The value $\phi_{h}$ (see Fig. 1 and Fig. 2) is responsible for “hysteresis loss”. The eddy current loss is dictated by the Electrical conductivity (reciprocal of resistivity).

It is important that all the values are entered with the correct units, as specified in FEMM.

For linear materials, the material can be set to anisotropic, by choosing different values for x and y directions.

Fig. 1. Loss angle for Air, set to zero: $\phi_{hx} = \phi_{hy} = 0$

For non-linear materials there is just one parameter$\phi_{hmax,deg}$. Unfortunately, most magnetic materials in the FEMM database have the “loss angle” $\phi_{h}$ parameter set to zero.

An exception is 1006 Steel, which has the angle set to 20 deg (Fig. 2).

Fig. 2. Loss angle for 1006 Steel

This value can be easily set by trial-and-error method if the loss is known (e.g. from manufacturer's datasheet). To find out an approximate value the following steps have to be taken:

Set up a simulation, in which a block of this material is magnetised in a uniform way, in the whole volume (e.g. thin sheet in a closed yoke). For ferrites this is easier, because eddy currents can be mostly neglected and the conductivity can be set to zero, so almost any shape will do. For conductive materials this is more difficult, because the sample has to be very thin so that the eddy currents are negligible. It is advised to set this up as a very thin lamination, for instance with the thickness less than 10x the skin depth (see also: https://www.e-magnetica.pl/skin_depth)

A good geometry is a very thin cylinder (toroid), excited with a single turn of primary winding, inside the cylinder. A ratio of outer diameter to inner diameter OD/ID < 1.1 (like a pipe with a fairly thin wall) guarantees uniform magnetisation, which is important.

The dummy model should be set such that the flux density is uniform. As shown in Fig. 3 this can be done with the toroidal sample, with the magnetising winding positioned exactly at the centre. There is no need for the returning wire of the coil.

Fig. 3. Dummy model of a “thin toroid”

Set this dummy model such that the flux density in the material is close to the operating point in question, obviously at the required frequency. In this example, we assume B = 1.0 T and P = 1.5 W/kg

Get the real loss value (e.g. from the manufacturer's datasheet) and convert it to a value in W/m³. If the value is specified in W/kg this can be converted to W/m³ by using the density D of material which is given in kg/m³:

$$ P_{W/m^3} = P_{W/kg} · D_{kg/m^3}$$

For example, if the target loss is 1.5 W/kg and the material density is 7650 kg/m³. Therefore, the loss density is 1.5 * 7650 = 11775 W/m³. This is the target value to be achieved in the dummy simulation.

Adjust the current (by trial and error, or better by scaling of the current by the error in B) in the magnetising wire until B is exactly 1.0 T. The value of B is to be measured (left mouse click, with the grid snapping disabled) at the point indicated by the black arrow in Fig. 3.

Use the block integral, and calculate Total loss density of the dummy sample which will give a numerical value in W/m³.

Adjust the value of loss angle (trial and error, etc. starting for example with a value of 1 deg) until the loss density is the same as the calculated target value (11475 W/m³ in this case).

Check the value of B, because it could change slightly. If it does, then just repeat the steps in another iteration (first adjust the current to set the B, then adjust the angle to set the loss).

• Note, if conductivity is set to some non zero value, the loss value should be very low (if eddy currents are negligible). With the conductivity enabled, it is likely to see B changing with added loss angle. If this is the case, just go through several iterations of setting current and loss angle until B = B_target and P = P_target.

Use the values of loss in W/m³.

With the loss angle set to zero, for very thin sample the loss should be very small compared to the real value (e.g. less than 5%). If it is not then the sample must be made thinner, to further reduce the eddy currents.

The exception is if the material is set as laminated in its settings, because then they can be used with the default conductivity, with any thickness, because the “laminating” approach takes care of homogenisation of properties.

If the simulated loss is smaller than the target value, then increase the loss angle. If the simulated loss is larger than the target value, then decrease the loss angle.

A good approach can be to double or halve the values to get closer to the target, so that coarse steps are done first.

Re-run the simulation and compare the losses with the target value. Once the losses agree, use the approximated loss angle in the real simulation.

Note: for large departure in amplitude and frequency a new angle will have to be found.