Hello,
Today, I have worked with Marc-O on the amplifier for the receiver.
We succeded in designing an inverting band pass filter. This filter is very selective and give use an amplification of 20dB at 20kHz.
Then, we gain an other 20dB by using the resonant frequency of the RLC circuit.
As a result we have an amplifier of 40dB.
With 12mA in the coil, we measured a tension of 180mV at 30cm :).
And we can compare this result to what the amplifier of the Hydra should look likes.
40 dB gain seems quite good. I would suggest not to aim much higher to avoid self oscillation ( some of the signal at the end of the amplifier leaking to the input=> oscillation).
Your goal is to have a signal at least a few lsb of your adc ( in fact, you can go lower using oversampling and dittering).
You can then use digital filtering to recover the received signal.