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Lecture 26

# Lecture 26 - Lecture 26 Mutual Inductance and...

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Lecture 26 Mutual Inductance and transformers (how to change something’s impedance)

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Mutual inductance Two coils who share magnetic fields Current generates magnetic flux Change in flux generates voltage If two currents cause flux, voltages respond to both Proportionality set by each inductance, mutual inductance, M M depends on coupling coefficient, k Can re-describe for sinusoidal steady state in complex form Draw as two inductors with arrow for coupling ( 29 ( 29 1 2 2 2 2 1 1 1 1 2 1 2 2 2 2 1 1 1 2 2 1 1 2 1 1 1 , , , MI I L j V MI I L j V k k L L M dt dI M dt dI L V dt dI M dt dI L V dt d V dt d V bI aI + = + = < < - = + = + = Φ Φ + Φ ϖ ϖ + V1 - + V2 - I 1 I 2 k + V1 - L1 L2 I 1 + V2 - I 2
Impedance transformation: k + V1 - L1 L2 I 1 + V2 - I 2 Zo Z1 ( 29 ( 29 ( 29 ( 29 + - + = + - - = + - = + - = - = + = + = Zo L j k L j Zo L j Z Zo L j M L L Zo L j I V Zo L j I M j I L j V Zo L j MI j I Zo I MI I L j V MI I L j V 2 2 2 1 1 2 2 2 1 2 1 1 1 2 1 2

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