Does hysteresis still occur if saturation is not achieved in a core?

Question

When looking at a BH curve, what happens if the H field is raised to some level below saturation. For example we apply an H field that is only half way to saturation. On a BH plot this will trace a line from the origin to some positive B value. When we decrease the applied H field back to 0, will we ride back down the same curve back down to the origin? Ie. there will be no hysteresis and we stay inside the BH curve rather than ride outer lines?

Similarly, if a core was previously saturated and is therefore magnetized even when the applied H field is 0, does applying an H field in the opposite direction so that it just reaches the coersive force and then reducing H to 0 demagnetize the core and bring us back to the origin on the BH graph? Or will this demagnetize the core for only as long as the H field is applied?

Thanks

Answer 1

Yes:

From: https://www.researchgate.net/figure/A-family-of-B-H-loops-of-grain-oriented-electrical-steel_fig1_264585820

Query (for reference, further reading): https://www.google.com/search?q=b-h+loop+family

The loop area gets smaller, but not proportionally so; losses vary nonlinearly with amplitude. The modified Steinmetz approximation works well enough for most materials, but does have error on the order of 20% for many. It's just an empirical curve fit formula, with different parameters for each material.

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As for decaying from peak, generally it will trend towards the middle (degaussing), yes.

But, magnetic materials are weird.

I once observed, playing around with a stripwound core, that after applying some DC bias (saturating it to one side), then letting it relax (under AC bias), it would go high impedance (towards the middle of the curve, or away from saturation anyway), then over some seconds, drift back into saturation! This might've been due to leakage current in the AC source (it was an electrolytic coupling capacitor, I believe), but it might've been in the core.

On another occasion, I had a toroidal power transformer, driven by an H-bridge inverter circuit; this inevitably has some DC offset (due to timing errors in switching the inverter), and within some seconds of starting, made an infernal racket -- the core becomes much noisier as it saturates (magnetostriction), translating current into mechanical deformation -- hence it becomes audible. This corresponded with the measured inverter current, which was highly asymmetrical, as saturation current was drawn on one edge of the waveform, increasing inverter losses. The imbalance was then addressed by adding a coupling capacitor with damping, and this worked perfectly fine for new transformers -- but the previously-saturated unit always drifted back into saturation, as though it had taken a "set", a permanent magnetization, or perhaps even stranger had adopted some sort of ratcheting effect where, even though resting field strength might be whatever (depending on when during the cycle it was stopped), it would always gravitate towards that one-side-saturated condition.

NiZn ferrites are also generally recommended to avoid mechanical stressing, and magnetic saturation, lest their (small-signal) properties be altered.