Steinmetz's equation

Steinmetz's equation, sometimes called the Power equation, is a physics equation used to calculate the core loss of magnetic materials due to magnetic hysteresis. The equation is named after Charles Steinmetz, who proposed a similar equation in 1892. The equation is as follows:

where Q is the loss per volume, η is the hysteresis coefficient, and B is the maximum induction. The equation can also be expressed as

where k, a, and b are material parameters generally found by curve fitting. The equation is a simplified form that only works with a sinusoidal frequency and does not take into account factors such as DC offset. However, because most electronics expose materials to non-sinusoidal flux waveforms, various improvements to the equation have been made. An improved generalized Steinmetz equation, often referred to as iGSE, can be expressed as

where ${\displaystyle \Delta B}$ is the flux density from peak to peak and ${\displaystyle k_{i}}$ is defined by

where a, b, and k are the same parameters used in the original equation. This equation can calculate losses with any flux waveform using only the parameters needed for the original equation, but it ignores the fact that the parameters, and therefore the losses, can vary under DC bias conditions. DC bias cannot be neglected without severely affecting results, but there is still not a practical physically-based model that takes both dynamic and nonlinear effects into account. However, this equation is still widely used because most other models require parameters that are not usually given by manufacturers and that engineers are not likely to take the time and resources to measure.

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