## Linear Variable Differential Transformer (LVDT)

Linear Variable Differential Transformer (LVDT) the most widely used inductive transducer to converts the linear motion or displacement into electrical signals.

Construction

The transformer consists of a single primary winding and two secondary winding S1 and S2 wound on a cylindrical former. Both the secondary winding have an equal number of turns and are identical placed on either side of the primary winding. The secondary windings are connected in series opposition so that the emfs induced in the coils oppose each other. The primary winding is connected to an alternating current source. 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 linear voltage differential transformer measures force in terms of output voltage. The frequency of a.c. applied to the primary winding may be between 50Hz to 200 kHz.

Working

When primary winding is connected to an a.c. supply and a soft iron core is placed inside the former; e.m.fs. ES1, and ES2 are induced in two secondary winding S1 and S2 respectively. Their magnitudes depend upon the flux linking with them. The working of LVDT is explained in three cases

Case-I

When the core is in the centre position, the induced e.m.fs. in the two secondaries are equal. Since the windings are cross connected, their e.m.fs. oppose each other, the output voltage will be zero volt.

Case-II

When an externally applied force moves the core to the left hand side position, more magnetic flux links with the coil S1 than coil S2. The induced e.m.f. of coil S1, (i.e. ES1) is, therefore, larger than the induced emf. of Coil S2 (i.e. ES2). The magnitude of the output voltage is then equal to the difference between the two secondary voltages (i.e.ES1 – ES2) and it is in phase with the voltage of the coil S1.Case-III

When the core is forced to move to the right hand side position, more flux links with the coil S2 than coil S1. The induced emf. in coil S2 (i.e. ES2) is, therefore, larger than the induced e.m.f. in coil S1, (i.e. ES1). The magnitude of the output voltage is then equal to the difference between the two secondary voltage (i.e. ES1 – ES2) which is in phase with the voltage of the coil S2.Thus. the output voltage of Linear Variable Differential Transformer (LVDT) is the function of the core position. This output voltage is measured to determine the displacement or applied force. The output signal may also be applied to a recorder or to a controller that can restore the moving system to its normal position. The output voltage of an LVDT is a linear function of core displacement within a limited range of motion (say about 5mm from its reference position) and hence the name linear variation differential transformer. Beyond this range. the curve starts to deviate from a straight line.

## Single Phase Induction Type Energy Meter

Introduction to Single Phase Induction Type Energy Meter

Single phase induction type energy meter is the most common form of a.c. meters met with in every day domestic installations. These meters measure the electric energy in kilo-watt hours (KWH). The measurement of energy is the same process as measurement of power except that the instrument is not merely indicates the power or rate of supply of energy but must take into account also the length of time for which the rate of energy is continued.

Principle

The basic principle of induction type energy meter is electromagnetic induction. When an alternating current flow though two suitably located coils produces a rotating magnetic field which is cut by the metallic disc suspended near to the coils, thus emf induced in the disc which is circulates eddy current in it. by the interaction of rotating magnetic field and eddy currents, torque is developed and cause the disc rotates.

Constructions

The construction of this meter is more or less similar to an induction type wattmeter.  The main alterations are the provision of only one pressure coil upon the central limb of the shunt magnet and only one copper shading band upon this limb.  A single phase phase induction type energy meter has the following main parts of the operating mechanism;

1. Driving system
2. Braking system
3. Moving system
4. Recording mechanism

1.Driving System:

The driving system of the meter consists of two electromagnets. The core of these electromagnets is made up of laminated silicon steel. The coil of one of the electromagnets is excited by the load current. This coil is called current coil.  The coil of second electromagnet is connected across the supply and this coil carries the current proportional to the supply voltage. This coil is called pressure coil. The two electromagnets are known as series and shunt magnets respectively.

In order to obtain deflecting torque, current in the pressure coil must lag behind the supply voltage by 900. For this purpose, copper shading bands are provided on the central limb. The position of these bands is to bring the flux produced by the shunt magnet exactly in quadrature with the applied voltage.

1. Moving System

This consists of aluminum disc mounted on a light alloy shaft. This disc is positioned in the air gap between series and shunt magnets. The upper bearing of the rotor is steel pin located in a hole in the bearing cap fixed to the top of the shaft. Since there is no control spring, the disc makes continuous rotation under the action of deflecting torque. The unique design for the suspension of the disc is used in the floating-shaft energy meter.

1. Braking System

A permanent magnet positioned near the edge of the aluminium disc forms the braking system. The aluminium disc moves in the field of this magnet and thus provides a braking torque. By adjusting the position of the braking magnet speed of the disc can be controlled. If the braking magnet is moves toward the centre of the disc, flux cut by the disc is less which reduces the induced current and thus braking torque is reduced. Hence, by the inward movement of the magnet, braking torque decreases but the speed of the disc increases and vice-versa.

4.Registering or Counting Mechanism

The function of registering mechanism is to record continuously a number which is proportional to the revolutions made by the moving system. The numbers of revolutions made by disc is a measure the electrical energy passing through the meter.Working

When the single phase induction type energy meter is connected in the circuit, the current coil carries the load current and the pressure coil carries the current proportional to the supply voltage. The pressure coil winding is highly inductive as it has a large number of turns. The agnetic field produces by pressure coil is quadrature with the applied voltage. The magnetic field produced by the series magnet is in phase with the line current. Thus, a phase difference exists between the fluxes produced by the two coils. This sets up a rotating field which interacts with the disc and produces driving torque and, thus, disc starts rotating. The number of revolution made by the disc depends upon the energy passing through the meter. The spindle is geared to the recording mechanism so that electrical energy consumed in the circuit is directly registered in kWh.

Theory

When induction type energy meter is connected in the circuit to measure energy, the pressure coil carries current proportional to the supply voltage and the series magnet carries the load current. Therefore, expression for the driving torque is the same as for induction wattmeter.

Driving torque, Td  α power

Power α n

Power * t α nt

Energy α N

N = (nt) is the total number of revolutions in time t.

Meter Constant

Meter constant, K = No. of revolutions/kWh

Hence the number of revolutions made by the disc for 1 kWh of energy consumption is called meter constant.

Single phase induction type energy meter is extensively used for the measurement of electrical energy in a.c. circuits.

## Dynamometer Type Wattmeter

A Dynamometer type wattmeter variably used for measurement of ac power as well as dc power.

Working Principle

It works on the dynamometer principle. This principle says a mechanical force exists when current flows through two current carrying conductor.

Constructional Features or Construction

There are two coils are used in this wattmeter. One is called current coil (CC) and the other is called potential coil (PC). Current coil is a fixed coil which is connected in series with the load and carries load current. While potential coil is a moving coil connected across the load through a series resistance R and carries a current which is proportional to the voltage across the load. The current coil or fixed coil is splitted into two parts. The controlling torque is provided by two spiral springs which also lead the current into and out of moving coil. Damping is provided by light aluminium vanes moving in an air dashpot. A pointer is attached to the movable coil that moves over a calibrated scale.Working

When the wattmeter is connected in the circuit to measure power. Current coil carries the load current I1 and produce a magnetic field. Potential coil carries current (I2) proportional to the load voltage and produces another magnetic field. The magnetic fields of the current and potential coils react on one another, causing the movable coil moves the pointer over the scale. The pointer comes to rest at a position where deflecting torque is equal to the controlling torque.The change of direction of current reverse current reverse current in both the current coils and potential or movable coil. So that, the direction of deflecting torque remains unchanged. Hence, these instrument suitable for the measurement of dc as well as ac power.

Deflecting Torque

Deflecting torque Td α I1 I2

Deflecting torque, Td α VI1 α load power

1. High degree of accuracy
2. Uniform scale

1. Errors due to stray field acting on the potential coil.
2. Error due to inductance of potential coil.
3. It produce errors due to eddy currents.

## Moving Iron Instruments

The most common ammeters and voltmeters for laboratory or switch board use at power frequencies are moving iron instruments. These instruments are quite cheap in cost, simple in construction and reasonably accurate at fixed power supply frequency. These instruments can be used on a.c. as well as on d.c.Moving iron instruments are use either as voltmeter or ammeter only.

Classification of Moving Iron Instruments

These instruments are divided into two type; (i) Attraction type and (ii) Repulsion Type

Attraction Type Moving Iron Instruments

Working Principle

When a soft iron piece is placed in the magnetic field of a current carrying coil, it is attracted towards the centre of the coil. This is because the piece tries to occupy a position of minimum reluctance. This results, a force of attraction is exerted on the soft iron piece and deflection in the needle takes place.

Construction

The coil is flat and has a narrow slot like opening. The moving iron is a flat disc or a sector eccentrically mounted. The controlling torque is provided by springs but gravity control can be used for panel type of instruments which are vertically mounted. Damping torque is provided by air friction with the help of light aluminium piston which moves in a fixed chamber.

Working

When the instrument is connected in the circuit, the operating current flows through the stationary coil. A magnetic field is set up and the soft iron piece is magnetized which attracted towards the centre of the coil. Thus, the pointer attached to the spindle is deflected over the calibrated scale.

Note:

If current in the coil is reversed the direction of magnetic field produced by the coil will reverse, also magnetism produced in the soft iron piece will reverse. Hence the direction of deflecting torque remains unchanged. Thus, Attraction type MI instruments can be used on d.c. as well as on a.c.

Deflecting torque

Td = I2

The controlling torque is provided by the spring

Tc = θ

Where θ is angle of deflection

Repulsion Type Moving Iron Instruments

Working Principle

The basic principle of a repulsion type repulsion type moving iron is that the repulsive forces will act when two similarly magnetized iron pieces are placed near to each other.

Construction

There are two different designed are in common;

1. Radial vane type: In this type, the vanes are radial strips of iron. The strips are placed within the coil. This fixed vane is attached to the coil and the movable one to the spindle of instrument.
2. Co-axial vane type: In this type of instrument, the fixed and moving vanes are section of co-axial cylinders.

The controlling torque is provided by spring control method while damping torque is provided by air friction.

Working

When the instrument is connected in the circuit, the operating current flows through the coil. A magnetic field is set up along the axis of the coil. This field magnetises both pieces similarly i.e. both the pieces attain similar polarities. A force of repulsion acts between the two, therefore, movable piece moves away from the fixed piece. Thus, the pointer attached to the spindle deflects over the calibrated scale.

Note:

If the current in the coil is reversed, the direction of the magnetic field produced by the coil is reversed. Although the polarity of the magnetized soft iron pieces is reversed but still they are magnetized similarly and repel each other. Hence, the direction of defecting torque remains unchanged. Thus, these instruments can be used on d.c. as well as a.c.

Deflecting torque

Td = I2

The controlling torque is provided by the spring

Tc = θ

Where θ is angle of deflection

• These instruments are cheap and robust in construction.
• They can be used on both a.c. and d.c.
• They are reasonably accurate.
• They posses high starting torque.

• They cannot be calibrated with a high degree of precision with d.c. on account of the effect of hysteresis in the iron rods.
• They are not very sensitive.
• They have non-uniform scale.

Errors in MI instruments

• Error due to hysteresis
• Error due to stray magnetic field
• Error due to temperature
• Error due to change in frequency

Range

Ammeters : From about 0-20mA to 0-800mA maximum with current transformer.

Voltmeters: From about 0-1V to 0-800V maximum without potential transformer.

## Thermistors

Thermistor is a contraction of a term “thermal resistors”. Thermistors are essentially composed of semiconductor materials. Although positive temperature coefficient of units are available, most thermistors have a large negative coefficient of temperature resistance i.e. their resistance decreases with increase of temperature. The negative temperature coefficient of resistance can be as large as several percent per degree celcius . This high sensitivity to temperature change makes the thermistors extremely suitable to precision temperature measurement, control and compensation.

Construction of Thermistors

Thermistors are composed of sintered mixture of metallic oxides, such as manganese, nickel, cobalt, copper, iron and uranium. They are available in variety of sizes and shapes. They have resistance ranging from 0.5Ω to 0.075MΩ. A smallest size of thermistor is 0.015mm to 1.25mm  diameter in the shape of beads. The beads may be seal in the tips of solid glass rods to form probes which are somewhat easier to mount than beads. They are also available in the shape of rod and discs. The disc type thermistor with long vertical leads are most common in use. The discs are made by pressing thermistor material under high pressure into a flat cylindrical shapes with diameters varying from 2.5mm to 25mm.Resistance-Temperature Characteristics of Thermistors

As already discussed, the resistance of a thermistor decrease with increase in temperature non-linearly. The relation between resistance and absolute temperature is given by the mathematical expression;

Where RT1  = resistance of the thermistor at absolute temperature T­1 (in K)

RT2 = resistance of the thermistor at absolute temperature T2 ( in K)

β = a constant which depends upon the thermistor material typically its value varies from 3500 to 4500 K.

Applications

• Thermistors are widely used to compensate the change of resistances of various components of electrical and electronic circuits because thermistors have a negative temperature coefficient of resistance.
• Thermistors are used in temperature control circuits.
• They are used to measure thermal conductivity.
• They are used measure power at high frequencies.
• They are used to provide time delay in the circuit operation and so on.

## Piezoelectric Transducers

A piezoelectric material is one in which as electric pressure appears across certain surfaces of a crystal if the dimensions of the crystal are changed by the application of a mechanical force. 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. This effect is known as piezoelectric effect. Piezoelectric transducers do not need any external power source and is, therefore, known as active transducers.

The piezoelectric effect can be made to respond to (or cause) mechanical deformations of the material in many different modes. The modes can be : thickness expansion, transverse expansion, thickness shear and face shear.

A piezoelectric element used for converting mechanical motion to electrical signals.

Working

In these transducers, a crystal is placed between a solid base and the force summing member. When an external force, entering the transducer through its pressure port, applied pressure at the top of the crystal, this produces an e.m.f. across the crystal. The magnitude of the induced e.m.f. is proportional to the magnitude of the applied pressure. Since the induced e.m.f. is very small of the order of millivolts, an amplifier is used to amplify this e.m.f. signal being measured.

Piezoelectric transducers do not need any external power source and is, therefore, known as active transducers.

Common piezoelectric materials include Rochelle salts, ammonium dihydrogen phosphate, lithium sulphate, quartz and ceramics. Except for quartz and ceramics, the rest are man-made crystal grown from aqueous solutions under carefully controlled conditions.

## Synchroscope

A synchroscope is used to determine the correct instant for closing the switch connects an alternator to the generating station busbars. This process of connecting at the correct instant or synchronizing is necessary when an unloaded incoming alternator is to be connected to the busbars in order to share the load.

The operation on connecting an alternator in parallel with another alternator or with common bus-bars is called synchronizing.

The correct instant of synchronizing the incoming alternator to bus-bars is when :

1. The magnitude of terminal voltage of the incoming alternator is same as that of the bus-bar voltage.
2. The terminal voltage of the incoming alternator must be the same as bus-bar voltage.
3. The speed of the incoming machine must be such that its frequency equals bus-bar frequency.
4. The phase of the alternator voltage must be indentical with the phase of the bus-bar voltage. It means that the switch must be closed the instant the two voltages have correct phase relationship.

Types of Synchroscope

• Electro-dynamometer (KILESTON) type synchroscope
• Moving iron type synchroscope

## Dynamometer Type Three-Phase Power Factor Meter

A dynamometer type three-phase power factor meter gives correct readings only when the load is balanced.

Principle

The basic principle of dynamometer type three-phase power factor meter of operation of this instrument is similar to that of dynamometer type wattmeter i.e. when the field produced by moving system tries to come in line with the field produced by the fixed coil, deflecting torque torque is exerted on the moving system which deflects the pointer attached to it.

Construction

It consists of two fixed coils FF connected in series in one of the phase and carries the load current. The moving coils are so placed that the angle between their planes is 1200. They are connected across two different phases of the supply circuit. Each coil has a series resistance. There is no necessity for phase splitting by artificial means, since the required phase displacement between currents in the two moving coils can be obtained from the itself.

Working

When the instrument is connected in the circuit, under balanced load conditions, the phase angle through which the pointer is deflected from the unity power factor position is equal to the phase angle of the circuit, because the two moving coils are fixed 1200 apart. The deflections in these instruments are independent of frequency and waveform, since the currents in the two moving coils are affected in the same way by change of frequency.

## Dynamometer Type Single Phase Power Factor Meter

Before studying about dynamometer type single phase power factor meter, we have to know about power factor.

Power factor of an electrical circuit can be determined from the wattmeter, ammeter and voltmeter readings suitable connected in circuit.

This method involves mathematical calculations. Sometimes it is required to measure the power factor of the circuit instantaneously when the power factor of the load is varying continuously. This purpose is served by connecting a power factor meter in the circuit. Power factor meter directly indicates, by a single reading, the power factor of the circuit to which they are connected. In this article, we will study about the dynamometer type single phase power factor meter.

Principle

The basic principle of operation of this instrument is similar to that of dynamometer type wattmeter i.e. when the filed produced by moving system tries to come in line with the field produced by the fixed coil, deflecting torque torque is exerted on the moving system which deflects the pointer attached to it.

Construction

It  consists of a fixed coil which acts as the current coil. The coil is split into two parts and carries the current of the circuit under test. Therefore, the magnetic field produced by the current coil is directly proportional to the  load current. Two identical moving coils A and B pivoted on a spindle constitute the moving system. Moving coil A has a non-inductive resistance R connected in series with it, and coil B has a highly inductive choke coil L connected in series with it. The values of non-inductive resistance R and inductance L are so chosen that for the normal frequency, the current in the two moving coils are same. Thus the field produced by the two coils are of same strength. The field produced by the coil B lags behind the field produced by the coil A slightly less than 900 and same angle between the planes of the coils.

There are no controlling torque provided in this instrument. Connections to moving coils are made through thin silver or gold ligments which are extremely flexible and thus give a minimum control effect on the moving system.

Working

When the power factor meter is connected in the load circuit, current flows through the fixed coil FF and moving coils A and B, flux is set by the fixed coils and moving coils. By the alignment of field produces by fixed coil and moving coils, torque develops i.e. the resultant field produced by the moving coils tries to come in line with the field produced by the fixed coils and torque develops till both of them come in line with each other. There are three extreme conditions in which this instrument is connected in the circuit.

When power factor of the circuit is unity:

In this case, current is in phase with circuit voltage. The current flowing through potential coil A is in phase with voltage which is also in phase with the current flowing through fixed coil FF. At the same time current flowing through potential coil B lags behind voltage as well as the current flowing through current coil FF by 90°. Thus pressure coil A will experience a turning moment so its plane will come in position parallel to the plane of the current coil FF. The torque acting on the pressure coil B is zero. Thus, the pointer indicates unity power factor on the scale.

When power factor of the circuit is zero lagging:

In this case, current lags behind the circuit voltage by 90°. Therefore, the current flowing through pressure coil B will be in phase with current in fixed coil FF, both being lagging behind the circuit voltage by 90°. Thus a turning moment acts on the pressure coil B and bring its plane parallel to the plane of fixed FF and pointer indicates zero power factor lagging.

When power factor of the circuit is zero leading:

In this case, current leads the Circuit voltage by 90°. Therefore, the current flowing through moving coil A lags the current in fixed coil FF by 90° and current flowing through pressure coil B lags the current in fixed coil FF by 180°. Thus, field produced by the moving system is just reversed to that in case (ii). Hence, an opposite turning moment acts on the pressme coil B and bring its plane parallel to the plane of current coil FF and pointer indicates zero power factor leading.

## Difference Between Current Transformer (CT) and Potential Transformer (PT)

There are a few differences in current transformer (CT) and potential transformer (PT).  These are mentioned below:-

 Sr. No. Current Transformer (CT) Potential Transformer (PT) 1. It is a basically step up transformer. It is a basically step-down transformer. 2. Primary winding has one or a few turns of thick wire. Primary winding has large number of turns of fine wire. 3. The secondary winding having large number of turns of fine wire. The secondary winding has much smaller number of turns. 4. Current transformer is connected in series with one line and a small voltage exists across its terminals. Potential transformer is connected in parallel with the circuit and full line voltage is impressed upon its terminals 5. The primary current of CT is independent of secondary circuit conditions rather it depends upon the line or load current In PT, the primary current depends upon secondary burden. 6. In current transformer, line or load current vary over a large range, therefore exciting current in CT varies over a large range. Under normal working conditions, the line voltage applied across the PT remains almost constant, therefore, the exciting current in a potential transformer varies only over a restricted range. 7. Ammeter is used in conjunction with a current transformer for measurement of current. Voltmeter is used in conjunction with a potential transformer for measurement of voltage. 8. Current transformer works under short circuit conditions. The secondary winding of potential transformer can be open-circuited without any damage being caused either to the operator or to the transformer. 9. From the constructional point of view, there are two types of current transformers : (i)                 Wound Type:-  A current transformer having a primary winding of more than one full turn wound on core. (ii)               Bar Type: – A current transformer in which the primary winding consists of a bar of suitable size and material is forming an integral part of transformer. The potential transformer is made shell type because this condition develops a higher degree of accuracy.