1. 11. Magnetically Coupled Circuits
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CIRCUITS by Ulaby & Maharbiz

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3. Magnetic Coupling Current i1 induces flux Φ11 in coil 1
And flux Φ12 in coil 2
Magnetic linkage in coil 1:
In coil 2:
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4. Dot Convention: Defines directions of windings
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Dot Convention: Defines directions of windings

5. Polarities All rights reserved. Do not copy or distribute.
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8. Equivalent Inductance
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Equivalent Inductance

9. Transformers
The coupling coefficient k defines the degree of magnetic coupling between the coils: 1. loosely coupled pair: k < tightly coupled coils: k > perfectly coupled coils: k = 1. The magnitude of k depends on the physical geometry of the two-coil configuration and the magnetic permeability μ of the core material.
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10. Coupling Coefficient
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11. Input Impedance All rights reserved. Do not copy or distribute.
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15. Ideal Transformers All rights reserved. Do not copy or distribute.
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16. Thevenin Equivalent As seen by source 1 As seen by source 2
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17. Autotransformers All rights reserved. Do not copy or distribute.
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18. Three-Phase Transformers
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19. Three-Phase Transformers
n = N2/N1
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Summary

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Summary (cont.)