Beef-O-Matic Metal Detector

The BEEF-O-MATIC is a beat frequency oscillator (BFO) metal detector based on the design at http://www.easytreasure.co.uk/bfo.htm, which should be regarded as the primary source of information. Here is my take on things.

A beat frequency oscillator metal detector works by having two RLC circuits, each oscillating at around 100 kHz. The inductive elements in these are hand-wound coils typically made from enamelled copper wire of about 33 SWG. One coil (the search coil) is essentially flat and has a large diameter (say, 15 cm). This coil is sensitive to the presence of metal objects as discussed below. The second coil (the reference coil) is wound much more tightly (diameter < 1 cm) like a solenoid. This coil is arranged so that the inductance can be adjusted, for example by turning a brass nut. In operation, the reference coil is adjusted until the beat frequency between the two RLC circuits is at an audible frequency of about 100 Hz. This heterodyne signal is amplified and fed into headphones, so that one can listen for changes.

Let's think about this...

The inductance of the search coil is L ~ n²Dµ where n is the number of turns, D is the diameter, and µ is the permeability. However, I don't think this is what counts here. What counts so far as I can see is that the magnetic field lines spread out around the coil in a volume ~ D³. If we now insert into this volume a metal object (essentially, with infinite relative permeability compared to free space), the inductance should change by dL / L ~ V / D³, where V is the volume of the object. The RLC circuit frequency ~ 1 / sqrt(L), so this should correspond to a fractional change in frequency of the RLC circuit of about half this amount. Now let's work backwards to see what this means. Suppose we can hear changes of about 10 Hz (this is about the difference between two notes on a piano). In terms of the primary search coil, this corresponds to a frequency shift of 10 Hz / 100 kHz, or 1 part in 10⁴. Hence we should be able to detect metal objects with volume V ~ 2×10^-4 D³. For a coil of diameter D = 15 cm, this works out to be V ~ 0.5 cm³, which is about the volume of a 20 pence piece. And indeed, the detector can find a 20 pence piece underneath the search coil, so long as it is within a few cm of the coil.

The BEEF-O-MATIC is constructed largely following the instructions at http://www.easytreasure.co.uk/bfo.htm. The tricky bits are the coils. For the search coil, I cut the top off a 15 cm diameter plastic food container, which had a handy groove for winding the coil. A chopped down plastic ruler plus a plastic toy golf club were taped together to mount the search coil in a convenient assembly. For the reference coil, I followed the suggestions on the easytreasure web page very closely. The coil was wound on a short length of wooden dowel, which was inserted into the plastic side entry arm of a cheap ball valve assembly. A brass nut threaded onto this provides the tuning capacity. Suitable brass nuts can be obtained from plumbing supply shops. The actual electronics assembly is not that hard. In practice I found the amplifier stage can be truncated. The circuit diagram is shown here:

Note that the clock speed in a modern CPU is > 1 GHz so that 100 kHz is practically DC from the point of view of modern electronics (the CPU in your laptop will have done > 10,000 clock cycles in the time it takes for the RLC circuits in this project to undergo one cycle!). This is convenient as it means that a basic (eg, 20 MHz) USB oscilloscope can see what is going on. In this case a Hantek 6022BE two-channel 20 MHz (48 MS/s) USB digital storage oscilloscope was used to check the behaviour during assembly:

Here are some images of the device, which is very basic but importantly lightweight: