1. Magnetically Coupled Circuits
Chapter 13
Magnetically Coupled Circuits
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2. Mutual Inductance
The magnetic flux created in one inductive coil can couple into a nearby coil, a process called mutual inductance.
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3. Mutual Inductance
The double headed arrow indicates that these inductors are coupled.
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4. The Dot Convention
A current entering the dotted terminal of one coil produces an open circuit voltage with a positive voltage reference at the dotted terminal of the second coil.
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5. Dot Convention: Four Cases
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6. Combined Self- and Mutual-Induction Voltages
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7. Combined Self- and Mutual-Induction Voltages
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8. Physical Basis for Dot Convention
The assumed currents i1 and i2 produce additive fluxes.
Dots may be placed either on the upper terminal of each coil or on the lower terminal of each coil.
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9. Example: Voltage Gain Show that V2/V1 =6.88e -j16.70◦
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10. Energy in Coupled Inductors
This equation implies a limit on M:
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11. The Coupling Coefficient
The coupling coefficient k measures how tightly coupled the two inductors are:
where 0 ≤ k ≤ 1
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12. The Linear Transformer
Transformers have a primary (source side) and a secondary (load side).
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13. Transformer: Reflected Impedance
The impedance Zin seen by the source is
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14. The “T” Equivalent Network
Consider the mesh-current equations to show that these circuits are equivalent.
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15. The “Delta” Equivalent Network
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16. The Ideal Transformer
In an ideal transformer, k=1 and the inductances are assumed large in comparison to the other impedances. The turns ratio a is defined as
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17. Transformer Applications
Step Up
Step Down
Electronics
Power
Step Down to Household
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18. Transformer Applications
Impedance matching: Current adjustment: Voltage adjustment:
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19. Example: Transformer Calculations
Determine the average power dissipated in the 10 kΩ resistor.
Answer: 6.25 W
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20. Thévenin Equivalent
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21. Example: Thévenin Equivalent
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