# Ferrite mystery

Pieter-Tjerk de Boer, PA3FWM pa3fwm@amsat.org

(This is an adapted version of parts of articles that I wrote for the Dutch amateur radio magazine Electron, July and December 2015.)

While attempting to build a phantom power supply circuit using an inductor, I ran into the following (reproducible) problem.

Take an FT50-43 toroidal core, apply about 10 turns of wire, and briefly let some 200 mA of DC current flow through it. After this, measure the coil's impedance: it turns out to have a dip at 190 kHz. So, it resonates, without a capacitor being connected to it! How's that possible?

This phenomenon led to an e-mail exchange with Bob van Donselaar, ON9CVD, who came up with the explanation: magnetostriction. Magnetostriction is the phenomenon that a piece of material changes its shape or size under the influence of a magnetic field. Thus, it connects magnetic fields to mechanical effects.

In my case, apparently the temporary application of a strong external field (caused by the 200 mA of DC current) has permanently magnetised parts of the toroid, giving the external magnetic field "grip" on the toroid's material.

Thus, the magnetic field of a current in the coil will also cause a mechanical force in the material, which will then propagate in the material as a soundwave. And then the reverse of magnetostriction occurs: the mechanical movement of the magnetized pieces of the toroid gives a change of the magnetic field, which induces an electrical voltage in the wire wound on the core.

Normally, we use a coil for its self-inductance: one sends a current through the coil, which causes a magnetic field, which in turn induces a voltage in the coil. The magnetostriction now adds a second effect, which again is from an applied current to an induced voltage, but using a detour via the mechanical movement. So if there are specific frequencies on which the toroid resonates mechanically, that will show up in the measured impedance.

And indeed, as Bob calculated: an FT50-43 has a mean circumference of 32.04 mm; for a soundwave to travel that distance 190 000 times per second (resonance at 190 kHz), then the speed must be 6088 m/s. And sound speeds of about 6 km/s are indeed normal for such materials, according to literature.

A good theory makes predictions that can be verified, and so does this one.
(i) If the resonance frequency is only determined by the size of the toroid and the speed of sound in the material, it should not depend on the current used for the initial magnetization: indeed, after applying 300 instead of 200 mA, I get the same resonance frequency.
(ii) A smaller core of the same material should resonate at a higher frequency: indeed, an FT37-43 resonates at 265 kHz; calculating from its size, we find a sound velocity of 6135 m/s: less than 1% difference from what we found before.
(iii) The effect should disappear after the toroid is heated above the so-called Curie temperature: indeed, after holding the toroid in front of a hot-air paint stripper, the resonance is gone.
(iv) It's a mechanical effect, so it should be possible to influence it mechanically: indee, if one squeezes the toroid firmly between ones fingers while measuring, there is no resonance, presumably damped too much.

It's not very useful, but quite instructive...