A few weeks ago I realised that there might be an easier way then to have a antenna analyzer circuit. What if the antenna, for a frequency, is always tuned in the same position of the variable capacitor?

Playing with my magloop yielded exactly that result. Even by changing slightly the geometry, it would still be tuned in the same position of the variable capacitor.

That simplifies the problem greatly. You can pre-record best stepper position for a few frequencies in a band, and then derive all intermediary positions.

PoC done, and now I'm making the build which I'll publish, with steps, when I'm done.