Experiments with the current drive

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The air core should not have current distortion unless it can vibrate mechanically or there is some iron nearby. Do you think this was the case or are we seeing the limitations of the amplifier?
Yes; that's why I wrote "to show approx. measurement limits above ~200Hz".

why would it increase below 100 Hz?
I did not investigate the cause. Like I said, those were done using the headphone output of an audio interface through a 100Ω resistor. It's probably a combination of the headphone amp distorting a bit along with perhaps some thermal modulation of the sense resistor (1/4W metal film).
The main point of that test was to show the odd-order harmonics in the current through the midrange and treble as these are mostly caused by the nonlinear behavior of the steel in the magnetic circuit.