Apparent and incremental magnetic permeability

Magnetic permeability is a measure of the material response to the magnetic field application. Magnetic flux density B and magnetic field strength H correlate, but shape of the plot B(H) may be very different for different materials.

In application, where this characteristic is linear within the working range, magnetic properties of the material may be defined by a single constant called magnetic permeability μ = B/H. In non-linear case the slope of the curve B(H) varies, and two characteristic of the each magnetic state may be considered:

• Apparent permeability μ_apparent = B/H.
• And differential or incremental permeability μ_incremental = dB/dH,
  where dB and dH are small variations of B and H.

In majority of QuickField magnetic formulations we use "permeability" as a synonym of the apparent, or static magnetic permeability.

However, when non-linear magnetic materials are subjected to magnetic field with large DC offset and small AC component, it is possible to avoid time-consuming transient electromagnetic analysis with full nonlinear B(H) characteristics. It may be replaced it by fast solution of two coupled magnetic problems - non-linear DC magnetic analysis for calculating the levels of media saturation, and then - linear AC magnetic analysis with incremental permeability imported from DC magnetics. AC Magnetic problem thus will have correct material data for media response of each part of magnetic material to the small variations of the magnetic field around the working point.

And if the incremental permeability is imported to DC or AC magnetic problem - then incremental permeability will be used in further simulations and shown in QuickField postprocessor.