Steinmetz's equation
Steinmetz's equation, sometimes called the power equation, is an empirical equation used to calculate the total power loss (core losses) per unit volume in magnetic materials when subjected to external sinusoidally varying magnetic flux. The equation is named after Charles Steinmetz, a German-American electrical engineer, who proposed a similar equation without the frequency dependency in 1890. The equation is: where formula_2 is the time average power loss per unit volume in mW per cubic centimeter, formula_3 is frequency in kilohertz, and formula_4 is the peak magnetic flux density; formula_5, formula_6, and formula_7, called the Steinmetz  coefficients, are material parameters generally found empirically from the material's "B-H" hysteresis curve by curve fitting. In typical magnetic materials, the Steinmetz coefficients all vary with temperature. The energy loss, called core loss, is due mainly to two effects: magnetic hysteresis and, in conductive materials, eddy currents, which consume energy from the source of the magnetic field, dissipating it as waste heat in the magnetic material. The equation is used mainly to calculate core losses in ferromagnetic magnetic cores used in electric motors, generators, transformers and inductors excited by sinusoidal current. Core losses are an economically important source  of inefficiency in alternating current (AC) electric power grids and appliances. If only hysteresis is taken into account (à la Steinmetz), the coefficient formula_6 will be close to 1 and formula_7 will be 2 for nearly all modern magnetic materials. However, due to other nonlinearities, formula_6 is usually between 1 and 2, and formula_7 is between 2 and 3. The equation is a simplified form that only applies when the magnetic field formula_4 has a sinusoidal waveform 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 formula_14 is the flux density from peak to peak and formula_15 is defined by