Presentation on theme: "CHAPTER 5: TRANSFORMER AND MUTUAL INDUCTANCE"— Presentation transcript:
1CHAPTER 5: TRANSFORMER AND MUTUAL INDUCTANCE Review of Magnetic InductionMutual InductanceLinear & Ideal Transformers
2Magnetic Field LinesMagnetic fields can be visualized as lines of flux that form closed pathsThe flux density vector B is tangent to the lines of flux
3Magnetic FieldsMagnetic flux lines form closed paths that are close together where the field is strong and farther apart where the field is weak.Flux lines leave the north-seeking end of a magnet and enter the south-seeking end.When placed in a magnetic field, a compass indicates north in the direction of the flux lines.
8Flux Linkages and Faraday’s Law Magnetic flux passing through a surface area A:For a constant magnetic flux density perpendicular to the surface:The flux linking a coil with N turns:
9Faraday’s Law Faraday’s law of magnetic induction: The voltage induced in a coil whenever its flux linkages are changing. Changes occur from:Magnetic field changing in timeCoil moving relative to magnetic field
10Lenz’s LawLenz’s law states that the polarity of the induced voltage is such that the voltagewould produce a current (through an external resistance) that opposes the original change in flux linkages.
17Mutual inductance of M21 of coil 2 with respect to coil 1 2 coilsMutual inductance of M21 of coil 2 with respect to coil 1Coil 1 has N1 turns and Coil 2 has N2 turns produced1 = 11 + 12Magnetically coupled
18Mutual voltage (induced voltage) Voltage induced in coil 1:Voltage induced in coil 2 :M21 : mutual inductance of coil 2 with respect to coil 1
19Mutual InductanceMutual inductance is the ability of one inductor to induce avoltage across a neighboring inductor, measured in henrys (H)When we change a current in one coil, this changes the magnetic field in the coil.The magnetic field in the 1st coil produces a magnetic field in the 2nd coilEMF produced in 2nd coil, cause a current flow in the 2nd coil.Current in 1st coil induces current in the 2nd coil.
20Mutual inductance of M12 of coil 1 with respect to coil 2 2 coilsMutual inductance of M12 of coil 1 with respect to coil 2Coil 1 has N1 turns and Coil 2 has N2 turns produced2 = 21 + 22Magnetically coupled
21Mutual voltage (induced voltage) Voltage induced in coil 2:Voltage induced in coil 1 :M12 : mutual inductance of coil 1 with respect to coil 2
22Dot Convention Not easy to determine the polarity of mutual voltage – 4 terminals involvedApply dot convention
25Frequency Domain Circuit For coil 1 :For coil 2 :
26Use of the Dependent Source Model for Magnetically Coupled Circuits Draw dependent sources in each circuit with + in same orientation as the dot in that circuit's coil.If the other circuit's current is entering its dot terminal then the induced voltage of the dependent source is positive, otherwise: negativeWe'll redraw the previous circuit to show how this works:
32Energy In A Coupled Circuit Energy stored in an inductor:Unit : JouleEnergy stored in a coupled circuit:Positive sign: both currents enter or leave the dotted terminalsNegative sign: one current enters and one current leaves the dotted terminals
34Energy In A Coupled Circuit Energy stored must be greater or equal to zero.orMutual inductance cannot be greater than the geometric mean of self inductances.
35Energy In A Coupled Circuit The coupling coefficient k is a measure of the magnetic coupling between two coilsorWhere:or
36Energy In A Coupled Circuit Perfectly coupled : k = 1Loosely coupled : k < 0.5- Linear/air-core transformersTightly coupled : k > 0.5- Ideal/iron-core transformersCoupling coefficient is depend on :1. The closeness of the two coils2. Their core3. Their orientation4. Their winding
37Example 2Consider the circuit below. Determine the coupling coefficient. Calculate the energy stored in the coupled inductor at time t=1s if
47Types of IDEAL Transformers When n = 1, we generally call the transformer an isolation transformer.If n > 1 , we have a step-up transformer (V2 > V1).If n < 1 , we have a step-down transformer (V2 < V1).
56Applications of Transformers To step up or step down voltage and current (useful for power transmission and distribution)To isolate one portion of a circuit from anotherAs an impedance matching device for maximum power transferFrequency-selective circuits
57Applications: Circuit Isolation When the relationship betweenthe two networks is unknown,any improper direct connectionmay lead to circuit failure.This connection style canprevent circuit failure.
58Applications: DC Isolation Only ac signal can pass, dc signal is blocked.