INDUCTORS AND TRANSFORMERS



INTRODUCTION:Inductors or coil or choke is an electromagnetic device consisting of a conducting wire wound in cylindrical or spiral form to obtain concentrated magnetic flux. The base on which the coil is wound is known as core. The core may be a magnetic material such as iron, ferrite or air.Induction by alternating current:When an alternating current flows through a coil of wire, a magnetic field will be developed surrounding the coil. The magnetic field produced in the coil will be changing at the rate of change of current. This varying magnetic field links with the conductor producing an emf( ELECTRO MOTIVE FORCE) in it. This phenomenon of magnetic field linking with a conductor, inducing an emf is called electromagnetic induction which is found in inductors.Induced voltage is the result of flux cutting across a conductor. This action can be produced by physical motion of either the magnetic field or the conductor. circuit diagram b)Magnetic field around an alternating current carrying conductorIt is observed from the figure that, during the positive half cycles of current, as the current increases in value, the magnetic field expands outward from the conductor and as the current decreases the field collapses into the conductor. Where during the negative half cycles of current the field expands and collapses again but in opposite direction.The result of expanding and collapsing field then is same as that of field in motion. This moving flux cuts across the wire itself. Furthermore any other conductor in the whether carrying current or not, also is cut by the varying flux and has induced voltage.FACTORS AFFECTING THE VALUE OF INDUCTANCE:It is found that whenever current through an inductor changes (i.e.., increases or decreases), a counter emf is inductor in it which tends to opposes this change,The property of the coil due to which it opposes any change of current through it is called inductance(L)L= ?.a.N2 (henrys) l Where,?0 = absolute permittivity of air or vacuum?r = Relative permittivity of the core materialA = Cross sectional area of coreN = Number of turns of the coill = Core lengthSELF INDUCTANCE:It is the ability of a conductor to induce voltage in itself when the current change is called self inductance or inductance. It is denoted by Letter ‘L’ ant its units are HENRYS (H).VL= -Ldi/dt. VL= Induced Voltage in Volts (V). L=Inductance in henries (H). di/dt= Rate of change of current in amperes per second (A/Sec).The minus (-) sign indicates that polarity of induced voltage opposes the change in current.MUTUAL INDUCTANCE:When two coils are placed closely in such a way that the flux produced in one coil cuts into other, the change of current in one coil induce e.m.f in other coil. This is known as mutual inductance between two coils. The unit of mutual inductance is Henry (H). and symbol LM or M “The ability of varying current in one coil to induce voltage in a near by coil is known as mutual inductance”. M=VL2 / di/dt).Mutual inductance can be expressed asWhere VL2 Is the mutually induced e.m.f produced in the second coil. di/dt is the rate of change through the first coil.COUFFICIENT OF COUPLING: K =M / √ L1 L2The degree of magnetic coupling is known as coefficient of coupling. Denoted by letter K. If L1 and L2 are the inductance of two inductors then the coefficient of coupling is expressed as The coefficient of coupling between two coils is given by Flux linkage between L1 & L2 K = ------------------------------------- total flux produced by L1If all the flux due to one coil (L1) links with the other then (K=1). If flux of one coil ( L1) does not links with the other coil ( L2) then K=0. Thus K is a constant whose values lies between 0 and 1.K=1( iron core)b) K=0 ( air core) A light value of k=1, called tight coupling allows the current in one coil induce more voltage in another coil.A low value of k=0 called loose coupling induces less voltage for K=0 no mutual inductance (the two coils are kept apart)CLASSIFICATIONS OF INDUCTORS:Inductors are classified in many ways. Some of them are as follows.On the basis of core material used:Air core inductors. Iron core inductors.Ferrite core inductors.On the basis of frequency of operation :Audio Frequency (A.F) coils.Radio Frequency coils (R.F) coils .On the basis of winding are:Single layer coils.Multi layer coils. On the basis of operation are:Fixed coils. b. Variable coils.SPECIFICATIONS OF INDUCTORS:The main specifications of a inductor areInductance valueType of winding Insulation resistancePower ratingTemperature coefficientCore material INDUCTORS ARE IN SERIES:INDUCTORS ARE IN SERIES WITHOUT MUTUAL INDUCTANCE:V=V1+V2Consider two inductors L1 and L2 are connected in series across a supply of V volts as shown in figure. There is only one path for current ‘i’ i.e.., current is same through out the circuit Ls be the total inductance applied voltage V is equal to the sum of the drop across inductors i.e..,In series current is same in all inductors Fig: Inductors in series without M.Let L1 = Self inductance of coil-1L2 = Self inductance of coil-2 i = Current flowing through coils Ls = Total inductance of the series combinationThen Self induced emf in coil-1 is e1 = -L1 di/dt e2 = -L2 di/dt Self induced emf in coil-2 is Total induced e.m.f = Sum of individual e.m.f`s es = e1+ e2 = -[ L1 di/dt + L2 di/dt] -Ls di/dt = -(L1 + L2) di/dtLs = L1+L2 The total inductance of the series combination is given by formulaL = L1+L2+L3+……….+Ln INDUCTORS ARE IN SERIES WITH MUTUAL INDUCTANCE:Series aidingIn figure two coils are connected in series such that their fluxes are addictive i.e.., in same direction and is known as series aiding. Series aidingTotal induced emf will be the addition of self inductance of coils1 & coil 2 and the mutual inductance of coil1 and coil2.Then Self induced e.m.f in coil-1 is e1 = -L1 di/dtMutually induced e.m.f in coil-1 due to current in coil-2 is e’1 = -M di/dtSelf induced e.m.f in coil-2 is e2 = -L2 di/dtMutually induced e.m.f in coil-2 due to current in coil-1 is e’2 = -M di/dtTotal induced e.m.f = Sum of individual e.m.f`s es = e1+ e’1+ e2+e’2 = -[L1 di/dt +M di/dt+L2 di/dt +M di/dt] -Ls di/dt = -(L1 + L2+2M) di/dtLs = L1+L2+2M Series opposing:In figure two coils are connected in series such that their structures are additive i.e…, in same direction and such is known as series aiding.Total induced EMF will be the addition of self inductance of coil1& coil2 and the mutual inductance of coil1 and coil2.Then Self induced e.m.f in coil-1 is e1 = -L1 di/dtMutually induced e.m.f in coil-1 due to current in coil-2 is e’1 = M di/dtSelf induced e.m.f in coil-2 is e2 = -L2 di/dtMutually induced e.m.f in coil-2 due to current in coil-1 is e’2 = -M di/dtTotal induced e.m.f = Sum of individual e.m.f`s es = e1+ e’1+ e2+e’2 = [-L1 di/dt +M di/dt-L2 di/dt +M di/dt] -Ls di/dt = -(L1 + L2-2M) di/dtLs = L1+L2-2M INDUCTORS ARE IN PARALLEL:INDUCTORS ARE IN PARALLEL WITHOUT MUTUAL INDUCTANCE:Consider two inductors L1 and L2 are connected in parallel across a voltage source of V volts as shown in fig. the total current divides in two parts as i1 flowing through L1 and i2 flowing through L2 across each inductor is same. In parallel we know that i=i1+i2 El = -L di/dtBy the definition of inductance we know that Let L1 = Self inductance of coil-1 L2 = Self inductance of coil-2 Lp = Total inductance of the parallel combinationThen Self induced e.m.f in coil-1 is e1= -L1 di1/dt Self induced e.m.f in coil-2 is e2= -Ldi2/dtwe have, i=i1+i2 di =di1+di2 but e = Lp di/dt =L1di/dt = L2di/dt e.dt /Lp = e.dt/L1 +e.dt/L2 1/Lp= 1/L1+1/L2AUDIO FREQUENCY CHOKES:These are generally iron core coils having one to several 100HS These are used to provide high impedance to audio frequency (20-20KHZ)TO get high inductance values laminated iron cores are used To prevent eddy currents, these laminated pieces are covered with insulating layer APPLICATIONS:AF chokes are used in power supplies for providing pure Dc or smooth Dc and also used in radio and TV receivers. Modulation chokes in transmitters, audio and power transformers and in magnets and relaysRADIO FREQUENCY CHOKES (RF);These are made with air or iron or ferrite core Mostly ferrite cores are used to increase inductance valuesIt has inductance value in MH and ?H ranges .These have high reactance to any part of radio frequency spectrum (>500KHZ)APPLICATIONS:These are used to select desired radio frequency signal and reject all others in Conjunction with capacitors in TV and radio receivers .COMPARISON OF AF CHOKES AND RF CHOKES:PARAMETERAF CHOKES RF CHOKESInductance valueHigh (up to several 100 Henries)Low (MH and ?H)Size Big SmallCore IronAir or ferriteSymbolTRANSFORMERS;It is a static device which transfers the electrical power from one circuit to another circuit, without change in its frequency.The Transformer works on the principle of electromagnetic induction or mutual inductance.It has the primary and secondary windings.The purpose of transformer is to transfer power or energy from primary to secondary.Primary winding: The winding or coil to which the input voltage applied.Secondary winding: The coil which delivers power to load (or) receives from primary.Working:When AC voltage is applied to the primary window of transformer, an alternating magnetic flux in the secondary winding is linked by this flied and is induced in two windings.The emf induced in secondary winding drives current through the load connected to this winding.The introduced emf is given by e=-Nd?/dt Where, e=induced emf ?=flux“-ve” Sign indicates that induced emf opposes the effect causing itTRANSFORMER CONSTRUCTION;The transformer consists of three elements.FormerCoreCoilsFormer: It is a hollow insulating material that is paper or plastic.It separates the metallic core and coil wires.It has a rectangular or cylindrical shape.Core:The core is to support the wires or windings which are wounded on former mechanically.It also reduces the leakage of flux.Types of cores are fertile, air and powdered iron.Windings (or) coils;The primary and secondary windings are wounded on the two limbs (or) on the central limb of core.In CORE type construction, the primary and secondary windings are located or wounded on the opposite limb of the coreThat means, half the primary and half the secondary have been placed side by sideIn SHELL type construction, the most of the windings are enclosed by the coreIn this the windings are made over the central limb one after other & separated by insulatorsPOWER TRANSFORMER;Power transformer is to operate on the mains ac supply of 50 Hz or 60 Hz of single frequency.Construction:In this, the primary and secondary windings are wounded over core material with high degree of coccpling The core is shell type and made with 4% silicon steel laminations The primary and secondary coils are wounded one over other on central limb, with insulators provided between themWorking:Primary of power transformer is connected to ac source The flux inducted in the primary is magnetically coupled to secondary coilThe emf induced in the secondary depends in its number of terms.Applications of power transformer:Used in Radio, TV etcIn CRO’S In MilitaryAUDIO FREQUENCY TRANSFORMER:The construction of AF TRANSFORMER is similar to lower transformer. but the core is nickel, iron with high permeability These are used to transfer electrical signals of entire audio frequency range (20HZ TO 20KHZ). Primary and secondary are wounded on core of laminated silicon steel. Primary and secondary layer type wounds keeping secondary outside.These are used in audio amplifiers for inter stage coupling {impendence matching] as show in fig i.e., for coupling microphones to amplifiers and amplifiers to speakers RADIO FREQUENCY {RF] TRANSFORMER;RF transformers are for operation at very high frequency To reduce EDDY current losses, RF transformer is either made with air core or ferrite core These are provided with tuned secondary and tuned primary as shown in fig Tuned means connecting a variable capacitor across the inductor, then to operate the winding at particular frequency.The co-efficient of coupling is from 0.1 to o.3INTER MEDIATE FREQUENCY (IF) TRNSFORMER;If transformers are made with air core or ferrite core .These are used to operate at a fixed frequency called intermediate frequency These are used tuned primary, as well as tuned secondary. PULSE TRANSFORMER:It is a wideband transformer that transfers pulses from one circuit to another circuitConstruction:Nickel iron is used as core material.The primary and secondary are split into two equal parts to reduce leakage inductance and capacitance.Diagram: Working:When an input pulse is applied rise the voltage at the secondary and charges capacitance via series leakage inductance.This gives overshoot and oscillations.This overshoot is reduced by increasing capacitance but this results in increased rise time.To overcome this problem, Mn-Zn ferrites are used with less number of turns.If low frequency response is poor, the output shows droop.To improve low frequency response, inductance is increased.The understand is due to low shunt impedance of transformer.SPECIFICATIONS OF TRANSFORMER:Signal or communication transformer are rated byCurrent rating, power ratingInput and output impedancesFrequency rangePower transformers are rated byPrimary secondary voltagesCurrent or powerAnd alsoTurns rationType of coreAPPLICATION OF TRANSFORMERS:Power transformers are used in power supplies such asa radio and TV refrigerator etc..,AF transformers are used in stereo amplifiers and other audio systemsIF transformers are used in radio and TV receiversRF transformers are used in RF amplifiers of Radio, TV and satellite receivers.Transformers are used in resonant circuits for detecting FM signals.Pulse transformers are used to trigger thyristors like SCR’sLOSSES IN TRANSFORMERS:Copper losses:These losses are due to resistance of wire used for windings.It is expressed as I2R.This loss can be minimized by use of lesser resistance of wire for windings.Core losses:Flux losses: This loss is caused when all the flux lines of primary are donot pass through secondaryThis loss is minimized by interleaving the primary and secondary windings. Eddy current losses:The iron core of transformer is a conducting materialDue to change in flux, EMF is induced in the core material, resulting in the flow of small local currents called eddy currents.The Flow of eddy current in core produces a loss which is similar to I2R lossThese are reduced by using thin strips of silicon steel as core.Hysteresis losses:Depending upon the frequency of applied AC voltage, the core material gets magnetized and demagnetized and changes polarity a number of times in one secondThis change of polarity is opposed by magnetic ferrite called Hysteresis and so loss is present.This is reduced by using soft iron core and silicon steel as core material.FAULTS IN INDUCTORS AND TRANSFORMERS:Open Circuit: It is due to excess currentShort circuit: When enameled wire is hot and melts.Loss of insulation between core and winding: It is occurred when core is broken it will cause air gap.Leakage between windings or between winding and core: It occurs due to melting of insulation point ( ENAMEL)Loose core: It is due to vibrations and cause electrical noise. ................
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