1. EE 1270 Introduction to Electric Circuits Suketu Naik 0 EE 1270: Introduction to Electric Circuits Lecture 16: Mutual Inductance Chapter 6 Inductance, Capacitance, and Mutual Inductance Sections 6.4, 6.5

2. EE 1270 Introduction to Electric Circuits Suketu Naik 1 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 40000 V)

3. EE 1270 Introduction to Electric Circuits Suketu Naik 2 Mutual Inductance Where, μ=magnetic constant=magnetic permeability [N/A 2 ] N 1 =number of turns in left coil N 2 =number of turns in right coil ϕ 11 =magnetic flux produced by current i 1 through N 1 turns ϕ 21 =magnetic flux produced by current i 1 through N 1 and N 2 turns ϕ 22 =magnetic flux produced by current i 2 through N 2 turns ϕ 12 =magnetic flux produced by current i 2 through N 1 and N 2 turns M=M 21 =M 12 =mutual inductance [H], k=coefficient of coupling Mutual inductance is the ability of one inductor to induce a voltage across a neighboring inductor [unit=H].

4. EE 1270 Introduction to Electric Circuits Suketu Naik 3 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

5. EE 1270 Introduction to Electric Circuits Suketu Naik 4 Analysis using Mesh Current Method

6. EE 1270 Introduction to Electric Circuits Suketu Naik 5 Example 6.6: Current in Magnetically Coupled Coils Write Mesh-current Equations

7. EE 1270 Introduction to Electric Circuits Suketu Naik 6 P6.45: Design of Transformer Check out the transformer design for Switching Mode Power Supply: http://www.digikey.com/en/pdf/w/wurth-elektronik/cookbook-transformer-design