Transformers??

Phil Hobbs, you have put a term on something I ran into in tech school 40 years ago and never found a discussion about it since. The term is small-field nonlinearity of the core. At the tech school each student was given a 5 Henry choke and ask to measure the impedance. as I recall we used a frequency generator, the answers the class got calculated out something like a .15 Henry choke. Teacher didn't care, no other students cared. I went on a mission. That's when I learned about B/H curves and slope of the curve. I concluded the frequency generator output was so low that we were measuring very low on the B/H curve. I've always wondered why transformers at the input of a radio* work when they still follow the rule of 4 times the impedance of the stated use impedance. Ex: 50 ohm system, transformer primary 200 ohm at minumum frequency of use. Mikek

It's worse than that. When they give B-H curves (when they even bother to..), it's the single loop hysteresis model.

So tell me: where's the initial permeability in that curve?

The real measurement is called a butterfly curve: it pinches in the middle. I've never seen one published for an actual material. Purely academic, so it would seem.

Micrometals has graphs of incremental permeability versus AC flux density for most of their powder core materials, which is handy to illustrate. Those are more modest, with the worst offenders only being like +10% of zero bias.

There's also the matter of AC permeability and losses versus DC bias, which is broadly ignored and forgotten in much the same way. This one can be significant because some materials (powder materials I think?) have 2-3 times higher losses under bias.

In this case, they are already defined for small signals. (Keep that in mind next time you specify a ferrite bead -- even the really massive ones (SMT chip or bead-on-lead) saturate in the 100s of mA range.) It also helps that the lower-mu ferrites are essentially partial air-gap, so they are less nonlinear than others.

That would be a nasty surprise, if your tuning coil shifted in an amplitude-dependent manner, but that's also quite rare; the RF powder materials are usually well behaved. And quite low mu (lots of distributed air gap).

You definitely don't want to, say, build an IF strip with medium or high mu (ungapped) ferrites. Resonance in saturation is interesting: as you drop frequency from above resonance to below, you observe a small blip. You would think gain is small and inductance is high. Now raise frequency through the same range. It toes in the same way, but continues rising, higher and higher: until, snap, oh, no more resonance for you! Hysteresis loop in frequency response. Nonlinearity, state dependence! Augh! :-)

Tim

Acrually, *if* your load is resistive the core becomes in quadrature so what looks terrible at 4 to 1 actually isn't so bad at 16 to 1.

That is the impedance is sqrt(50^2+200^2) in quadrature, so not so bad

Yup. It's often miscalled remanence or coercivity, but both of those effects can exist with no zero-field nonlinearity. It's much more analogous to static friction.

The stickiness magnetic domain motion also gives rise to Barkhausen noise in magnetic heads.

Cheers

Phil Hobbs

No! The transformer's inductive reactance appears in parallel with the load resistance, so you'd add the *admittances* in quadrature. You are correct that the nett impedance is not too badly affected, though.

Jeroen Belleman

True, I wrote that super sloppy. Ok, this is a 50 ohm transformer with 200 ohm reactance core. With 50 ohm source and 50 ohm load, that's a 25 ohm 'net' parallel impedance to a 'reactive' 200 ohms in parallel, or approx sqrt(25*25+200*200) which "... is not too badly affected, though."

Add admittances, not impedances! So 1/sqrt(1/25^2 + 1/200^2) = 24.8 Ohms.

Jeroen Belleman

Ok, but less sloppy his time. By now, I'd just stick into LTspice modeling and be done with it.