Steinmetz Core Loss
Ferrite core loss from datasheet Steinmetz coefficients — loss density plus total dissipation for your core volume.
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The engineering
The Steinmetz equation is the standard curve-fit for core loss in soft magnetic material under sinusoidal excitation: loss density scales as frequency to the α and peak flux density to the β. This card uses the common ferrite-datasheet convention — f in kHz, B̂ in tesla, loss density in kW/m³ (numerically identical to mW/cm³) — then multiplies by effective core volume Vₑ for total watts. Pull k, α, β from your material's datasheet fit or extract them from two points on the loss-density chart.
Two gotchas. First, coefficients are only valid inside the fitted range — a k/α/β set fit at 100 kHz, 100 °C says nothing reliable at 500 kHz or 25 °C (ferrite loss has a temperature valley, typically minimum near 80–100 °C). Second, B̂ is the peak of the AC flux swing: for a symmetric bipolar swing B̂ = ΔB/2. With β typically 2.5–3, backing peak flux off just 20% roughly halves the loss — usually the cheapest thermal fix in a magnetics design.
Classic Steinmetz assumes sinusoidal flux. For square-wave and PWM converters the improved Generalized Steinmetz Equation (iGSE) reuses the same three coefficients but weights by dB/dt — expect this card to run somewhat optimistic for high-ripple triangular flux at the same B̂.
Where this math comes from
In 1892 Charles Proteus Steinmetz — a 27-year-old immigrant working at Rudolf Eickemeyer's machine works in Yonkers, four years off the boat from Germany — presented "On the Law of Hysteresis" to the AIEE. From painstaking measurements on iron samples he showed hysteresis loss per cycle followed B to the 1.6 power, replacing guesswork in transformer and motor design with a number you could compute. The paper made him famous overnight; General Electric bought Eickemeyer's company in 1892 largely to get Steinmetz and his patents.
Steinmetz's original law had no frequency exponent — at power-line frequencies, loss per cycle was all that mattered. Twentieth-century ferrites running at tens to hundreds of kilohertz forced the modern three-parameter form with α on frequency and β drifting up toward 2.5–3, and the switch-mode era added waveform corrections: the iGSE of 2001–2002 extends the same fit to the triangular and trapezoidal flux every converter actually produces.
- 1881James Alfred EwingCoins 'hysteresis' and maps the B-H loop that stores the loss.
- 1892Charles P. SteinmetzPublishes 'On the Law of Hysteresis' — loss per cycle ∝ B^1.6.
- 1892General ElectricAcquires Eickemeyer's firm to bring Steinmetz and his hysteresis work in-house.
- 2001Li, Abdallah & SullivanGeneralized Steinmetz Equation extends the fit to arbitrary flux waveforms.
- 2002Venkatachalam, Sullivan et al.iGSE — the waveform-corrected form now standard in SMPS magnetics design.
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