Magnetic cores

A transformer, a motor stator, an inductor and a wireless charging pad all do the same thing: they carry a magnetic field that reverses continuously, and they want to carry as much of it as possible while losing as little energy as possible in the reversing.

That is a soft magnetic material, and it is defined by what it does not do. It magnetises easily, demagnetises just as easily, and retains nothing. A permanent magnet is the opposite specification — it resists being demagnetised, which is precisely the property that would make it useless here.

The two losses that matter are hysteresis and eddy currents, and every soft magnetic material is a different compromise between them. Hysteresis loss is the energy spent walking the magnetisation around its loop and scales with frequency. Eddy current loss is current induced in the core itself by the changing field, wasted as heat, and scales with the square of frequency — which is why the answer at 50 hertz and the answer at 500 kilohertz are different materials rather than different grades.

Eddy currents are the reason a solid iron core is unusable and the reason the whole field is organised by frequency.

A changing magnetic field induces a voltage in any conductor inside it, including the core. In a solid conductive core that voltage drives circulating currents that do nothing but heat the metal. The two defences are to break up the current paths and to raise the material's electrical resistance.

Laminations do the first. A mains transformer core is a stack of thin insulated sheets rather than a solid block, because each sheet confines the induced current to its own small loop. Thinner sheets, lower loss, and more of them to stack — which is a manufacturing cost, so lamination thickness is chosen against frequency.

Alloying does the second. Adding a few per cent of silicon to iron roughly quadruples its resistivity, which is most of why electrical steel exists.

Above about twenty kilohertz neither is enough, because eddy losses rise with the square of frequency and no lamination is thin enough. The answer there is to stop using a metal: a ferrite is a ceramic with a resistivity millions of times that of steel, so eddy currents essentially cannot flow. It saturates at a much lower field and carries far less flux, and above about twenty kilohertz that trade is worth making.

Core loss is a running cost that never stops, and at grid scale it is enormous. A distribution transformer is energised for its whole thirty- or forty-year life whether or not anything is drawing power from it, so its no-load loss is paid for every hour of every year.

That is why minimum efficiency standards for transformers exist in the EU, the United States and elsewhere, and why grain-oriented electrical steel — which is more expensive and lower loss — is specified over cheaper grades by regulation rather than by the buyer's preference. The purchaser of a transformer is frequently not the party paying its losses, which is the classic split-incentive problem, and the regulation exists because of it.

The same arithmetic drives motor efficiency classes. Electric motors are somewhere near half of world electricity consumption, and a percentage point of core loss across that is a very large number.