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

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)

Transformer: Basics Voltage Ratio= Current Ratio=

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

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

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

Analysis using Mesh Current Method

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

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