For the start I would consider RC4558 or NE5532
I've picked up the RC4558
Do you plan to use a MCU with a lookup table to correct for the S curve errors ?
Haven't quite planned that far ahead. But I have managed to get a function generator. This morning I hooked it up to the main coil and managed to see a waveform on one of the output coils. It was faint but there. Tomorrow I'll build the audio amplifier circuit to drive the coil properly.
Very nicely wound, very neat and even. Did you do it by hand or did you use some mechanical aids?
I mounted the 3D printed tube to a drill and wound the coils under power. I used a small amount of tape to secure each layer in place which also helped the next layer wind over it neatly. The inductance calculator is pretty handy.
A first test would be with function generator and scope, to get an idea of the signal level (depends on the core) and also suitable core length. The form with 3 coils in series depends quite a bit on the core length. The simpler form would be with only 2 coils side be side and the 3rd coild wound on top in the center, possibly all the way over the others.
Well the first test today was close to this. I input a signal to the centre coil and had the scope connected to one of the side coils. For the core I used a 10mm x 30mm dowel pin that happened to be on my desk. Sliding the dowel pin back and forth did cause the amplitude of the output waveform to vary which I was happy about. A small screwdriver I used to push the pin into the coil seemed to be magnetized to the pin so I used that to move it. I might experiment with other coil configurations after seeing how well 2 seem to work.
For the solution with µC / ADC the drive signal should ideally use the same reference as the ADC.
I've picked up a triple output power supply. I was just looking for a dual rail one but then this one was really well priced. It has +-12v and a 5v supply. I thought I might use that to power the amplifier and a uC.
I've attached a picture of the testing, the oscilloscope shows a good sine wave on the output coil. I had to turn the resolution way up, reading a 37mV peak to peak at around 1kHz! The output voltage of the function generator dropped down a lot when connected to the coil, I think I won't use it to drive them directly haha.