How to balance antiphase Rx coil in metal detector?
For the Thermo metal detector I designed, I used an input transformer to act as a Balun. The reason is because of electric field asymmetry when connecting a normal oscilloscope probe directly to the anti-phase receive coil output.
The two wires from the anti-phase receive coils must feed into either a differential amplifier or a balanced input to maintain electric field symmetry or, you'll never adequately balance the receive output.
Get your self a little ferrite core and use 5:5 windings is my advice. On my design I think I implemented something like 3:15 step-up so that the tuning capacitance on the secondary was 25 times smaller in value.
You don't need to use a centre-tap on either winding.
As you design progresses, what you will find is that the Balun ferrite core will cause some unwanted phase shift with temperature changes and, your tuning will slightly move causing a small phase change in your received signal. This is because the ferrite core material has a temperature dependency. To counter this, you will need to use a gapped ferrite core probably made from something like 3D3 ferrite material.
You're not at this stage yet so don't worry about it.