Introduction to magnetic circuits

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:

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

Intro to magnetic circuits in transformers and machinery

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

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

Exercises: Read pages 89-92 of the Labview for Electric Circuits book Do Labview exercises on pages 92-95

If the reluctance of the air gap dominates

Homework In Fitzgerald, do problems 1-4 on pages 43-44.

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

Hysteresis loops

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

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.