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Mutual Inductance. Consider two circuits “linked” by a magnetic field (magnetically-coupled coils). “Self-Inductances” are L 1 and L 2 . The “Mutual” Inductance is M. The voltage induced in one circuit is related to the time-varying current in the other circuit. Analysis.

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mutual inductance
Mutual Inductance
  • Consider two circuits “linked” by a magnetic field (magnetically-coupled coils).

ECE 201 Circuit Theory I

slide2

“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

analysis
Analysis
  • Easiest with mesh-current method.

ECE 201 Circuit Theory I

write the circuit equations in terms of the coil currents
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

determination of voltage polarities
Determination of Voltage Polarities
  • “Dot convention”
    • Dots indicate the direction in which the coils are wound.

ECE 201 Circuit Theory I

the rule for using the dot convention
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

alternate rule for the dot convention
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

for this example
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

for this example9
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

write the mesh equations
Write the Mesh Equations

ECE 201 Circuit Theory I

example 6 6 page 206
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