1. ECE 1270: Introduction to Electric Circuits
Lecture 16:
Mutual Inductance
Chapter 6
Inductance, Capacitance, and Mutual Inductance
Sections 6.4, 6.5

2. Transformers and Their Applications
Transmission Line Transformer
(7200 V to 240 V or 120 V)
Center Tapped Transformer
(power distribution, microphone, automobiles, AC-to-DC rectifiers)
Ignition Coil (12 V to V)

3. Transformer: Basics
Voltage Ratio=
Current Ratio=

4. Mutual Inductance
Mutual inductance is the ability of one coil to induce a voltage
across a neighboring coil [unit=H].

5. Mutually Coupled Coils: Dot Convention
When the current enters the dotted terminal in one coil, the polarity of induced voltage in other coil is positive at its dotted terminal
When the current leaves the dotted terminal in one coil, the polarity of induced voltage in other coil is negative at its dotted terminal
Polarity of induced voltage in L2: dot convention
1) Vg->clockwise i1->enters dot=>induced voltage in secondary coil = + at the dot
From i2->leaves dot->induced voltage in primary coil=- at the dot
Also
2) If –Vg->anticlockwise i1=> leaves dot=>induced voltage in secondary coil=- at the dot

6. Mutual Inductance
Mutual inductance is the ability of one coil to induce a voltage
across a neighboring coil [unit=H].
Where, μ=magnetic constant=magnetic permeability [N/A2]
N1=number of turns in left coil
N2=number of turns in right coil
ϕ11=magnetic flux produced by current i1 through N1 turns
ϕ21=magnetic flux produced by current i1 through N1 and N2 turns
ϕ22=magnetic flux produced by current i2 through N2 turns
ϕ12=magnetic flux produced by current i2 through N1 and N2 turns
M=M21=M12=mutual inductance [H], k=coefficient of coupling

7. Analysis using Mesh Current Method

8. Example 6.6: Current in Magnetically Coupled Coils
Write Mesh-current Equations

9. P6.45: Design of Transformer
Check out the transformer design for Switching Mode Power Supply: