Remarks on the surface impedance formulation (3D)


For a 3D application in which the skin effect is pronounced, viz. the value of the penetration depth is much smaller in comparison with the thickness of the part to be heated, it is recommended to solve the magnetic problem by using the surface impedance formulation. This paragraph deals with the conditions of using the software with this formulation:

  • (1) limitations for the description of the materials with both nonlinear and temperature T dependent B(H,T) characteristic;
  • (2) specific description of thermal sources

Limitation for the materials

When a volume conductive region with pronounced skin effect is described by using a surface region of the solid conductor type described by the surface impedance formulation, it is not possible to use for this region a magnetic nonlinear material whose magnetization is also T temperature dependent, i.e. a B(H,T) characteristic.

Thus, you must choose one of the following solutions:

  • description with B(H) characteristic: magnetic nonlinear , but temperature T independent (magnetic permeability μ = B/H dependent on the magnetic field strength H, but temperature dependent);
  • description with μ(T) characteristic: magnetic linear , but temperature T dependent (magnetic permeability independent of the magnetic field strength H, but temperature dependent)

Characteristic of description the sources

For a Steady State AC Magnetic coupled with Transient Thermal application, the transfer of the power dissipated by Joule effect is carried out by means of the conducting regions (of solid conductor type) as depicted in the table below.

Name Thermal definition Magnetic definition Material
Thermal conducting region Region of solid conductor type  
+ eventual heating source
Heat computed by Joule effect in electromagnetic solving process


With the formulations of the surface impedance type, the power dissipated by Joule effect is automatically transferred as a source of the thermal problem. This is carried out completely automatically by the software, and the user must not mark off the case: + possible heating source