Mutual Inductance

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# Mutual Inductance - PowerPoint PPT Presentation

Mutual Inductance. Consider two circuits â€œlinkedâ€ by a magnetic field (magnetically-coupled coils). â€œSelf-Inductancesâ€ are L 1 and L 2 . The â€œMutualâ€ 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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Presentation Transcript
Mutual Inductance
• Consider two circuits “linked” by a magnetic field (magnetically-coupled coils).

ECE 201 Circuit Theory I

“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
• Easiest with mesh-current method.

ECE 201 Circuit Theory I

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
• “Dot convention”
• Dots indicate the direction in which the coils are wound.

ECE 201 Circuit Theory I

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
• 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
• 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 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

ECE 201 Circuit Theory I

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