Core loss is the dominant loss mechanism in high-frequency magnetics. Here is how to calculate it with the Steinmetz equation, where to get the coefficients, and a worked example comparing ferrite and powder cores.
Introduction
When a magnetic component operates at 100 kHz or higher, core loss usually exceeds copper loss. Get it wrong and your inductor or transformer overheats, saturates, or fails the efficiency target. The industry-standard tool for estimating core loss is the Steinmetz equation — a simple power-law formula fitted to measured material data.
Shaanxi SiRui Technology Co., Ltd. supplies low-loss magnetic cores (Mn-Zn ferrite, Ni-Zn ferrite, Sendust, High Flux, MPP, nanocrystalline and amorphous) for high-frequency power designs worldwide. Contact: sales@sirui-tech.com | Web: www.sirui-tech.com
1. What Is Core Loss?
Core loss is the power dissipated inside the magnetic material itself when it is excited by an alternating field. It has three components:
- Hysteresis loss: energy lost as the B-H loop is traced each cycle. Proportional to frequency and loop area. Dominant at low frequency.
- Eddy-current loss: circulating currents induced inside the core. Proportional to the square of frequency. Ferrite’s high resistivity keeps this low; laminated and powder cores limit it with thin layers or insulated particles.
- Residual loss: relaxation and resonance effects, significant only above ~1 MHz.
All three scale with flux swing, which is why “smaller core = more loss per volume” — you push flux density up to shrink the core, and loss climbs steeply.
2. The Steinmetz Equation
The classic Steinmetz equation (also called the General Steinmetz Equation’s simplest form) is:
Pv = k × f^α × B^β
- Pv = core loss per unit volume (mW/cm³ or kW/m³)
- f = operating frequency (kHz or Hz — keep units consistent with the data sheet)
- B = peak flux density (mT or T)
- k, α, β = material coefficients fitted to measured loss curves
For total loss in a core of volume V: P = Pv × V.
The equation works well for sinusoidal excitation. For square-wave or arbitrary waveforms, use the improved versions — the iGSE (improved General Steinmetz Equation) or the MSE (Modified Steinmetz Equation) — which replace peak B with an equivalent flux density based on dB/dt.
3. Where to Get k, α and β
You do not need to fit the coefficients yourself in most cases:
- Material data sheets: ferrite and powder core vendors publish loss vs frequency and loss vs flux curves; many also give explicit k, α, β values.
- Curve fitting: if only curves are published, digitize two or three points and solve Pv = k·f^α·B^β numerically (log-log linear regression works well).
- Core manufacturer calculators: most magnetic component suppliers (including SiRui-Tech) provide application support to select a core and estimate loss from real datasheet data.
Warning: coefficients are only valid for the stated frequency and temperature range. A ferrite’s k and β change dramatically above 100 °C or beyond its recommended frequency band. Never extrapolate far outside the fitted range.
4. Worked Example: Ferrite vs Powder Core at 200 kHz
Compare two candidate cores for a 200 kHz inductor running at B = 100 mT:
| Material | Typical Pv @ 200 kHz, 100 mT | Comment |
|---|---|---|
| Mn-Zn ferrite (power grade) | ~80 – 150 mW/cm³ | Best low-loss choice at this frequency |
| MPP (powder) | ~200 – 400 mW/cm³ | Lowest loss of the powder family |
| Sendust (powder) | ~350 – 600 mW/cm³ | General-purpose, higher loss than ferrite |
| Iron powder | ~800+ mW/cm³ | Line-frequency / cost-driven designs |
If the core volume is 10 cm³ and the ferrite Pv is 100 mW/cm³, total core loss is 1 W. The same volume in Sendust would dissipate roughly 3.5–6 W — five times more heat. That is exactly why high-frequency power stages use ferrite, and why high-DC-bias stages (where ferrite cannot hold inductance) accept powder-core loss as the price of saturation performance. See our ferrite vs powder core comparison for the full trade-off.
5. How Core Loss Scales with Frequency and Flux
- Frequency: loss rises roughly with f^1.0–1.7 (hysteresis term) plus f^2 (eddy term). Doubling frequency can triple or quadruple loss.
- Flux density: loss rises with B^2.0–3.0 for ferrite, and often higher for powder cores. A 20% flux increase can raise loss by 50% or more.
- Temperature: ferrite loss typically bottoms out near 80–100 °C and rises sharply above; powder cores are more stable but still shift with temperature.
6. Common Core Loss Calculation Mistakes
- Using peak-to-peak B instead of peak B in the Steinmetz equation.
- Mixing units — kHz with T, or Hz with mT — without converting to the data sheet’s reference.
- Using the AC-loss coefficient for designs with large DC bias. DC bias does not create core loss by itself, but it changes the operating point and, for gapped ferrite, adds fringing loss.
- Ignoring temperature. The same core at 25 °C and 110 °C can differ by 2–3× in loss.
- Extrapolating coefficients beyond the datasheet frequency range.
7. Low-Loss Core Materials from SiRui-Tech
At Shaanxi SiRui Technology Co., Ltd., we supply cores characterized for real operating conditions, not just catalog values:
- Mn-Zn ferrite cores (EE, EI, EFD, PQ, ER, ETD, EP, toroid) with published loss curves for 20 kHz – 1 MHz power designs
- Ni-Zn ferrite cores for MHz-range filtering and suppression
- Sendust, High Flux, MPP and iron powder cores with DC-bias-annotated loss data
- Nanocrystalline and amorphous cores for the lowest loss at high flux and high temperature
Start with our Magnetic Core Selection Guide to shortlist materials, then request loss curves for your exact frequency and flux operating point. For DC/DC inductor specifics, see our Buck Converter Inductor Design Guide.
Web: www.sirui-tech.com | Email: sales@sirui-tech.com
FAQ
Q1. What is the Steinmetz equation used for?
It estimates core loss per unit volume from frequency and peak flux density using three material-specific coefficients. It is the standard first-pass estimate for inductor and transformer thermal design.
Q2. How accurate is the Steinmetz equation?
Within ±20–30% for sinusoidal excitation inside the datasheet range — adequate for preliminary design. For final loss prediction, use measured data or iGSE/MSE for non-sinusoidal waveforms.
Q3. Does DC bias affect core loss?
AC core loss is driven by the flux swing around the operating point. DC bias shifts the operating point and, for gapped ferrite, adds fringing losses near the gap. Powder cores with distributed gaps avoid fringing loss entirely.
Q4. Which material has the lowest core loss?
For 20 kHz – 1 MHz power conversion, Mn-Zn ferrite generally has the lowest loss per volume. At higher flux and temperature, nanocrystalline can outperform ferrite; at very high frequency, Ni-Zn ferrite is preferred.
Conclusion
Core loss calculation is the difference between a design that works on paper and one that survives thermal testing. Use the Steinmetz equation with datasheet coefficients, keep units consistent, respect temperature and frequency limits, and validate with measurement. A few minutes of calculation up front prevents a full redesign later.