ee212_3 - EE212 Passive AC Circuits Lecture Notes 3 Click...

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Click to edit Master subtitle style EE212 Passive AC Circuits Lecture Notes 3 Transformers 11
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Magnetic Circuit What is the relationship between electric When do we have to consider it? What is the relationship between magnetic flux and magnetomotive force, Fm? Fm = Rm ± Magnetic field strength, H = Fm / l 22
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Magnetic Circuit Consider a coil around a magnetic core. If a current i flows through the coil, a magnetic flux φ is generated in the core. N = number of turns in the coil Rm = constant known as reluctance (depends on the magnetic path of the flux) a b i φ L vab = L d i d t φ = N i in webers (Wb) Obj104 Direction of flux by Right-Hand Rule Fingers curled around coil – direction of current Thumb – direction of flux Rm = in ampere- turns/Wb Obj105 l = length of magnetic path A = cross-section area μ = permeability 33
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B-H Curve Flux Density, B = in teslas, T Obj106 Magnetic field strength, H = in AT/m Obj107 B = μ H 44
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Coupled Circuits Circuits that affect each other by mutual magnetic fields a b i 1 φ 1 L 1 v a b c d v c d φ 2 L 2 i 2 The flux φ 2 generated by current i2 in Coil 2 induces a voltage in Coil 1, and vice-versa. v ab = L 1 dt di 1 ± M dt di 2 v cd = L 2 dt di 2 ± M dt di 1 ± depending on whether the fluxes add or oppose each other L1, L2: self inductance M: mutual inductance ratio of induced voltage in one circuit to the rate of change of current in another circuit 55
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Coupled Circuits in Phasors If input signals are sinusoidal waveforms, coupled circuits can be in phasor representation v ab = L 1 dt di 1 ± M dt di 2 v cd = L 2 dt di 2 ± M dt di 1 ± depending on flux directions a b V a b I 1 L 1 c d V c d I 2 L 2 M 66
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Equivalent Circuit with Dependent Sources 77
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Dot Convention Dots are placed at one end of each coil, so that currents entering the dots produce fluxes that add each other. a b i 1 φ 1 L 1 c d φ 2 L 2 i 2 a b I 1 L 1 c d I 2 L 2 (currents entering the dots produce upward fluxes) The dots provide information on how the coils are wound with respect to each other. A current i entering a dotted terminal in one coil induces a voltage M with a positive polarity at the dotted terminal of the other coil. Obj108 Vab = (j ϖ L1) I1 + (j ϖ M) I2 for the currents as shown (+) if both currents enter the dotted terminals (or the undotted terminals). (-) if one current enters a dotted terminal and the other current enters an undotted terminal. 88
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Coefficient of Coupling, k k = 0 ≤ k ≤ 1 k depends on the magnetic properties of the flux path. When k = 0, no coupling k = 0.01 to 0.1, loosely coupled k > 0.5, close coupled, e.g. air core k ≈ 1.0, e.g. power transformer all the flux generated by one coil is linked to the other coil (i.e. no leakage flux) k = 1.0 ideal transformer 2 1 L L M 99
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E 1 N 2 E 2 N 1 I φ + - V 1 + - V1 = -E1 I φ φ E 1 E 2 Transformer Faraday’s Law i φ v 1 N 1 + - e 2 N 2 + - e 1 primary winding secondary winding dt d φ e2 =
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ee212_3 - EE212 Passive AC Circuits Lecture Notes 3 Click...

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