Think of driving two elliptical coils in range of 50-200kHz with high VAR at resonance and measure the difference in current for series or voltage parallel tuned after balancing each to a null difference. Stepup auto transformers are allowed .
The phase shift and amplitude difference is essentially the differential impedance of each coil as it is waved past the gap between the planar coils, but measured in PPM changes in impedance.
Think how you would do this using PLL's and differential amplifiers such that the SNR is > 60dB using PLL's
Then you can detect a pin at 30cm distance. The loop diameter is most sensitive when > than the distance of the ferrous metal. that alters the Impedance of the reflected H field which loops orthogonal to the magnet wire loops. Litz wire will raise your Self Resonant Frequency (SRF) .
As well guys as I have many hours spend building homemade detectors, let me tell you some things.
The coil is criticall - you can't ballance it propperly without an osciloscope as well a good coil is tough to build.
You have to use a high quality epoxy resign, it must be shielded to prevent the capacitive effects of the ground.
If you are not very good in building equipement I would not recomend you to start with this. You can get a good detector for several hundred dollars.
This is the best detector for the money from a very popular bulgarian manufacturer: http://www.goldenmask.eu/
Search "Golden Mask metal detector" in youtube
If you have something very high end get XP DEUS - the best of the best.
If you need for the beach get some Minelab E-Track or a good PI detector.
All depends what you need. Tell me and I will give you the best advise.
These seem to be similar to US metal detectors for $250 using 18kHz.
coil must be rigid so inductance does not change with vibration. The common tap connection for both coils are driven equally, to detect a differential Impedance change. with amplitude and phase shift amplified to sound or log meter.
The limit of a good metal detector is about 30 cm in soil with low mineralisation for 1 Euro coin. The equivalent of this is about 40- 45 cm air drtrction. This is impossible for 90% of the mass produced detectors. Building a deep detector is an art. I've spend many hours tuning the electronic and ballancing the coil of my last detector and it is deeper then my e-track.