1. Introduction to magnetic circuits

2. Intro to magnetic circuits
Assumption: we can represent a 3-D field problem with a 1-D circuit
Assumptions: If displacement currents
Maxwell’s equations (Ampere’s Law and Gauss; Law for magnetic fields) give:

3. Intro to magnetic circuits
Magnetomotive force
Simplification:
Use right hand rule for direction of H

4. Intro to magnetic circuits
in transformers and machinery

5. Energy conversion devices have moving elements which require an small air gap:

11. Practical magnetic materials
m varies with flux level
But, if : m is large the variation does not have a significant effect, if the dominant reluctance is in the air gap
Fringing fields-increases the effective area of the gap
We will ignore the effect of fringing fields in this course

13. Exercises: Read pages 89-92 of the Labview for Electric Circuits book
Do Labview exercises on pages

14. If the reluctance of the air gap dominates

15. Homework
In Fitzgerald, do problems 1-4 on pages

16. Ferromagnetic material: The most common
Magnetic material: Magnetic dipole moments line up in the same direction
Non-magnetic material: Magnetic dipole moments are randomly oriented
Applying an external magnetic field will line up dipoles in the direction of the external field
Effective m= B/Happlied when all the moments line up with external field, saturation
When the applied field is taken away, moments will retain a component in the direction of the applied field, hysteresis

17. Hysteresis loops

19. Due to hysteresis, the excitation current to produce the sinusoidal flux is non-sinusoidal

20. Hysteresis losses: energy is required to move around the magnetic dipoles; proportional to the area of the hysteresis curve, and the frequency
Eddy current losses: Arise from changed in the magnetic field (Faraday’s Law); creates magnetic fields that oppose the applied fields. Results in a fatter hysteresis loop.