UNIT I

1.1 FUNCTIONAL ELEMENTS OF AN INSTRUMENT

Measurement:The Measurement of a given quantity is essentially an act or the result of

comparison between the quantity and a predefined standard.

Basic requirements

The standard used for comparison purposes must be accurately defined and should be commonly accepted and

The apparatus used and the method adopted must be provable.

Significance

The famous Physicist Lord Kelvin says, “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”

1.1.1Methods of Measurement

Direct Method: The unknown quantity is directly compared against a standard, expressed as a numerical number and a unit. (Length, Mass and Time)

Indirect Method: Direct Method always not possible, feasible and practicable. Results are inaccurate, because they involve human factors. Less sensitive.

Instrument:

The instrument serves as an extension of human faculties and enables the man to determine the value of unknown quantity or variable.

1.1.2 Various Instrument

Mechanical Instruments:

It is very reliable for static and stable conditions. Unable to respond rapidly to measurements of dynamic and transient conditions.

Because, rigid, heavy and bulky and consequently having a large mass. Potential source of noise and cause noise pollution.

Electrical Instruments:

Normally depends upon a mechanical meter movement as indicating device. Some inertia and limited time.

Electronic Instruments:

It is steadily become more reliable on account of improvements in design and manufacturing process of semi-conductor devices.

Very fast response (in order of ms or μs). CRO : 10-9s Very weak signals can be detected by using pre-amplifiers and amplifiers. Ability to obtain indication at a remote location which helps in monitoring

inaccessible or dangerous locations. Non electrical quantity is converted into electrical form through the use of

transducers. Higher sensitivity, Faster response, Greater flexibility, Lower weight, Lower

power consumption and Higher degree of reliability than their mechanical or electrical counterparts.

1.1.3 Classification of Instruments

Absolute Instruments: It give the magnitude of the quantity under measurement in terms of physical constants of the instrument. (Tangent Galvanometer)Secondary Instruments: It observing the output indicated by the instrument. (Voltmeter)

Absolute Instruments

Deflection Type Instruments

The value of measured quantity depends upon the calibration of the instrument.

It produces a mechanical displacement of the moving system of the instrument.

Opposing effect is built-in and directly observed. Magnitude increases with increase of mechanical displacement of the moving

system caused by the quantity under measurement. When effects are equal, balance is achieved.

Null Type Instruments

Zero or Null indication leads to determination of the magnitude of measured quantity.

It maintain the deflection at zero by suitable application of an effect opposing that generated by the measured quantity.

It requires, o Effect produced by the measured quantityo The opposing effect, whose value is accurately known o Detector (Automatic or manual)

Summarize: Null à More Accurate. Null à Highly Sensitive. Deflection à More suited for measurements under dynamic conditions.

Secondary Instruments

Analog Signals: Signals that vary in a continuous fashion and take on an infinite number of values in any given range.

Digital Signals: Signals which vary in discrete steps and thus take up only finite different values in a given range.

Difference: Analog is a continuous function while the digital output is a discrete number of units. (Computer)

1.1.4 Functions of Instruments and Measurement Systems

Indicating function: It is obtained as a deflection of a pointer of a measuring instrument. (Speedometer, Pressure gauge)

Recording function: It makes a written record, usually on paper, of the value of the quantity under measurement against time or some other variable. (Strip Chart Recorder)

Controlling function: Especially in the field of industrial control process. The system to control the original measured quantity

1.1.5 Applications of Measurement Systems

Monitoring of Process and Operation: It simply indicate the value or condition parameter under study and their readings do not serve any control functions. (Voltmeter, Energy meter)

Control of Process and Operation: Automatic control systems. It has been very strong association between measurement and control. (Temperature, Pressure, etc.,)

Experimental Engineering Analysis: Theoretical and experimental methods are available.

Testing the validity of theoretical predictions. Determination of system parameters, variables and performances. Solutions of mathematical relationship with the help of analogies.

1.1.6 Types of Instrumentation Systems Advent of µP has completely revolutionized the field of instrumentation and control.

Intelligent Instrumentation Systems:

To evaluate a physical variable employing a digital computer to perform all signal and information processing.

After measuring, whether in digital or analog form is carried out to refine the data. (Purpose of presentation to observer or CPU)

Dumb Instrumentation Systems: Once the measurement is made, the data must be processed by the observer. Information and Signal Processing:

Information: It is the data or details relating to an object or event. Signals: They carry the information about magnitude or time relating to an

object.

Elements of a Generalized Measuring System

Systematic organization and analysis of measurement systems. It is a device which is designed to maintain a functional relationship between

prescribed properties of physical variables and must include ways and means of communication to a human observer. It remains valid as long as the static calibration of system remains constant.

Three main functional elements are, Primary Sensing Element Variable Sensing Element Data Presentation Element

Primary Sensing Element:

The quantity under measurement makes its first contact with the primary sensing element of a measurement system.

Element of quantity is sensed converted into analogous form, this O/p is converted into electrical signal by transducer.

First Stage: Detector Transducer Stage.

Variable Conversion Element: O/p of primary sensing element, it may be electrical signal of any form

(Voltage, frequency or other). This element, convert this output to some other suitable form (A/D Converter) Many instruments do not need any variable conversion element.

Variable Manipulation Element: To manipulate the signal presented to it preserving the original nature of the

signal. Only change in numerical value of the signal. (Electronics Amplifier)

Data Transmission Element: When the elements of an instrument are actually physically separated, it becomes necessary to transmit data from one to another. (Space-Crafts à radio signals)

Data Presentation Element:

The information about quantity to be conveyed to the system for monitoring, control or analysis purpose.

It must be in a form Intelligent Instrumentation System. The data to be monitored, visual display devices are needed. Devices may be

analog or digital. The data to be recorded, like magnetic tapes, storage type CRT, Analog and

Digital CPU, μP are used. For control and analysis, μP or CPU may be used. (Bourdon Tube Pressure

Gauge)

PRIMARY SENSING ELEMENT

VARIABLE CONVER-SION ELEMENT

VARIABLE MANIPULATION ELEMENT

DATA TRANSMISSION ELEMENT

DATA CONDITIONING ELEMENT

INTERMEDIATE STAGE DETECTOR TRANSDUCER STAGE

TERMINATING STAGE

QUANTITY TO BE MEASURED

DATA PRESENTATION ELEMENT

1.2 STATIC CHARACTERISTICS

It involves the measurement of quantities that are either constant or vary slowly with time.

The main static characteristics are:

True value Static error Static correction Scale range and span reproducibility Noise Accuracy Drift Static sensitivity Dead zone

True value:The true value of quantity to be measured may be defined as the average

of an infinite number of measured values.

Static error:It is the difference between the measured value and the true value of the

quantity.ΛA = Am – At

Where, ΛA-Error Am-Measured value of quantityAt -True value of quantity

Static correction:It is the difference between the true value and the measurement value of

the quantity.ΛC = At – Am = - ΛA

Pbm: A meter reads 127.50V and the true value of the voltage is 127.43V. Determine

(a) Static error (b) Static correction for this instrument.Ans:(a) ΛA = +0.07 V(b) ΛC = - 0.07 V

Pbm: A thermometer reads 95.45º C and the static correction curve is – 0.08º C.

Determine the true value of the temperature.Ans: At = 95.37º C

Scale Range and Span: It is the difference between the largest and smallest reading of the instrument. Xmax; Xmin and calibration Scale Span = Xmax - Xmin

Reproducibility: It is the degree of closeness with which a given value may be repeatedly

measured. No Drift.

Drift: It means that with a given input the measured value do not vary with time.It may be classified as;

Zero Drift: If the whole calibration gradually shifts due to permanent set.

Span Drift: If there is an proportional change in the indication all along the upward scale.

Zonal Drift: It occurs only over a portion of an instrument. Noise:

A spurious current or voltage extraneous to the current or voltage of interest in an electrical or electronic circuit is called Noise.

It is a signal that does not convey any useful information. It may be generated inside the system.

Sources of Noiseo Generated noise:The Noise generated inside the system.

(Amplifier)o Conducted noise:Input to the system with noise signal.

(Spikes, Ripples or Random deviations)o Radiated noise:

The noise generated around the system. It may be electric or magnetic fields. Such disturbances signals are radiated into the interior of the system.

Accuracy:It is the closeness with which an instrument reading approaches the true

value of the quantity being measured.

Sensitivity:It is the ratio of the magnitude of the output signal to the magnitude of

input signal or the quantity being measured.

Dead zone:

It is defined as the largest change of input quantity for which there is no output of the instrument.

Speed of response:It is the rapidity with which an instrument responds to changes in the

measured quantity. Fidelity:

The instrument indicates the changes in the measured variable without error

Lag:A delay in response of an instrument to changes in the measured value.

Dynamic Error:It is the difference between the true value of a quantity changing with time

and the value indicated by the instrument, if no static error is assumed.

1.3 ERRORS IN MEASUREMENT

No measurement can be made with perfect accuracy but it is important to find out what accuracy actually it is and how different errors have entered into the measurement.

It classified as; Gross Errors Systematic Errors Random Errors

1.3.1 Gross Errors

It occurs due to human mistakes in reading instrument and recording and calculating measurement results.

The responsibility of the mistake normally lies with the experimenter. Complete elimination of error probably impossible. It may be of any amount and therefore their mathematical analysis is impossible. It can be avoided by adopting means; Great care should be taken in reading and recording the data. Two, three or even more readings should be taken for the quantity under

measurement.

1.3.2 Systematic Errors

It contains Three categories;A. Instrumental errorsB. Environmental errors

C. Observational errors

1.3.2.1 Instrumental Errors

It arises due to three main reasons Inherent shortcomings Misuse of the instrument Loading effects of the instrument

Inherent shortcomings:

o Mechanical structureo Due to construction, calibration or operation of the instrument or

measuring device.o It may be read too low or too high

To reduce by, Procedure of measurement must be carefully planned. Substitution method

or calibration against standards may be used. Correction factors Re-calibrated carefully.

Misuse of the instrument:

Instruments are better than the people who use them. Due to the fault of the operator than that of the instrument. A good instrument used in an unintelligent way may give erroneous results.

Loading effects of the instrument:

One of the most common errors committed by beginners, is the improper use of an instrument for measurement work.

1.3.3 Random Errors

It has been consistently show variation from one reading to another. It due to a multitude of small factors which change or fluctuate from one

measurement to the other. The happenings or disturbances about which we are unaware are lumped together

and called “Random” or “Residual”

STATISTICAL EVALUATION OF MEASUREMENT DATA

Two forms of tests:

1.4.1Multi Sample Test: Repeated measurement of a given quantity.1.4.2 Single Sample Test: Identical conditions excepting for time.1.4.3Types: Arithmetic mean, Range, Deviation, Standard deviation and variance.

Arithmetic mean:

The most probable value of measured variable is the arithmetic mean of the number of readings taken. A.M, X = (x1+x2+….+xn) /n = Σx/n

Where, X à Arithmetic meanx1+x2+….+xn à Readings or samplesn à number of readings

Range: It is the simplest measurement. It is the difference between greatest and least values of data.

Deviation: It is departure of the observed reading from the arithmetic mean of the group of readings.

Let, x1 à d1 and x2 à d2, d1 = x1 – X, d2 = x2 – X….dn = xn – X X = Σ (xn – dn) / n The algebraic sum of deviation = d1+d2+d3+…+dn = 0

Standard Deviation:

The square root of sum of the individual deviations squared, divided by the number of readings.

S.D = σ = sqrt{(d12+d22+…+dn2)/n} = sqrt(Σd2/n)…….. (>20)

S = sqrt(Σd2/n-1)…….. (<20)

Variance: Mean square deviation.

V = (S.D)2 V = {(d12+d22+…+dn2)/n} = (Σd2/n)…….. (>20) V = S2 = (Σd2/n-1)…….. (<20)

A circuit was tuned for resonance by eight different students and the values of resonant frequency in kHz were recorded 532, 548, 535, 546, 531, 543 and 536. Calculate (a) the arithmetic mean

(b) deviation from mean (c) Standard deviation (d) Variance

Ans: (a)539.25 kHz

(b) d1 = -7.25 kHz, d2 = +8.75 kHz, d3 = +3.75 kHz, d4 = -4.25 kHz, d5 = +6.75 kHz, d6 = -8.25 kHz, d7 = +3.75 kHz, d8 = -3.25 kHz.

(c) = 6.54 kHz (d) = 42.77 (kHz) 2

1.5 STANDARDS

A standard is a physical representation of a unit of measurement. The term standard is applied to a piece of equipment having a known measure of physical quantity.

It classified as,

International standards Primary standards Secondary standards Working standards

1.5.1 International Standards

Defined on the basis of international agreement. Regularly checked and evaluated against absolute measurement in terms of

fundamental units. Maintained at the International Bureau of Weights and Measures. It represents the unit of measurements which are closest to the possible accuracy

attainable with present day technological and scientific methods.

1.5.3 Secondary Standards

It is used in industrial measurement laboratories. Maintenance and calibration lies only with the industry. Normally sent periodically to National standards laboratories for calibration and

comparison against primary standards. They are sent back to the industry with a certification.

1.5.4 Working Standards

It is the major tools of a measurement laboratory. Check and calibrate by general laboratory for their accuracy and performance.

1.5.5 CALIBRATION Calibration of all instruments is important since it affords the opportunity to check

the instruments against a known standard and subsequently to find errors and accuracy.

Calibration Procedure involve a comparison of the particular instrument with either a Primary standard a secondary standard with a higher accuracy than the instrument to be

calibrated. an instrument of known accuracy.

2.1 PRINCIPLE AND TYPES OF ANALOG AND DIGITAL VOLTMETERS, AMMETERS AND MULTIMETER

• What is Analog Instrument?

An analog is a device is one in which the output or display is a continuous function of time and bears a constant relation to its input. Analog instrument extensively used in present day applications although digital in instruments are increasing in number and applications.

• It may be classified according to the quantity they measure. For example, measurement of current is called Ammeter and measuring the voltage is called Voltmeter. In addition to above, we have watt meters, power factor meters, etc.,

• There is no fundamental difference in principles between analog Voltmeters and Ammeters. Except electrostatic type of instruments, all meters depends upon a deflecting torque produced by an electric current.

• Ammeters are connected in series in the circuit whose current is to be measured. It have a low electrical resistance so that they cause a small voltage drop and consequently absorb small power.

• Voltmeters are connected in parallel with the circuit whose voltage is to be measured. It have a high electrical resistance, in order that the current drawn by them is small and also power consumed is small.

2.1.1 Classification:

Indicating Instruments: It indicate the magnitude of quantity being measured. They generally make use of dial and pointer for this purpose. Ordinary voltmeters,

ammeters and watt meters belong to this category.

Recording Instruments: It gives a continuous record of quantity being measured over a specified period. The variations of quantity being measured recorded by pen on a sheet of paper

fixed or moving.

Integrating Instruments: It totalize events over a specified period of time. Which they give the product of time and an electrical quantity. (Ampere hour and

watt hour (Energy) meters).

2.1.2 Principle of Operation:The secondary analog instruments may be classified according to the principle of

operation they utilize. The effects are: (1) Magnetic effect (2) Heating effect (3) Electrostatic effect (4) Electromagnetic effect (5) Hall effect

Magnetic Effect:

From fig. 1(a), The conductor carrying current it produce a magnetic field in anticlockwise direction. We have a uniform magnetic field from fig.1(b).

Let the current carrying conductor be placed in this magnetic field. Thus the resultant field as shown in fig.1(c). This results in distortion of magnetic field causing a force F to act from left to right.

Force of Attraction or Repulsion:

When a piece of soft iron is brought near the end of the coil, it will be attracted by the coil. This effect is “attraction type moving iron instrument”

If we have two pieces of soft iron placed near the coil the two will be similarly magnetized and there will be force of repulsion between them. This effect is “Repulsion type moving iron instrument”

Force between a current carrying coil and a permanent magnet:

A permanent magnet is brought near to the imaginary permanent magnet which carrying current. If the coil is mounted on a spindle between bearings, there will be a movement of the coil. This effect is “Permanent magnet moving coil instruments”

Force between two current carrying coils:

The two produce unlike poles near each other and thus there is a force of attraction and if one the coils is movable and the other is fixed, there will be a motion of the movable coil. This effect is “Dynamometer type”Thermal Effect:

The current to be measured is passed through a small element which heats it. The temperature rise is converted to an emf by a thermocouple attached to the element.

Induction Effect:

When a non-magnetic conducting pivoted disc is placed in a magnetic field excited by alternating current. If a closed path is provided, the emf forces a current to

flow in the disc. The force produced by interaction of induced currents and the alternating currents makes the disc move. This effect is mainly utilized in AC Energy Meters.

Hall Effect:

If a strip of conducting material carries current in the presence of a transverse magnetic field, an emf is produced between two edges of conductor. The magnitude of the voltage depends upon the current, flux density and a property of conductor called “Hall Effect Co-efficient”

Effect Instrument

Magnetic EffectAmmeters, Voltmeters, Watt meters, Integrating Meters

Heating Effect Ammeters and Voltmeters, Watt meters

Electrostatic Effect Voltmeters

Induction EffectA.C. Ammeters, Voltmeters, Watt meters, Energy meters

Hall Effect Flux meters, Ammeters and pointing vector watt meter

2.1.3 Types of Instruments

• Permanent Magnet Moving Coil (PMMC)• Moving Iron Instruments• Electro-dynamometer• Hot wire• Thermocouple• Induction• Electrostatic• Rectifier

Permanent Magnet Moving Coil

The PMMC instrument is the most accurate type for D.C Measurement.

Construction:

Moving Coil:

The moving coil is wound with many turns of silk covered copper wire and mounted on a rectangular aluminium former which is pivoted on jeweled bearings.

Most voltmeter coils wound on metal frames to provide electro-magnetic damping. Most ammeter coils wound on non-magnetic frames, b’coz the coil itself provides electro-magnetic damping.

Magnet systems:

There has been considerable developments in materials for permanent magnet.

In old style magnets are U-shaped magnet having soft iron piece. Now a days, materials like Alcomax and Alnico has high co-ercive force, it is possible to use smaller magnet lengths and high field intensities. The flux density is 0.1 to 1 Wb/m2.

Control:When the coil is supported between two jewel bearings the control torque

is provided by two phosphor bronze hair springs. It also serves to lead current in and out of the coil.

Damping:This torque is produced by movement of aluminium former moving in the

magnetic field of permanent magnet. Pointer and Scale:

The pointer is carried by the spindle and moves over a graduated scale. A fine blade helps to reduce parallax error in the reading of the scale.

• Errors: Weakening of permanent magnet due to ageing at temperature effects. Weakening of springs due to ageing and temperature effects. Change of resistance of the moving coil with temperature.

• Advantages: Scale is uniformly divided. Power consumption is very low as 25 to 200 μW. The torque-weight ratio is high which gives a high accuracy. It may be used for different voltages and current ranges by using different

values for shunts and multipliers.• Disadvantages:

It useful only for D.C. The torque reverses if the current reverse. Cost of these instruments is higher than that of moving iron instruments.

Moving Iron Instruments

The most common ammeters and voltmeters for laboratory or switchboard use at power frequencies are the moving iron instruments. It is still cheap as compared to any other type of AC instruments of same accuracy and ruggedness.

o Principle:A soft iron piece of high permeability steel forms the moving element of

the system. It is so situated that it can move in a magnetic field produced by a stationary coil. The coil is excited by voltage or current, when it excited it becomes electromagnet and the iron piece moves in such a way to increase the flux of electromagnet. Thus the force produced is always in such a direction so as to increase the inductance of the coil.

o Classification: (1) Attraction Type (2) Repulsion Type

• Attraction Type: The coil is flat and has a narrow slot like opening. The moving iron is a flat

disc. When the current flows through the coil, a magnetic field is produced and the

moving iron moves from weaker field outside the coil to stronger field inside it.

The controlling torque is provided by springs but gravity control can be used for panel type of instruments which are vertically mounted.

Damping is provided by air fiction with the help of light aluminium piston which moves in a fixed chamber closed at one end.

Moving Iron: Repulsion Type

• Repulsion Type: In this case, two vanes inside the coil one fixed and other is movable. When

current flows through the coil and there is a force of repulsion between the two vanes.

Two different design: Radial type and Co-axial type Radial type:

Here vanes are radial strips of iron. The fixed vane is attached to the coil and the movable one to the spindle of the instrument.

Co-axial type: Here two vanes are co-axial type. The controlling torque is provided

by springs. Gravity control can also be used in vertical type instruments.

Whatever the direction of current, the iron vanes are magnetized that there is always a force of attraction in attraction type and force of repulsion in repulsion type. These instruments can be used on both A.C and D.C

Electrodynamometer Type

Electrodynamometer type of instruments used as A.C Voltmeter and Ammeters both in range of power frequencies and lower part of the audio frequency range.

• Principle:In this type, the field can be made to reverse simultaneously with the

current in the movable coil if the fixed coil is connected in series with the movable coil.• Construction: Fixed coil:

The field be produced by the fixed coil and it is divided into two sections a uniform magnetic field is produced at the center and to allow the passage of the instrument shaft.

The coils are usually wound with heavy wire carrying main current in ammeters and watt meters and is of stranded to reduce eddy current losses in conductors.

Moving coil: It is wound with a non-metallic former. This former type cannot be used as

eddy currents would be induced in it by the alternating field. Light but rigid construction.

Control:

The controlling torque is provided by two control springs. These springs which leads in or out of the coil.

Moving system:It is mounted on an aluminium spindle and it carries a counter weights and

truss type pointer. A suspension may be used at high sensitivity. Damping:

Air friction damping is employed and is provided by a pair of aluminium vanes, attached to the spindle of the bottom

.Thermocouple Instruments:

Principle: Conversion of heat energy to electrical energy at the junction of two

conductors.• When two metals having different work functions are placed together, a

voltage is generated at the junction which is nearly proportional to the temperature. This junction is called Thermocouple.

• The heat at the junction is produced by a electric current flowing in the heater element and thermocouple produces an emf at its output terminal which can be measured with help of PMMC meter. The emf produced is proportional to temperature and rms value of current.

• It can be used for both A.C and D.C and most attractive feature is measurement of current and voltage at very high frequencies.

• It is very accurate well above a frequency of 50 MHz.

2.1.4 Classification of Alternating and Direct current Meters

Meter Type Suitability Major uses

PMMC D.C

Most widely used meter for d.c. current andvoltage and resistance measurement in lowand medium impedance circuits.

Moving Iron D.C or A.C

Inexpensive type used for rough indicationof currents and voltages. Widely used inIndicator type applications such as onpanels.

ElectrodynamometerD.C or A.C

Widely used for precise A.C current andVoltage measurements at power frequencies. Used as standard meter forcalibration and also as transfer instrument.

Thermocouple D.C or A.CMeasurement of Radio frequency A.CSignals.

Moving Coil: A single instrument has one moving coil. It is wound with non-metallic

former. A series resistor is used in the voltage circuit, and the current limited to

100mA.

• Control: The controlling torque is provided by two control springs. These springs which

lead current in or out of the coil.

• Moving System: The moving coil is mounted on an aluminium spindle and it also carries a counter

weight and truss type pointer.

• Damping:Air friction damping is employed for these instruments and is provided by a pair

of vanes, attached to the spindle at the bottom.

• Scales and Pointers:They are equipped with mirror type scales and knife edge pointers to remove

reading errors due to parallax.

2.2.2 Power Measurement in 3 Phase 3 Wire System

2.2.3 Blondel’s Theorem

If a network is supplied through n conductors, the total power is measured by summing the readings of n wattmeter's so arranged that a current element of wattmeter is in each line and the corresponding voltage element is connected between that line and a common point.

Consider the 3 Phase, 3 Wattmeter wire system and load.The potential coils of the wattmeter's are connected to a common point C.

The potential of point C is different from that of the neutral point O of the load.The instantaneous power in the load,

P = V1i1+V2i2+V3i3 Reading of wattmeter, P1 = V1`i1;Reading of wattmeter, P2 = V2`i2;Reading of wattmeter, P3 = V3`i3;Now, V1 = V+V1`, V2 = V+V2`, V3 = V+V3`, P1 = (V1 – V)i1, P2 = (V2 – V)i2 & P3 = (V3 – V)i3 Sum of Wattmeter readings = P1+ P2+ P3

= (V1 – V)i1+(V2 – V)i2+(V3 – V)i3

= V(i1+i2+i3)Apply Kirchoff’s Current Law, i1+i2+i3 = 0Sum of wattmeter readings = V1i1+V2i2+V3i3 = P2.2.4 Two Wattmeter Method

Phasor diagram

• It consists of two separate watt meter movements mounted together in one case with the two moving coils mounted on the same spindle.

• There are two current coils and two pressure coils. A current coil together with pressure coil is known as element. In this case, it has 2 elements.

• The torque on each element is proportional to the power being measured by it. The total torque on the system is equal to the sum of the deflecting torque of the two systems.

• Deflecting Torque of element 1 α P1; Deflecting Torque of element 2 α P2 and Total Deflecting torque α (P1+ P2) α P

• Hence the total deflecting torque on the moving system is proportional to the power.

2.2.6 Energy Meters• What is Energy?

Energy is the total power delivered or consumed over a time interval.Energy = Power x time

• Types:

Single Phase Induction type energy meter Polyphase Energy Meters

2.2.6.1 Single phase Induction Type Energy Meter

• It consists of two AC magnets namely M1 and M2. M1 is called series magnet or current magnet and is excited by line current. M2 is called shunt magnet or voltage magnet.

• The flux Φ1 is produced by M1 is directly proportional to line current and also Φ1 is in phase with the line current.

• M2 is connected across the supply and it carries a current I2 proportional to supply voltage V. The flux Φ2 is produced by M2 lags behind the voltage by 90°. The exact 90° displacement is achieved with the help of copper shading band.

• An aluminium disc AD mounted on a spindle is placed between two magnets. The two fluxes Φ1 and Φ2 induce emf in the disc cause circulatory eddy currents in the disc.

• The interaction between eddy current and flux develop a driving torque on the disc hence its starts rotating.

• The braking torque is obtained from a pair of brake magnet. • The speed of the disc is proportional to energy consumed by the load.• The disc achieve a steady speed when the driving torque and braking torque are

equal.

2.2.6.2 Poly Phase Energy Meter

• It can be measured by a group of single phase energy meters. The total energy is the sum of reading of all energy meters.

• Similar to the case of watt meters for measurement of power in polyphase circuits. The elements are mounted on the same spindle which drives the registering mechanism, it register the net effect of all the elements.

• It may be multi-disc type or single disc type. In multi-disc, each element drives a separate disc. In single disc, all element drives the same disc.

• Two Element Energy Meter: To prevent interaction between eddy currents produced by one element with the flux produced by another element.

• The driving torque of the two elements be exactly equal for equal amount of power passing through each.

2.3 MAGNETIC MEASUREMENTS

• Properties of ferro - magnetic materials.• The magnetic measurement and their characteristics of a magnetic material is of

utmost importance in designing and manufacturing electrical equipment.• Principle: Measurement of magnetic field strength in air. Determination of B-H curve and hysteresis loop for soft ferro-magnetic materials. Determination of eddy current and hysteresis losses of soft ferro-magnetic

materials subjected to alternating magnetic fields. Testing of permanent magnets.• Inherent accuracies: The conditions in the magnetic specimen under test are different from those

assumed in calculations. The magnetic materials are not homogenous. There is no uniformity between different batches of test specimens even if such

batches are of same composition.2.3.1 Types of Test: (1) Ballistic Test (2) AC Testing (3) Steady State Test

2.4.2 Step by Step Method: The magnetizing winding is supplied through a potential divider which have a

large number of tapping. The magnetizing force H is increased by number of suitable steps, up to the desired maximum value.

Now, the tapping switch s2 is set on tapping 1 and switch s1 is closed. Some value of flux density B1 is increased it is observed by galvanometer. The value of corresponding force H1 calculated by amount of current through magnetizing winding at tapping 1.

Then, the force is increased to H2 by switching s2 is suddenly step on tapping 2 and corresponding increase in flux density ΛB is observed by galvanometer.

Then the flux density B2 corresponding to magnetizing force H2 is given by B1+ ΛB.

This process is repeated for other values of H up to the maximum point and complete the B-H curve.

2.4.3 Measurement of Iron Loss• Alternating current magnetic Testing:

– This test is done to determine the iron loss of magnetic materials at different flux density and frequency, to separate the components of iron loss. i.e, hystersis loss and eddy current loss.

• Iron loss curve: When a magnetic material is subjected to an alternating current, there is a loss in

power occurs to hysteresis and eddy current. This loss is called Iron or Core loss. The hysteresis loss determined by D.C too but somewhat different in actual

working condition of hysteresis under A.C. But, eddy current is obtained only from A.C supply.

The iron loss in ferro-magnetic material is of considerable importance for designers.

• Separation of Iron Loss: In order to analyze difference in apparatus design and different ferro-magnetic

materials, sometimes necessary to separate the total iron loss in to hysteresis and eddy current components.

Energy loss due to hystersis in per unit volume∫ H db = Area of hysteresis loop

Hysteresis loss per unit volume = frequency x Area of hysteresis loopHysteresis loss per unit volume, Ph = ηfBmk wattWhere,η à hysteresis co-efficientf à frequency, HzBm à Maximum flux density, Wb/m2

K à Steinmetz co-efficient, varies from 1.6 to 2Eddy current loss per unit volume,

Pe = (4kf2Bm2t2)/3ρ WattWhere,

kf à Form factor

t à thickness of laminations, mρ à resistivity of material, Ωm

Total iron loss per unit volume, Pi = Ph + PeP = ηfBmk + (4kf2Bm2t2)/3ρ

Hence total iron loss in a given specimen is,Pi = volume x {ηfBmk + (4kf2Bm2t2)/3ρ}

For a particular specimen volume, thickness t and resistivity ρ are constant.Pi= KhfBmk + Kekf2Bm2

As the hysteresis and eddy current losses have different lawsof variation with both frequency and form factor, it is possibleto separate the losses by variation of frequency or form factorif Bm can be maintained constant.2.5 INSTRUMENT TRANSFORMER

• What is transformer?Transformer is a static device which transfers energy from one end to

other end without change in frequency. In power system, heavy voltage and current cannot be measured by using normal

meters and cannot be measure by extending the range of low range meters. In such case, specially constructed ratio transformer is called “INSTRUMENT TRANSFORMER”

Such transformer can measure irrespective voltage and current as well as isolated from high voltage and high current measurements.

It is used in A.C systems for the measurement of current, voltage, power and energy. And also in connection with measurement of power factor, power frequency and for indication of synchronism.

CLASSIFICATION • Current Transformer• Potential Transformer

2.5.1 Current Transformer• Heavy currents cannot be measured by using normal meters but current Tr’ used

to measure the high current along with low range meters.• A Tr’ is a device which transfer energy from one side to other side with same

frequency. It has two windings; Primary and Secondary windings. • A high current is connected to the winding is called primary winding which has

small number of turns with heavy large cross-sectional area and it is connected in series with the load.

• The secondary which has large number of turns with small large cross-section area along with low range ammeter. One end of the secondary coil is grounded for

safety purpose. In CT, normally it is used for step up the voltage but obviously it used for to step down the current. For eg; if 500:5 range, i.e, primary winding is 500A it will reduced to 5A on secondary. But it step up the voltage 100 times.

• I1/I2 = N1/N2• The secondary coil should not be open circuit, it may be shorted or connected

with low range meters.

• If secondary coil is opened, current will be zero hence the Ampere turns of secondary becomes zero oppose the primary ampere turns to become zero.

• As there is no counter mmf unopposing the primary side it cause high flux at the core. Due to that, loss will be more and damage the insulation of the winding.

2.5.2 Potential Transformer• The construction of Potential Transformer (PT) is similar to that of CT.• PT is normally step up the current, but obviously its step down the voltage.• Here, the primary coil has large number of turns carrying high voltage and

secondary coil has small number of turns along with small range voltmeter, one side of secondary coil is connected to ground for safety purpose.

Use of Instrument Transformer• The extension of instrument range, so that the current, voltage, power and energy

can be measured with instruments or meters of moderate size.• In power system, handling the voltage and current are vary large, so direct

measurement are not possible.• The solution lies in stepping down these current and voltages with the help of

instrument transformers so that they could be metered with instruments of moderate sizes.

• The primary winding is connected to the current to be measured and the secondary winding is connected to ammeter. The C.T steps down the current to the level of ammeter.

• The primary winding is connected to the voltage to be measured and the secondary winding is connected to voltmeter. The P.T steps down the voltage to the level of voltmeter.

• The extension of range could be done by use of shunts for currents and multipliers for voltage measurements.

Advantages and Disadvantages• Advantages:

– The normal range voltmeter and ammeter can be used along with these transformer to measure high voltage and currents.

– The rating of low range meter can be fixed irrespective of the value of high voltage or current to be measured.

– These transformers isolate the measurement from high voltage and current circuits. This ensures safety of the operator and makes the handling of the equipments very easy and safe.

– These can be used for operating many types of protecting devices such as relays and pilots.

– Several instruments can be fed economically by single transformer.• Disadvantages:

– It can be used for only AC circuits and not for DC circuits.2.6 MEASURMENT OF FREQUENCY

• The meter which are used in the circuit to indicate the frequency of the supply voltage is called frequency meters.

• Classification:– Mechanical Resonance type frequency meter– Electrical Resonance type frequency meter– Weston type frequency meter

• Mechanical Resonance type frequency meter is called vibrating reed type frequency meter

• Electrical Resonance type frequency meter is called ferro dynamic frequency meter

2.6.1 Mechanical Resonance Type This meter consists of a number of thin steel strips called reeds. These reeds are

placed in a row alongside and close to the electromagnet. The electromagnet has a laminated iron core and its coil is connected in series with a resistance, across the supply whose frequency is to be measured. The reeds are approximately about 4 mm wide and 0.5mm thick.

The natural frequency of vibration of the reeds upon their weights and dimensions. The reeds are fixed at the bottom end are free at the top end.

when the frequency meter is connected across supply whose frequency is to be measured, the coil of electromagnet carries a current i which alternates at the supply frequency. The force of attraction between the reeds and the electromagnet is proportional to i² and therefore this force varies at twice the supply frequency.

For a frequency exactly midway between that of the reeds, both will vibrate with amplitudes which are equal in magnitude, but considerably less than the amplitude which is at resonance.

The usual frequency span of these meters is six Hz say 47Hz to 53Hz. Advantage: The indication is virtually independent of the waveform of the supply

voltage. Disadvantage: It cannot read much closer than half the frequency difference

between adjacent reeds. Thus they cannot be used for precision measurements2.6.2 Electrical Resonance Type

• It consists of a fixed coil which is connected across the supply whose frequency is to be measured is called magnetizing coil.

• The magnetizing coil is mounted on a laminated iron core. It has a cross-section which varies gradually over the length, being maximum near the end where the magnetizing coil is mounted and minimum at the other end.

• A moving coil is pivoted over this iron core. A pointer is attached to the moving coil. The terminals of the moving coil are connected to a suitable capacitor C. There is no provision for a controlling force.

• The magnetizing coil carries a current I and this current produces a flux Ф, being alternating in nature, induces and emf E in the moving coil. This emf lags behind the flux by 90º. The emf induced circulates a current Im in the moving coil. The phase of this current Im depends upon the inductance L of the moving coil and the capacitance C.

• The moving coil is assumed to be inductive and therefore current Im lags behind emf E by an angle α. The torque is Td α Im cos(90º+α)

• The moving coil is assumed to be largely capacitive and therefore current Im leads the emf E by an angle β. The deflecting torque is Td α Im cos(90º- β)

• The inductive reactance is supposed to be equal to the capacitive reactance and, therefore, the circuit is under resonance conditions.

2.6.3 Phase Sequence Indicators• These instruments are used to determine the phase sequence of three phase

supplies.• Two types: Rotating type and Static Type• Rotating Type:

– It consists of 3 coils mounted 120º apart in space. They are brought out and connected to 3 terminals marked RYB as shown in fig.

– The coils are star connected and are excited by the supply whose phase sequence is to be determined. An aluminium disc is mounted on the top of the coils.

– It produce a rotating magnetic field and eddy emf’s are induced in the disc. A torque is produced with the interaction of the eddy currents with the field.

– The disc revolves because of the torque and the direction of rotation depends upon the phase sequence of the supply.

– An arrow indicates the direction of the rotation of the disc. If the direction of the rotation is same as that indicated by the arrow head, the phase sequence of the supply is the same as marked on the terminals of the instrument.

• Static Type:– When the phase sequence is RYB, lamp 1 will be dim and lamp 2 will

glow brightly. – If the phase sequence is RBY, lamp 1 will glow brightly and lamp 2 will

be dim.

4.2 RECORDERS

A recorder thus records electrical and non-electrical quantities as a function of time.Currents and voltages can be recorded directly while the non-electrical

quantities are recorded indirectly by first converting them to equivalent currents or voltages with the help of sensors or transducers.Requirements:

The recording method should be consistent with the type of system.Two Types: 1.Analog recorders and

2.Digital recorders

4.2.1 Analog Recorders:a. Graphic recordersb. Oscillographic recordersc. Magnetic tape recorders

4.2.1.1 Graphic recorders It is a devices which display and store a pen-and-ink record of

history of some physical event. Classification:

Strip Chart Recorders: It records one or more variables with respect to time. It is an X-t recorder.

X-Y Recorders: It records one or more dependent variables with respect to an independent variable.

Features of Strip Chart Recorders: A long roll of graph paper moving vertically A system for driving the paper at some selected speed. Chart speeds of 1 –

100 mm/s are usually speed. A stylus for marking marks on the moving graph paper. It moves

horizontally in proportional to the quantity being recorded. A stylus driving system which moves the stylus in a nearly exact replica or

analog of the quantity being recorded. A range selector switch is used so that input to the recorder drive system

is within the acceptable level. Features of X-Y Recorders:

It is a instrument which gives a graphic record of the relationship between two variables.

In Strip chart usually self-balancing potentiometers are used, an emf is plotted as a function of another emf.

In this case, one self-balancing potentiometer circuit moves a recording pen (stylus) in the X direction while another self-balancing potentiometer circuit moves the recording pen (stylus) in the Y direction at right angles to the X direction, while the paper remains stationary.

It may not necessarily measure only voltages. The measured emf may be the output of a transducer that may measure displacement force, pressure, strain, light intensity or any other physical quantity.

With the help of X-Y recorders and appropriate transducers, a physical quantity may be plotted against another physical quantity.

4.2.1.2 Magnetic Tape Recorders: To record data in such a way that they can be retrieved or reproduced in

electrical form again. The most common and most useful way of achieving this is through the use of magnetic tape recording.

It basically low-frequency recorders but magnetic tape recorders have response characteristics which enable them to be used at higher frequencies.

Therefore magnetic tape recorders are extensively used in Instrumentation systems.

Advantages: It have a wide range of frequency range from d.c to several MHz. It have a wide dynamic range which exceeds 50db. It have a low distortion. The recorded signal is immediately available, with no time lost in

processing. When the information has been processed, the tape can be erased and

reused to record a new set of data.4.2.2 Digital Recorders:

It is a simplest method and usually requires one tape track for each channel. The signal to be recorded is amplified mixed with a high frequency bias and fed directly to the recording head as a varying electric current.Advantages:

It has a wide range of frequencies ranging from 50 Hz to about 2 MHz for a tape speed of 3.05 m/s.

It requires simple, moderately priced electronic circuitry. It has a good dynamic response and takes overloads without increase in

distortion.Disadvantages:

It may not be perfectly recorded owing to dirt or poor manufacture is called “Drop out”.

It is used only when maximum bandwidth is required and when variations in amplitude are acceptable

4.4 CATHODE RAY TUBE DISPLAY

• Cathode ray oscilloscope of a cathode ray tube (CRT), which is the heart of the tube, and some additional circuitry to operate the CRT.

• Main parts: Electron gun assembly, Deflection plate assembly, Fluorescent screen, Glass envelope and Base, through which connections are made to various parts.

• The “Electron gun assembly” produces a sharply focused beam of electrons which are accelerated to high velocity. This focused beam of electrons strikes the fluorescent screen with sufficient energy to cause a luminous spot on the screen.

• After leaving the electron gun, the electron beam passes through two pairs of “Electrostatic deflection plates”. Voltages applied to these plates deflect the beam.

• Voltages applied to one pair of plates move the beam vertically up and down and the voltages applied to the other pair of plates move the beam horizontally from one side to other. These two movements i.e. horizontal and vertical plates are independent of each other and thus beam may be positioned anywhere on the screen.

• The working parts of a CRT are enclosed in an evacuated glass envelope so that the emitted electrons are able to move about freely from one end of the tube to the other.

4.5 DIGITAL CRO

• The availability of electronic circuitry at low cost has enabled many digital features to be added to analog oscilloscopes. Eg: Digital display of the parameters; Integral digital voltmeter and counter; Remote control.

• A digital oscilloscope digitizes the input signal, so that all subsequent signals are digital. A conventional CRT is used, and storage occurs in electronic digital memory.

• The input signal is digitized and stored in memory in digital form. In this state it is capable of being analyzed to produce a variety of different information. To view the display on the CRT the data from memory is reconstructed in analog form.

• Digitizing occurs by taking a sample of the input waveform at periodic intervals. In order to ensure that no information is lost, sampling theory states that the sampling rate must be at least twice as fast as the highest frequency in I/P signal.

• The requirement of high sampling rate means that the digitizer, which is analog to digital converter, must have a fast conversion rate. This usually requires expensive flash analog to digital converters, whose resolution decreases as the sampling rate is increased.

4.8 DOT MATRICES: Dot matrices may be used for display of numeric and alpha numeric characters.

• A 3x5 Dot Matrix: A 3x5 Dot matrices as shown in fig. may be used for display of numeric characters.

• A 5x7 Dot Matrix: For display of Alphanumeric characters a 5x7 dot matrix as shown in fig.

4.6 LIGHT EMITTING DIODE (LED)• The LED is a PN junction device which emits light when a current passes through

it in the forward direction. It perhaps the most important of the display devices available today for use in instrumentation systems.

• Charge carrier recombination occurs at PN junction as electrons cross from N side and recombines with holes on the P side.

• When combination takes place, the charge carries give up energy in the form of heat and light. If the semi conducting material is translucent the light is emitted, and the junction is source of light.

• Typical LED charge carrier recombination's takes place in the P type material becomes the surface of the devices. For maximum light emission, a metal film anode is deposited around the edge of the P type material.

• The cathode connection for the device is usually a gold film at the bottom of the N type region.

• Semiconductor materials used for manufacture of LED are gallium arsenide phosphide (GaAsP) which emits red or yellow light of gallium arsenide (GaAs) which gives green or red light emission.

• LED’s are used extensively in segmental and dot matrix displays of numeric and alphanumeric characters.

• LED’s are available in many colors like green, yellow, amber and red.Advantages:

Miniature in size and they can be stacked together to form numeric and alphanumeric displays in high density matrix.

Smoothly controlled. Voltage drop of 1.2V and a Current of 20mA is required for full brightness. The switching time is less than 1ns They are economical and have a high degree of reliability. It can be operated over a wide range of temperature 0 - 70ºC.

4.7 LIQUID CRYSTAL DISPLAY (LCD)• Liquid Crystal Displays (LCD) are used in similar applications where LED’s are

used. These applications are display of numeric and alphanumeric characters in dot matrix and segmental display.

• Two Types: Dynamic Scattering and Field Effect Type• Dynamic Scattering:

– From Fig. the liquid crystal material may be one of the several organic compounds which exhibit optical properties of a crystal through they remain in liquid form.

– Liquid crystal is layered between glass sheets with transparent electrodes deposited on the inside faces.

– When a potential is applied across the cell, charge carries flowing through the liquid disrupt, the molecular alignment and produce turbulance.

– When the liquid is activated the molecular turbulance causes light to be scattered in all directions and the cell appears to be bright.

• Field Effect:– It is similar to that of the dynamic scattering, with the exception that two

thin polarizing optical filters are placed at the inside of each glass sheet.– The material used is twisted numeric type and actually twists the light

passing through the cell when the latter is not energized. It allows the light to pass through the optical filters and the cell appears bright.

– When the cell is energized, no twisting of light takes place and the cell appears dull.

Advantages: Low power consumption. It requires about 140 µW and low cost.

Disadvantages: Very slow devices. It turn ON and turn OFF times are quite large. Life span is quite small.

5.0 TRANSDUCERSA transducer is a device which converts energy from one form to another. It is a device which converts a physical quantity or a physical condition into an electrical signal.Advantages: Transducer

• Electrical amplification and attenuation can be done easily.• The mass-inertia effects are minimized.• The effects of friction are minimized.• The electrical or electronic systems can be controlled with a very small power

level.• The electrical output can be easily used, transmitted and processed for the purpose

of measurement.

• Telemetry is used in almost all sophisticated measurement systems.5.1 CLASSIFICATION OF TRANSDUCERS

On the basis of transduction form used, Primary and Secondary transducers, Passive and Active transducers, Analog and Digital transducers, Transducers and Inverse transducers. Based upon Principle of Transduction:

The basis of principle of transduction as resistive, inductive, capacitive etc., depending upon how they convert the input quantity into resistance, inductance or capacitance respectively. They can be classified as piezoelectric, thermoelectric, magneto restrictive, electro kinetic and optical

Primary and Secondary Transducer: The bourdon tube acting as a primary detector senses the pressure and

converts the pressure into a displacement of its free end. The displacement of the free end moves the core of a Linear Variable differential Transformer (LVDT). Which produces an output voltage which is proportional to the movement of the core, which is proportional to the displacement of the free end which in turn is proportional to the pressure.

Two stages of transduction, firstly the pressure is converted into a displacement by Bourdon Tube then the displacement is converted into an analogous voltage by LVDT. The Bourdon tube is called a “Primary Transducer” while the LVDT is called a “Secondary Transducer”

• Passive and Active Transducers:– Passive Transducer: It derive the power required for transduction from

an auxiliary power source. It also known as “externally power transducers”.

– Eg: Resistive, Inductive and Capacitive transducer– Active Transducer: Which do not require an auxiliary power source to

produce their output. It is an self generating type.– Eg: Velocity, Temperature

• Analog and Digital Transducers:– Analog Transducer: It convert the input quantity into an analog output

which is a continuous function of time. – Eg: Thermocouple– Digital Transducer: It convert input quantity into an electrical output

which is in the form of pulses.– Eg: Binary system symbols 0 and 1

• Transducers and Inverse Transducers :– Transducer: It is a device which converts non-electrical quantity into an

electrical quantity.– Inverse Transducer: It is a device which converts an electrical quantity

into an non-electrical quantity.

5.2 SELECTION OF TRANSDUCERS– Types of input & operating range: Input can be any physical quantity

and operating range may be a decisive factor in selection of a transducer for a particular application.

– Loading Effects: It should have no loading effect on the input quantity being measured.

– Sensitivity: It is not constant but is dependent upon the quantity.– Scale Factor: It is defined as the inverse of sensitivity.– Scale Factor: It is defined as the inverse of sensitivity.– Errors: Difference between input and output quantity– Non-Conformity: In which the experimentally obtained transfer function

deviates from the theoretical transfer function for almost every input.– Hysteresis: The output of a transducer not only depends upon the input

quantity but also upon input quantity previously applied to it.– Dynamic Error: It occur only when the input quantity is varying with

time.5.3 RESISTIVE TRANSDUCERS

• It involve the measurement of change in resistance are preferred to those employing other principles. This is because both alternating as well as direct currents and voltages are suitable for resistance measurement.

• The resistance of a metal conductor is expressed by a simple equation, R=ρL/A• Any method of varying one of the quantities involved in the above relationship

can be the design basis of an Electrical Resistive Transducer.• Strain Gauges work on the principle that the resistance of a conductor or a

semiconductor changes when strained.• Basically a potentiometer, or a simply a POT, it consists of a resistive element

provided with a sliding contact. This sliding contact is called a Wiper. The motion of sliding contact may be Translatory and Rotational.

• Translational elements are straight devices and have a stroke of 2mm to 0.5m. Rotational devices are circular in shape and are used for measurement of angular displacement.

• Full scale angular displacement as small as 10º• The POT is a passive transducer it requires an external power source for its

operation.• The resistive body of potentiometer may be wire wound. A very thin 0.01mm

diameter of platinum or nickel alloy is carefully wound on an insulated former.5.4.1 Linear Variable Differential Transformer (LVDT)The most widely used inductive to translate the linear motion into electrical signals is the Linear Variable Differential Transformer (LVDT)

Construction• The transformer consists of a single primary winding P and two secondary

winding S1 and S2 wound on a cylindrical former.• The secondary windings have equal number of turns and are identically placed on

either side of the primary winding. The primary winding is connected to an alternating current.

• A movable soft iron core is placed inside the former. The displacement to be measured is applied to the arm attached to the soft iron core.

• The core is made of high permeability, nickel iron which is hydrogen annealed. It gives low harmonics, low null voltage and a high sensitivity.

• The frequency of AC applied to primary windings may be between 50 Hz to 20 kHz.

working• The primary winding is excited by an alternating current source, it produces an

alternating magnetic field which in turn induces alternating current voltages in the two secondary windings.

• The output voltage of primary, S1 is E1 and that of secondary, S2 is E2.• The output voltage of the transducer is the difference of the two voltages.

Differential output voltage, E0 = E1 – E2.• When the core is at its normal position, the flux linking with both the secondary

windings is equal and hence equal emf’s are induced in them. E1 = E2.• When the core is moved to the left, more flux links with winding S1 and less with

winding S2. E0 = E1 – E2.• When the core is moved to the right, more flux links with winding S2 and less

with winding S1. E0 = E2 – E1.• Advantages:

• High range• Friction and Electrical isolation• Immunity from external effects• High input and high sensitivity• Ruggedness• Low Hysteresis• Low power consumption

• Disadvantages:• Relatively large displacements are required for appreciable differential

output• Sensitive to stray magnetic fields but shielding is possible• Performance is affected by vibrations.• A demodulator network must be used if a DC output is required.• Temperature affects the performance of the transducer.

5.4.2 Rotary Variable Differential Transformer (RVDT)• A variation of LVDT may be used to sense angular displacement.• It is similar to the LVDT except that its core is can shaped and may be rotated

between the windings by means of a shaft.• The operation of a RVDT is similar to LVDT. At the null position of the core, the

output voltage of secondary windings S1 and S2 are equal and in opposition. Therefore, net output is zero.

• The greater this angular displacement, the greater will be the differential output. Hence the response of the transducer is linear.

• Clockwise rotation produces an increasing voltage of a secondary winding of one phase while counter clock wise rotation produces an increasing voltage of opposite phase.

• The amount of angular displacement and its direction may be ascertained from the magnitude and phase of the output voltage of the transducer.

5.5 CAPACITIVE TRANSDUCERSThe principle of operation of capacitive transducers is based upon the familiar equation for capacitance of a parallel plate capacitor.

C = εA/dThe capacitive transducer work on the principle of change of capacitance which

may be caused by Change in overlapping area A, Change in the distance d between the plates, Change in dielectric constant. The change in capacitance may be caused by change in dielectric constant as in

the case in measurement of liquid or gas levels. The output impedance of a capacitive transducer is high. The capacitive transducer are commonly used for measurement of linear

displacement. The following effects: Change in capacitance due to change in overlapping area of plates Change in capacitance due to change in distance between the two plates.

5.5.1 Transducers using change in area of plates: The capacitance changes linearly with change in area of plates.

It is useful for measurement of moderate to large displacements say from 1 mm to several cm.

The area changes linearly with displacement and also the capacitance. For a parallel plate capacitor, the capacitance is C = εA/d The sensitivity is constant and therefore there is linear relationship

between capacitance and displacement.5.5.2 Transducers using change in distance between plates:

The effect of capacitance with changes in distance between the two plates. One is fixed and the displacement to be measured is applied to the other

plate which is movable. The capacitance C, varies inversely as the distance d, between the plates

the response of this transducer is not linear as shown in fig. The sensitivity of transducer can be increased to any desirable value by

making the distance between the plates extremely small.5.6 PIEZO-ELECTRIC TRANSDUCERSA piezo-electric material is one in which an electric potential appears across certain surfaces of a crystal if the dimensions of the crystal are changed by the application of a mechanical force.

This potential is produced by the displacement of charge. The effect is reversible, i.e., conversely, if a varying potential is applied to the

proper axis of the crystal, it will change the dimensions of the crystal thereby deforming it.

Common piezo-electric materials include Rochelle salts, ammonium dihydrogen phosphate, lithium sulphate, dipotassium tartarate, potassium dihydrogen phosphate, quartz and ceramics A and B.

Except for quartz and ceramics A and B, the rest are man-made crystals grown from aqueous solutions under carefully controlled condition.

They do not have piezo-electric properties in their original state but these properties are produced by special polarizing treatment.

Two categories: Natural Group and Synthetic Group. Quartz and Rochelle salt belong to natural group while materials like lithium

sulphate, ethylene diamine tartarate belong to the synthetic group. It can be made to respond to mechanical deformations of the material in many

different modes: Thickness expansion, Transverse expansion, Thickness shear and Face shear.

The mode of motion effected depends on the shape of the body relative to the crystal axis and location of the electrodes.

A piezo-electric element used for converting mechanical motion to electrical signals may be thought as charge generator and a capacitor.

Mechanical deformation generates a charge and it appears as a voltage across the electrodes. The voltage is E=Q/C.

The effect is direction sensitive. A tensile force produces a voltage of one polarity while a compressive force produces a voltage of opposite polarity.

The magnitude and polarity of the induced surface charges are proportional to the magnitude and direction of the applied force F. the polarity of induced charges depends upon the direction of applied force.

charge, Q = d x F coulomb

3.1 POTENTIOMETERS Two Types

D.C. Potentiometer A.C. Potentiometer

3.1.1 D.C. Potentiometer• A potentiometer is an instrument which is designed to measure an unknown

voltage by comparing it with a known voltage.• The advantage of this method to make use of balance or null condition at which

no current flows and hence no power is consumed in the circuit containing the unknown emf when the instrument is balanced.

Principle• The switch ‘S’ is in operate position and the galvanometer key ‘K’ is kept opened,

the Battery supplies the ‘working current’ through the rheostat and slide wire.• The working current is varied by varying the controlling rheostat.• The unknown voltage ‘V’ depends on the position of the sliding contact such that

the galvanometer shows zero deflection i.e., indicates null condition, when the galvanometer key ‘k’ is closed.

• The unknown voltage ‘V’ is equal to voltage drop ‘V1’ across the portion of XY of the slide wire.

• The slide wire has a uniform cross section and uniform resistance along its total length.

Types of Potentiometers1. Laboratory type D.C Potentiometer (Crompton’s)2. Duo-range (Two range) Potentiometer3. Vernier Potentiometer4. Potentiometer with true zero5. Deflectional Potentiometer

3.1.1.1 Laboratory type D.C Potentiometer• In this type, it consists of one slide switch with fifteen steps, each having a

precision resistor of single turn circular slide wire.• The slide wire has a resistance of 10Ω and the dial switch resistor having 10Ω

each and the total resistance of dial switch is 150Ω. Therefore each step of dial switch corresponds to 0.1V

• This potentiometer is provided with a two way switch which allows the connection of either standard cell or the unknown emf to be applied to the working circuit.

• A protective resistance of 10kΩ is used in the galvanometer circuit. In order to operate the galvanometer at its maximum sensitivity provision to short the protective resistor when near the balance condition

The following steps are adopted for this type:

1. The combination of slide wire and dial resistors to set the standard cell voltage. If the value of emf of standard coil is 1.0186V, the dial resistor is put at 1.0V and the slide wire is to be set at 0.0186.

2. Now the switch ‘S’ is thrown to the calibrate position and the galvanometer key is tapped while the rheostat is adjusted for zero deflection on the galvanometer. The protective resistor is kept at initial stage to protect the galvanometer from getting damaged.

3. When the balance point is approached, the protective resistor is shorted so as to increase the sensitivity of the galvanometer. Final adjustment is made with the help of rheostat. This is known as standardization process.

4. After completion of standardization process, the switch ‘S’ is thrown to operate position thus by connecting unknown emf in to the potentiometer circuit. The potentiometer is balanced with the protective resistance in the circuit by means of main dial switch and dial resistor.

5. When the balance is approached, the protective resistor is shorted, and final adjustment are made to obtain true balance.

6. The value of unknown emf is read off directly from the settings of the dial adjacent to the slide wire.

7. The Standardization is checked again by returning the switch ’S’ to calibrate position. The dial settings are kept exactly the same as in the original standardization process. If the new reading does not agree with the old reading, a second measurement of unknown emf must be made. The standardization should be again checked after the completion of measurement. This potentiometer is known as Crompton’s Potentiometer

3.1.1.2 Duo-range (Two range) Potentiometer• In this type, it consists of main dial in series with the slide wire, working battery

and a variable rheostat.• The design of circuit of a duo-range potentiometer should be such that it is

possible to change the measuring range without re-adjusting the rheostat or changing the value of working voltage of the battery.

• Once the instrument is calibrated on x1 range, then the calibration of x0.1 range is not necessary.

• The voltage Vxz remains same for both positions of range switch ‘S’.• This condition is satisfied only when the total battery current has the same value

for each measuring range.• In order to analyze the operation of this potentiometer by two circuits.• On the range x1, the resistors R1 & R2 in series, are in parallel with total

measuring resistance Rm.• On the range x0.1, the resistor R2 parallel with series combination of R1 and Rm.• The total current drawn from the battery, we have R2 = Rm.• This means the range of resistance R2 is equal to Rm. Now current through the

measuring circuit on x0.1 range should be 1/10 of the current in the measuring circuit on x1 range. Im’ = 0.1Im.

• Advantages:• Precision of reading is increased by one decimal place.

• A greater part of reading is made on the dial resistors which have inherently a greater accuracy then the slide wire.

3.1.1.3Vernier Potentiometer• In this type, the slide wire is eliminated. It has two stages.

– Normal range of 1.6V down to 10μV and– Lower range of 0.16V down to 1μV – It consists of three measuring dials. The first dial measures up to 1.5V (on

x1 range) in steps 0.1V, the middle dial measures up to 0.1V in steps of 0.001V, the third dial measures from 0.0001V to 0.001V in steps of 0.00001V (10μV).

– The resistance of middle dial shunts two coils of the first dial. The moving arm of middle dial carries two arms spaced two studs.

– The vernier potentiometer reads to increment of 10μV on range x1 and has readability of 1μV on x0.1 range. If a third range of x0.01 is provided, the readability becomes 0.1μV.

– Measurements are subjected to stray thermal and contact emfs in the potentiometer, galvanometer and the measuring circuits.

3.1.1.4 Potentiometer with true zero• In laboratory type, it is impossible to obtain true zero because of the two contacts

cannot coincide absolutely. This drawback is eliminated by this type.• The slide wire ‘ST’ is provided with shunt resistor tapped by ‘U’. The tapping is

made zero on the main dial.• The contact is in a position such r1/r3 = r2/r4 that zero. • The slide wire can travel a little lower than zero position giving a small negative

reading. The movement of slider above zero gives positive reading.• The range of slide wire is usually from -0.005 V to +0.150V.

3.1.1.5 Deflect ional Potentiometer• In this type, only one or two main dials, consisting of DRB (Decade Resistance

Box) and center zero galvanometer. • The galvanometer includes consist of two compensating resistors R1 and R2.• The value of R1 and R2 is viewed from the terminals where the unknown emf is

applied to the circuit and remains constant.• The current through the galvanometer which is always proportional to out of

balance current whatever may be the setting of main dial.• The value of unknown emf is obtained by adding the galvanometer reading in the

main dial setting. The main dial setting is kept nearly equal to the emf being measured.

3.1.2 A.C. POTENTIOMETER• The principle of AC Potentiometer is the same as that of the DC Potentiometer.• Main difference: In DC, only the magnitudes of the unknown emf and

potentiometer voltage drop have to be made equal to obtain balance. In AC, both magnitudes and phases of the two have to be same to obtain balance.

Important Factors for AC Potentiometer

It requires equal phase and magnitude of all instants. It means the frequency and waveform of the current in the potentiometer ckt must exactly be the same as that of voltage being measured.

A vibration galvanometer is a tuned device, is usually used as a detector. The ratio of two voltages be determined with a high degree of precision, the

accuracy with which the value in volt can be stated in determined by the accuracy with which the reference voltage.

Extraneous or stray emf’s picked up from stray fields or couplings between portion of the potentiometer ckt seriously effect the result.

Types• Two Types: Polar and Co-ordinate Type.• Polar Type:

– The magnitude of unknown voltage is read from one scale and its phase angle is read directly from second scale.

– Voltage is V<θ and phase angle up to 360º.• Co-ordinate Type:

– It provided with two scales to read respectively the inphase component V1 and quadrature component of V2 of the unknown voltage ‘V’. These components are 90º out of phase with each other.

– V = Sqrt(V1²+V2²) and θ = tan-1(V2/V1).– Types: Drysdale Polar Potentiometer and Gall-Tinsley (Co-ordinate Type

AC Potentiometer). 3.1.2.1 Drysdale Potentiometer

• Stator: Laminated Silicon Steel and Rotor: Laminated Structure having slots in which winding is provided.

• When current flows in stator wdg, a rotating field is produced, thereby inducing an emf in the rotor winding.

• The rotor can be adjusted at will through any required angle, the phase displacement of rotor emf being equal to the angle through which the rotor has been moved from its zero position.

• The scale is graduated both in degrees and cosines of the angles.• It is operated from a 1Ф supply, by means of a phase splitting device. This device

is necessary to have two separate windings displaced by 90º in space on the stator.• One winding is fed directly from supply and other is connected in series with a

variable resistance R & Capacitor C. • Both elements are adjusted until the current through two wdg’s are equal and 90º

displaced from each creating a uniform revolving field.3.1.2.2 Gall-Tinsley Potentiometer

• It consists of two separate potentiometer ckt’s enclosed in a common case. One is “In phase” and other is “Quadrature” potentiometer and phase difference is 90º.

• First: Measurement of “unknown” voltage which is in phase with the current. Second: Measurement of “unknown” voltage which is in phase Quadrature with the current.

• If these measured values are V1 and V2 , then unknown voltage, V = Sqrt(V1²+V2²) and θ = tan-1(V2/V1).

• T1&T2: Two step down transformer which supply about 6V to the potentiometer ckt. V.G: Vibration Galvanometer and K:Key. S1&S2: Two “Sign-Changing” switches which may be necessary to reverse the direction of unknown emf applied to the slide-wires. S3: Selector switch by which the unknown voltages to be measured are placed in the circuit.

3.2 BRIDGES• Two Types:

– D.C. Bridge– A.C. Bridge

3.2.1 D.C.BRIDGE• Classification of Resistance:

– Low: In order of 1Ω and Below.– Medium: From 1Ω upwards to about 0.1MΩ.– High: From 0.1MΩ and Above.

There are different methods used for measurement of medium resistances are:

Ammeter – Voltmeter Method Substitution Method Wheatstone bridge Method Ohmmeter Method

• A very important device used in the measurement of medium resistances. It has been in use longer than almost any electrical measuring instrument.

• The Wheatstone bridge is an instrument for making comparison measurements and operates upon a null indication principle.

• It has four resistive arms, consisting of resistances P,Q,R and S together with a source of emf and a null detector.

• The bridge is said to be balanced, When there is no current through the galvanometer or when the potential difference across the galvanometer is zero.

• For bridge balance, I1P = I2R à (1)• For galvanometer current to be zero,

I1 = I3 = E/(P+Q) à(2) I2 = I4 = E/(R+S) à(3)

Combining equ., (1), (2) & (3) P/(P+Q) = R/(R+S) à(4)

QR = PS à(5) P/Q = R/S

This is the expression for the balance of Wheatstone bridge.

Kelvin’s Double Bridge Method

• It is a modification of Wheatstone bridge and provides greatly increased accuracy in measurement of low resistances.

• Here r represents the resistance of the lead that connects unknown resistance R to standard resistance S. The galvanometer connection either to point ‘m’ or ‘n’. If the lead to point ‘m’ it indicates too low resistance and if it is to point ‘n’ it indicates too high resistance.

• If at point ‘d’ the resistance r divided into two parts r1 and r2 such that r1/r2 = P/Q

We have, R+r = P/Q*(S+r2)or r1/(r1+r2 )= P/(P+Q) or r1 = {P/(P+Q)}*r

(R + {P/(P+Q)}*r) = P/Q*(S+(Q/P+Q)*r)R = (P/Q)*S

3.2.2 A.C. BRIDGE• Alternating current bridge methods are of outstanding importance for

measurement of electrical quantities. Measurement of Inductance, Capacitance, Storage factor, Loss factor may be made conveniently and accurately by employing A.C. bridge networks.

• General Equation for Bridge Balance:The conditions for balance of bridge require that there should be no current

through detector.E1 = E2 à (1)

I1Z1 = I2Z2 à (2)Also at balance, I1 = I3 = E/(Z1+Z3) à (3)

I2 = I4 = E/(Z2+Z4) à (4)Substitute equ., (3) & (4) into equ.(2) gives

Z1Z4 = Z2Z3Measurement of Self Inductance

• Maxwell’s Inductance Bridge:

• It measures an inductance by comparison with a variable standard self – inductance.Let,

L1 à Unknown inductance of R1L2 à Variable inductance of fixed R2R2 à variable resistance connected in series with

L2R3, R4 à Non – Inductive Resistances.

At balance, L1 = (R3/R4)*L2R1 = (R3/R4)*(R2+r2)

• Maxwell’s Inductance – Capacitance Bridge:

Let, L1 à Unknown Inductance

R1 à Effective resistance of L1R2,R3,R4 àKnown non – inductive resistances C4 àVariable Standard capacitorAt balance,

(R1+jωL1)*(R4/{1+jωC4R4})= R2R3 R1R4 + jωL1R4 = R2R3+jωR2R3C4R4

Real and Imaginary terms,R1 = (R2R3)/R4 and L1 = R2R3C4

Hay’s Bridge

Let, L1àUnknown inductance having resistance R1

R2,R3,R4àKnown non – inductive resistance C4àStandard CapacitorAt balance,

(R1+jωL1)*(R4-j/ωC4) = R2R3R1R4+L1/C4+jωL1R4–jR1/ωC4 = R2R3

Real and Imaginary terms,R1R4+L1/C4 = R2R3 and L1=R1/ω2R4C4

Owen’s Bridge

Let,L1 à Unknown self inductance of R1R2 à Variable non – inductive resistanceR3 à Fixed non – inductive resistanceC2 à Variable standard capacitorC4 à Fixed standard capacitor

At balance,(R1+jωL1)*(1/jωC4) = (R2+1/jωC2)*R3Real and Imaginary parts,

L1 = R2R3C4 and R1 = R3(C4/C2)Schering Bridge

Let,C1 à CapacitanceC2 à Standard capacitor r1 à A series resistance in C1R3 à Non – inductive resistanceC4 à Variable capacitorR4 à Variable non – inductive resistance

At balance,(r1+{1/jωC1})*(R4/{1+jωC4R4})= {1/jωC2}R3(r1+{1/jωC1})*R4 = {R3/jωC2}*(1+jωC4R4) r1R4 – (jR4/ωC1) = {- jR3/ωC2}+(R3R4C4/C2)

Real and Imaginary parts,r1 = (R3C4)/C2 and C1 = C2*(R4/R3)

3.3 TRANSFORMER RATIO BRIDGE

• It become increasingly popular and are being used for a wide range of applications. A Transformer Ratio Bridge (TRB) consists of voltage Transformer whose performance approaches that of an ideal Transformer.

• The ratio transformer is provided with a no. of tappings in order to obtain voltage division (Fig. TRB-1). Voltage across winding of a Tr’ is E = 4kfNФmf Volts.

• It can be used for:– Measurement of Resistance, Capacitance and Inductance in comparison

with Standard Resistance Rs, Standard Inductance Ls and Standard Capacitance Cs.

– Measurement of amplifier gain and Phase shift.– Measurement of Transformer ratios.

3.3.1 Measurement of Resistance:– It is used for measurement of an unknown resistance R comparison with

standard resistance Rs, as shown in Fig.TRB-2.– Current through unknown resistance, I1=E1/R= K1N1/R.– Current through unknown resistance,I2=E2/R= K1N2/Rs– At Balance, I1 = I2

K1N1/R = K1N2/Rs (or) R = (N1/N2)*Rs.3.3.2 Measurement of Capacitance:

– From Fig.TRB-3. An unknown capacitance C is measured in comparison with a standard capacitance Cs. Resistance R represents the loss of the capacitor.

– At Balance, C = (N2/N1)*Cs , R = (N1/N2)*Rs.3.3.3 Measurement of Phase Angle:

– From Fig.TRB-4. An RC ckt is used where the capacitance is variable in order to get phase shift.

– The value of resistance should be large in order that there are no loading effects on the ratio Transformer.

– Phase angle, Ф = tan-1(-ωRC