Glad to hear your "plumbing work" is going well. Get that all fixed up so you can do some detecting!
Having more batteries in the control housing doesn't equate to necessarily having a higher power coil and transmitter. By using the headphone amp of the codec as a transmitter, Minelab is able to generate more than 20V peak across the coil, from a source of 3.3V.
I happen to believe that George Payne is one of the best (if not THE best) at understanding and explaining how metal detectors work. Here are exerpts from a couple short articles where Mr. Payne examines transmit voltage and sensitivity:
For metal detectors there are a ton of items that effect overall target sensitivity. But I would like to discuss the one I consider the most basic and least understood. Also, it was overlooked for years as a way to increase detector detection depth. In the following explanation the coil is in parallel with a capacitor to form a loop tank circuit. Also, the loop and capacitor combination is driven by an oscillator at the tank resonant frequency. The loop magnetic field strength at a particular point is related to what is called (amp) times (turns) or AT. This is the loop rms current times the number of turns in the transmit coil. You can have a Xmit coil with one amp and ten turns for 10AT. In another coil you can have 10 amps flowing with only one turn. The result again is 10AT. Both of these coils would produce the same sensitivity if used as a transmit coil in a loop because both are rated at 10AT. The air sensitivity of both coils would be the same. However, the coil impedances are entirely different. To establish the required current, 1 amp for one coil and 10 amps for the other, each coil would require different drive voltages. In this case the coil with 10 turns would require a much greater voltage across it to develop the required current. In other words, these coils would require two different voltages for operation but the resultant detector sensitivity would be the same in both cases.
The AT produce by a coil is a function of the coil turns and loop voltage. It has nothing to do with the operating frequency. It