253-4-transformers

# 253-4-transformers - Magnetically Coupled Circuits Mutual...

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EECE 253: Magnetically Coupled Circuits Slide 4.1 Magnetically Coupled Circuits • Mutual Inductance (Chap 13.2) • Energy in Coupled Circuits (Chap 13.3) • Linear Transformers (Chap 13.4) • Ideal Transformers (Chap 13.5) • Applications (Chap 13.9)

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EECE 253: Magnetically Coupled Circuits Slide 4.2 Self-Inductance Recall the way an inductor works: 1. A wire current i results in a magnetic field. 2. For a coil, this results in a magnetic flux φ through the coil. 3. A voltage v is “induced” across the coil when changes (Faraday’s Law): l A N di d N L dt di L dt di di d N dt d N v µ 2 where = = = = = is self-inductance . is magnetic permeability
EECE 253: Magnetically Coupled Circuits Slide 4.3 Mutual Inductance ; ) ( 1 1 1 1 12 11 1 1 12 11 1 dt di L dt d N dt d N v = = + = + = φ The changing may also result from a nearby coil. Consider the induced voltages in the 2 coils (side 2 is OC so i 2 (t) 0 A): This mutual inductance M (in henrys) is a measure of the ability of one inductor to induce a voltage across a neighboring inductor. dt di M dt d N v 1 21 12 2 2 = =

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EECE 253: Magnetically Coupled Circuits Slide 4.4 dt di L dt d N v 2 2 2 2 2 22 21 2 = = + = φ Mutual Inductance Similarly, if i 1 (t) 0 but i 2 (t) can change, Energy conservation can be used to show that M 12 =M 21 =M . dt di M dt d N v 2 12 21 1 1 = =
EECE 253: Magnetically Coupled Circuits Slide 4.5 Dot Convention M>0 but induced voltage polarity depends on physical coil windings. For convenience on schematics, the dot convention is employed to indicate polarity. If a current enters the dotted terminal of one coil, the reference polarity of the mutual voltage is positive at the dotted terminal of the 2 nd coil.

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EECE 253: Magnetically Coupled Circuits Slide 4.6 Dot Convention
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253-4-transformers - Magnetically Coupled Circuits Mutual...

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