How to calculate core loss in a transformer core (with worked example)
For sinusoidal excitation, core loss is estimated with the Steinmetz equation P = k · f^α · B^β per unit mass, using coefficients from the material datasheet. In practice engineers read the manufacturer loss curve at the operating frequency and flux density, then add copper loss to estimate temperature rise.
1. Separate the two physical mechanisms
Hysteresis loss depends on how many times per second the material is magnetised — it scales linearly with frequency and with the area of the B-H loop.
Eddy-current loss comes from circulating currents inside the strip — it scales with the square of frequency and with the square of strip thickness.
This is why the same grade at 400 Hz has far higher loss than at 50 Hz, and why thin strip (0.23 mm vs 0.35 mm) matters at higher frequencies.
2. Use the datasheet curve first
Every silicon steel datasheet gives loss at a reference point, typically 1.7 T / 50 Hz in W/kg.
To estimate at another flux density, scale with B^1.6 to B^2.2 — but this is only an approximation; read the actual curve for design decisions.
3. Worked example (50 Hz distribution core)
Core mass 12 kg, grade 27Q100 (1.00 W/kg at 1.7 T / 50 Hz), operating at 1.5 T.
Estimated loss = 12 kg × 1.00 × (1.5/1.7)^2 ≈ 9.3 W.
If the design target is 8 W, move to a thinner grade (23Q110) or increase core area to reduce flux density.
4. Do not forget the copper side
Total temperature rise is driven by core loss plus I²R copper loss. A core with excellent loss but a poor window fill factor can still overheat.
Rule of thumb: keep total loss density below what your thermal path can remove (natural convection, potting, forced air).
5. Sanity-check a supplier datasheet
Confirm the measurement point (frequency, flux, waveform), the sample size and whether the value is typical or guaranteed.
Ask for the loss curve at your operating flux, not just one number — a single point hides the shape of the curve.
Batch-to-batch spread on commercial grades is typically ±5–8% on loss; a supplier quoting a single best-case number is a red flag.
FAQ
Does annealing change the calculated loss?
Yes. Cutting and winding add stress; without annealing, measured loss can be 10–30% higher than the datasheet. Use post-annealing values for cut cores.
What frequency range does the Steinmetz equation cover?
Roughly 50 Hz to a few hundred kHz for modified forms, but coefficients must be fitted per material and frequency band.
