Hi Ray
I'm not going to give you the details YOU have the net for that and it would take me far to long but here is a brief description. BFO = beat frequency oscillator - two frequency's perfectly balanced a reference frequency set at round about 400hz and the coil frequency set at 400hz when the coil is passed over a metallic object the coil frequency will change causing an audio signal. (frequency is not so important but the balancing is)
PI = pulse induction this one is self describing a large magnetic pulse is created by sending electric pulses into a coil when the pulse is off the detector is listening for eddy currents should there be metal in the ground an audio signal is heard.
VLF = very low frequency generally it operates from 4Khz to 18Khz depending on what the designer had in mind this detector works on an audio frequency it consists of three coils a RX coil a TX coil and a bucking coil.
There you go now I suggest that you hit the net to get more info. You will see that there is a lot of reading up to do and even more if you want to understand how they work. Have fun it's a great subject
Regards Xavier
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Xavier