Mutual Inductance
• Consider two circuits “linked” by a
magnetic field (magnetically-coupled
coils).
ECE 201 Circuit Theory I
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“Self-Inductances” are L1 and L2.
The “Mutual” Inductance is M.
The voltage induced in one circuit is related to the
time-varying current in the other circuit.
ECE 201 Circuit Theory I
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Analysis
• Easiest with mesh-current method.
ECE 201 Circuit Theory I
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Write the circuit equations in terms of the
coil currents.
Arbitrarily assign the current directions.
There will be two voltages across each coil, the
“self-induced” voltage, L(di/dt), and a “mutually
induced” voltage, M(di/dt).
ECE 201 Circuit Theory I
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Determination of Voltage Polarities
• “Dot convention”
– Dots indicate the direction in which the coils
are wound.
ECE 201 Circuit Theory I
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The Rule for using the Dot Convention
• 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.
ECE 201 Circuit Theory I
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Alternate Rule for the Dot Convention
• When the reference direction for a current
leaves the dotted terminal of a coil, the
reference polarity of the voltage that it
induces in the other coil is negative at its
dotted terminal.
ECE 201 Circuit Theory I
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For this Example
• The voltage induced in coil 1 by the current in
coil 2 is negative at the dotted terminal of coil 1,
and is a voltage rise with respect to current i1.
ECE 201 Circuit Theory I
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For this Example
• The voltage induced in coil 2 by the current in
coil 1 is positive at the dotted terminal of coil 2,
and is a voltage rise with respect to current i2.
ECE 201 Circuit Theory I
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Write the Mesh Equations
di
di
v  i R  L
M
0
dt
dt
di
di
iR L
M
0
dt
dt
1
g
1
1
1
2
2
2
2
1
2
ECE 201 Circuit Theory I
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Example 6.6, page 206
• Write a set of mesh equations that
describe the circuit shown in terms of i1
and i2.
ECE 201 Circuit Theory I
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di
di
di
4  20i  5i  8  20i  8
 5i  0
dt
dt
dt
di
di
di
16  20i  60i  20i  8  16
0
dt
dt
dt
1
g
2
1
1
2
2
g
1
2
2
g
1
ECE 201 Circuit Theory I
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di
d
4  8 i  i   20 i  i   5 i  i   0
dt
dt
d
di
20 i  i   60i  16 i  i   8
0
dt
dt
1
g
2
1
2
1
g
1
2
1
2
2
ECE 201 Circuit Theory I
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13