Every magnetic design is a negotiation between two loss mechanisms that move in opposite directions. Make the core bigger and core loss falls while copper loss falls too — but cost, height and weight rise. Reduce turns and copper loss falls while flux swing and core loss rise. The optimum is not the minimum of either curve; it is the point where the sum is lowest at the actual operating temperature.
1. The two loss terms
Core loss = hysteresis + eddy current + residual loss, described by the Steinmetz equation Pv = k × f^α × B^β, with α typically 1.2–1.8 and β 2.0–2.8 for power ferrite. It scales with flux density and frequency, and it depends on temperature.
Copper loss = I_rms² × R_dc, plus the AC component from skin and proximity effect. It scales with turns squared (more turns, longer wire, higher resistance) and with current squared.
For a given core and window, adding turns raises inductance and lowers flux swing: core loss drops, copper loss rises. The curves cross somewhere, and that crossing point is the design target.
2. Why the AC copper loss is often the real problem
At 100 kHz a 0.5 mm round wire has a skin depth around 0.2 mm, so the effective AC resistance can be several times the DC value. In a transformer with a multi-layer winding, proximity effect between layers can push the AC-to-DC resistance ratio above 5. A design that looks balanced on the DC calculation alone may dissipate twice the expected heat.
- Keep the winding layer count low; a single layer has almost no proximity loss.
- Use Litz wire only where the AC component and frequency justify it — it costs window area and money.
- Interleave primary and secondary to reduce leakage and the field inside the window.
- Measure the wound part’s AC resistance on an impedance analyser, not just the DCR with a milliohm meter.
3. Temperature moves the optimum
Ferrite loss has a minimum near 80–100 °C for power grades; copper resistance rises 0.4% per kelvin. As the part heats up, copper loss grows faster than core loss shrinks, so the optimum at the hot spot is slightly toward a larger core than the 25 °C calculation suggests. Design at the hot-spot temperature, then verify at that temperature.
4. A worked comparison
| Design | Turns | Flux swing | Core loss | Copper loss | Total |
|---|---|---|---|---|---|
| A (under-turned) | 32 | 0.28 T | 7.1 W | 2.0 W | 9.1 W |
| B (balanced) | 40 | 0.22 T | 4.6 W | 3.1 W | 7.7 W |
| C (over-turned) | 52 | 0.17 T | 3.1 W | 5.2 W | 8.3 W |
Design B wins by 15% over A and 5% over C, with the same core and window. Note that A also loses inductance headroom and runs closer to saturation — the loss comparison alone does not capture the reliability cost.
5. Levers beyond turns
- Core material. A lower-loss grade at the operating frequency buys loss reduction without changing geometry, at a material cost premium of 10–30%.
- Core geometry. A taller, narrower core has more surface area for the same volume — better convection, lower hot spot.
- Gap distribution. A distributed gap spreads the fringing field, reducing the extra copper loss near the gap in a wound core.
- Winding window fill. A 40% fill factor wastes window; 60–70% is usually achievable with careful bobbin design.
- Frequency. Raising frequency shrinks the core but raises both loss densities — the crossover is set by the material, not by preference.
6. Measure, then decide
Build both candidates, run them at full load in the actual enclosure, and compare hot-spot temperature — not efficiency at 25 °C. A 0.5 W difference in calculated loss is noise; a 5 K difference in hot spot is a qualification decision.
Shaanxi SiRui Technology’s Magnetic Core series covers both sides of this trade-off — low-loss power ferrite for core-loss-limited designs and distributed-gap powder cores for bias-heavy inductors — so the balance can be optimised against the real material curves.
Send your loss budget to sales@sirui-tech.com.