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Chapter 13 - Chapter 13 Magnetically coupled circuits SJTU...

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SJTU 1 Chapter 13 Magnetically coupled circuits
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SJTU 2 φ Mutual inductance A single inductor: dt di di d N dt d N v N dt d v φ φ φ φ λ λ λ = = = = flux : turns; of number : N linkage flux : dt d N L while dt di L v φ = =
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SJTU 3 φ φ 12 11 1 φ φ φ + = dt di L dt d N v 1 1 1 1 1 = = φ dt di di d N dt d N v 1 1 12 2 12 2 2 12 2 φ φ φ φ = = = dt d N M while dt di M v 12 2 21 21 2 φ = = Mutual inductance of M 21 of coil 2 with respect to coil 1
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SJTU 4 φ 22 φ 21 N 2 N 1 v 2 v 1 i 2 (t) 22 21 2 φ φ φ + = dt di L dt d N v 2 2 2 2 2 = = φ dt di di d N dt d N v 2 2 21 1 21 1 1 21 1 φ φ φ φ = = = dt d N M while dt di M v 21 1 12 2 12 1 φ = = M M M = = 21 12 (for nonmagnetic cores)
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SJTU 5 dt di L dt di M v dt di M dt di L v 2 2 1 2 2 1 1 1 + = + = dt d N v and dt d N v and coil coil coil coil 2 2 2 12 2 2 1 1 1 21 1 1 φ φ φ φ φ φ φ φ = + = = + =
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SJTU 6 dt d N v and dt d N v and coil coil coil coil 2 2 2 12 2 2 1 1 1 21 1 1 φ φ φ φ φ φ φ φ = - = = - = dt di L dt di M v dt di M dt di L v 2 2 1 2 2 1 1 1 + - = - =
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SJTU 7 1 L 2 L M 1 v + - 2 v + - 1 i 2 i 1 L 2 L M 1 v + - 2 v + - 1 i 2 i dt di L dt di M v dt di M dt di L v 2 2 1 2 2 1 1 1 + - = - = dt di L dt di M v dt di M dt di L v 2 2 1 2 2 1 1 1 + = + = When the reference direction for a current enters the dotted terminal of a coil, the reference polarity of the voltage that it induces in the other coil is positive at its dotted terminal. Dot convention
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SJTU 8 1 L 2 L M 1 v + - 2 v + - 1 i 2 i Examples 1 L 2 L M 1 v + - 2 v + - 1 i 2 i dt di L dt di M v dt di M dt di L v 2 2 1 2 2 1 1 1 + - = - = dt di L dt di M v dt di M dt di L v 2 2 1 2 2 1 1 1 - + = - = How could we determine dot markings if we don’t know?
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