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Core loss calculation

# Core loss calculation

Alternating magnetic field causes the power losses in ferromagnetic materials, usually called core losses or iron losses. There are two main causes for the core losses: ohmic or Joule heating generated by the eddy currents, induced in the conductive media by the alternating magnetic field, and the losses caused in the ferromagnetic materials by the cyclic reversal of the magnetization and proportional to the area of the hysteresis loop.

If the magnetic core is built from insulated sheets (this technology is called "lamination") the electrical conductivity across the sheets should be considered zero, and corresponding block properties in QuickField should have zero value of the electric conductivity. QuickField simulation will show zero density of eddy currents in laminated blocks.

However, small eddy currents within thin sheets may produce power losses. And they are usually taken into account by empirical formulas which use several members to represent different physical effects jointly acting as core losses.

QuickField uses the empirical Bertotti formula for the core loss calculation:

*p* =
*k*_{h}*f B*^{2} + *k*_{c}*f*^{2}*B*^{2} + *k*_{e}(*f B*)^{1.5}

Here *B* - magnitude of the module of the flux density vector per period, *f* - problem frequency, *k*_{h}, *k*_{c}, *k*_{e} - olume power loss coefficients for specific magnetic material. Indexes *h*, *c* and *e* are related to *h*ysteresis, *c*onductive and *e*xcess losses in the magnetic cores.

Power loss coefficients *k*_{h}, *k*_{c}, *k*_{e}, as other material data, are responsibility of the QuickField user. They may be measured, or obtained from the magnetic material vendors.

Usually magnetic material vendors supply each material with the curves or tables of the core loss density vs. flux density on various frequencies. It is possible to approximate these experimental data by Bertotti formula by adjusting the loss coefficients. This process is called "curve fitting". Corresponding algorithms and utilities are available, and we provide our own implementation Core loss coefficients calculator in form of the Excel table, which may be used to calculate the core loss coefficients on given dataset.

The laminated core iron loss example demonstrates using our free tool for obtaining the loss coefficients and following calculation of the core losses in the transformer with the laminated core.