Magnetically Coupled Circuits

Wednesday, 13 March 2019

5:18 PM

Self-Inductance (L) Consider a current flowing through a coil with N turns. This current produces a magnetic flux 𝜙 (weber) which is proportional to the current in the coil Mutual-Inductance (M) Flux coupling - a current in one flux establishes a flux that affects a nearby second coil Voltage is proportional to the time rate of change of the current flowing through the first coil Inductance induces self-inductance in its own circuit, and mutual inductance on another nearby circuit ﷐𝑣﷮2﷯﷐𝑡﷯=﷐𝑀﷮12﷯﷐𝑑﷐𝑖﷮1﷯﷐𝑡﷯﷮𝑑𝑡﷯+﷐𝐿﷮1﷯﷐𝑑﷐𝑖﷮1﷐𝑡﷯﷯﷮𝑑𝑡﷯ ﷐𝑣﷮1﷯﷐𝑡﷯=﷐𝑀﷮21﷯﷐𝑑﷐𝑖﷮2﷯﷐𝑡﷯﷮𝑑𝑡﷯+﷐𝐿﷮2﷯﷐𝑑﷐𝑖﷮2﷯﷐𝑡﷯﷮𝑑𝑡﷯ Mutual inductance only occurs in a four-terminal layout, or a two inductor layout Mutual inductance is denoted either by an arch between two circuits, or by dots. Dot rule: When the reference current direction is into the dotted terminal of one coil, the reference polarity of the voltage term induced in the other coil is positive at its dotted terminal A current entering the dotted terminal of one coil produces a voltage that is positively sensed at the doted terminal of the second coil !!! Refer to picture on phone Self-Induction and Mutual Voltage ﷐𝑣﷮1﷯﷐𝑡﷯=﷐𝐿﷮1﷯﷐𝑑﷐𝑖﷮1﷯﷮𝑑𝑡﷯±𝑀﷐𝑑﷐𝑖﷮2﷯﷮𝑑𝑡﷯ ﷐𝑣﷮2﷯﷐𝑡﷯=﷐𝐿﷮2﷯﷐𝑑﷐𝑖﷮2﷯﷮𝑑𝑡﷯±𝑀﷐𝑑﷐𝑖﷮1﷯﷮𝑑𝑡﷯ + for positive sense − for negatve sense (actual inductance + mutual inductance (multiplied by the current) Analysis of circuits containing coupled coils Ink Drawings Ink Drawings Ink Drawings  
Analysis of circuits containing coupled coils For coil 1 - ﷐𝑉﷮1﷯=﷐﷐𝑅﷮1﷯+𝑗𝜔﷐𝐿﷮1﷯﷯﷐𝐼﷮1﷯+𝑗𝜔𝑀﷐𝐼﷮2﷯ For coil 2 - ﷐𝑉﷮2﷯=﷐﷐𝑅﷮2﷯+𝑗𝜔﷐𝐿﷮2﷯﷯﷐𝐼﷮2﷯+𝑗𝜔𝑀﷐𝐼﷮1﷯

 

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