Skin Depth for an Eddy Current Solution

Skin Depth for an Eddy Current T-W Solution

Induced currents allow magnetic fields to penetrate conductors only to a certain depth, of about 4-5 skin depths. The skin depth is approximated by the following formula:

where

w is the angular frequency, which is equal to 2pf (f is the frequency at which source currents and voltages oscillate during the solution).
s is the conductor's conductivity in siemens/meter.
m_r is the conductor's relative permeability.
m₀ is the permeability of free space, which is equal to 4 x 10^-7 H/m.

Currents are concentrated near the surface of the conductor, decaying rapidly past the skin depth. As the formula above indicates, the skin depth gets smaller as the frequency increases.

Note: Due to the skin concentration of current, AC inductances and resistances are not equal to their DC equivalents. This affects the inductance and resistance values computed during impedance computations.

Both the skin depth / proximity effects and the displacement effects must be specifically requested. Under the excitation setup, the respective effects can be specified for objects in the model as shown below:

Eddy (skin/proximity) effect can only be specified for objects with non-zero conductivity.

By default, eddy/displacement current effects are turned off. Including these in the calculation has a potentially significant impact on the solution time since the electric vector potential calculation is activated, causing the size of the solved matrix to increase significantly if the regions with the electric vector potential to be calculated have a large number of finite elements.

Displacement current calculation is normally activated in dielectrics (including vacuum) and allows electromagnetic waves to propagate. In such cases, a radiation boundary condition should also be used in the problem setup.