national standard

laboratories in different countries.

These standards represents fundamental units as well as electrical and mechanical derived units calibrated by absolute measurements at each national laboratories.

used for calibration and verification of secondary standards.

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SECONDARY STANDARDS Since primary standards are not available for

outside users, various industries need some reference.

They are used by measurement and calibration laboratories and are maintained by the particular industry to which they belong.

Each industry has its own standards.

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WORKING STANDARDS

These are the basic tools of a measurement laboratory

use to check and calibrate for accuracy.

ex: resistor industry maintains a standard resistor for checking the values of manufactured resistors.

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ERRORS

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SOURCES OF ERRORS1. Faulty design of instrument2. Insufficient knowledge of quantity

and design conditions3. Improper maintenance of the

instrument.4. Sudden change in the parameter to

be measured.5. Unskilled operator6. Effects of environmental conditions.

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TYPES OF ERRORSstatic errors are classified as,

1. Gross error2. Systematic error3. Random error

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GROSS ERROR: (PERSONAL ERRORS)

Occurs due to carelessness of human while reading, recording and calculating results. Due to incorrect adjustments of

instruments.

To eliminate error: Take care while reading, recording and

calculating results. Take 3 or more readings with 3 or more

persons.

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SYSTEMATIC ERROR A constant uniform deviation of operation in

instruments known as systematic error. Due to short comings and characteristics of the

material used in instrument like worn parts, ageing effects etc;

Types:a) Instrumental errorb) Environmental errorc) Observational error

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INSTRUMENTAL ERROR

shortcomings of instrument: Due to mechanical structure of the

instruments. Ex: Friction in bearings, Irregular spring tension, variation in air gap. To eliminate error:1. select proper instrument and select proper

procedure.2. Identify effect of errors and correct it.3. Calibrate the instrument.

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Misuse of instruments:Ex: poor initial adjustments improper zero setting using leads of high resistance

Loading effects: Ex: connecting a well calibrated

voltmeter across the 2 points of high resistance circuit.

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ENVIRONMENTAL ERROR They are due to temperature changes pressure changes thermal e.m.f stray capacitance cross capacitance

To eliminate error:1. proper correction factors given by the

manufacturer.2. make arrangements to keep surrounding

constant like using A.C.3. sealing the components to avoid dust,

humidity.4. providing magnetic or electrostatic shields.R.JhansiRani AP/ECE

OBSERVATIONAL ERRORerrors made by observersEx: parallax error while reading a meter, wrong scale selection

To eliminate error:1. use instruments with mirrors.2. knife edged pointers.

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RANDOM ERROR

Causes of errors which are unknown are random errors.

Due to accumulation of large number of small effects

They cannot be corrected by any method.

use statistical methods to obtain best approximation of reading.

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ERROR ANALYSIS

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STATISTICAL ANALYSIS Arithmetic mean and median: mean:

Median:

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Deviation from mean:

Average deviation (mean deviation):

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Standard deviation:

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Variance: mean square deviation

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