Thank you, I don't think I understand though. What would be done with the output of the sync detector?
You create a sync detector with analog switches and an inverting amplifier.
On + phase the positive amplifier is selected and on the negative phase, the inverting path is selected.
Thus you get a sync rectifier output, that can be averaged, and that cancels common mode injected noise.
Do you have a preferred opamp you use for general purpose things?
That depends on your final supply voltages and drive currents.
A drive resistor lets you experiment with voltage or more current-like drive.
I've made some progress today. I built a coil, see below. It's got 3 coils in line, 30mm long each and 3 layers thick of 0.25mm wire, putting each coil at around 360 turns. The tube is 14mm OD.
Nice.
The coils and core type/length will have far more influence on this, than the amplifier choice.
If you have a signal generator, you can get some quick curve-shapes from candidate coil designs, with a scope or voltmeter..
Another approach is two coils, current fed where the voltage developed is proportional to inductance.
Or you can make a local LR Oscillator using something like a 4060 + Analog switch that alternates each coil, every 2^N clocks, to convert L1-> Hi Time & L2 => Low Time, MCU timer compatible.
Do you plan to use a MCU with a lookup table to correct for the S curve errors ?