It has occured to me that rather than the complex instructable linked below, it might be easier to purchase an off-the-shelf BTL (high voltage => greater power) amplifier to drive 2W over a small (0.3m dia) air-loop antenna. The AC input signal from the phone's USB DAC is about 0.77V RMS. Let's power the amp with two consumer off-the-shelf 9V batteries in series (18V). Assuming ~1-2 (1.5 here) ohms of internal resistance, the total current draw should not exceed 250mA or the voltage will drop below 8.6V. The loop antenna therefore needs 10 ohms of impedence, and a tuning capacitor to make it resonant (fully resistive). The AC signal needs a coupling capacitor to remove any DC component, followed by a bias resistor to tie the amps signal input to ground. Each amp signal output needs a coupling capacitor because no way will I be able to correctly calculate the tuning capacitance correctly, and also because the antenna won't be a fixed loop. The most efficient use of those 10 ohms is with litz wire, which at 20 awg comes to 300 meters with a 450nF tuning capacitor... which is not happening. Let's shoot for 30m of 20-awg non-litz wire and make up the difference with a 8.8 ohm resistor. 2w across 32 coils @ 10 ohms corresponds to 0.45 A, which at a meter's distance comes to about 0.6 uT... ridiculously tiny. Will it work to activate the circuit? I don't know. However this antenna is simply wasteful - it would be better to switch to a ferrite core design. The magnetic moment of a ferrite core increases more with coil diameter than coil length... but to target 10 ohms resistance at resonance might require a coil length greater than diameter. I haven't really looked into it.
To conserve battery you need an amplifier with a shutoff pin. These are always logic pins (DC on/off), which entails a diode/capacitor/resistor combination tuned to detect and convert AC input to on/off with a configured decay time, i.e. keep the amp powered on for X seconds without signal. Unfortunately the logic pins require high voltage relative to the power source (battery) and 0.77 Vrms just won't cut it. This then entails adding a transistor to shunt power to the shutdown pin from the battery. Then I had a look at a sample schematic of the TPA3116 amplifier, and there are so many pins to wire. At this point the project isn't any simpler than the linked instructable.
I talked to somebody more knowledgeable than I and the hard part about winding your own ferrite loop is determining then balancing the inductance with the tuning capacitor. Measuring equipment is pricey!
To conserve battery you need an amplifier with a shutoff pin. These are always logic pins (DC on/off), which entails a diode/capacitor/resistor combination tuned to detect and convert AC input to on/off with a configured decay time, i.e. keep the amp powered on for X seconds without signal. Unfortunately the logic pins require high voltage relative to the power source (battery) and 0.77 Vrms just won't cut it. This then entails adding a transistor to shunt power to the shutdown pin from the battery. Then I had a look at a sample schematic of the TPA3116 amplifier, and there are so many pins to wire. At this point the project isn't any simpler than the linked instructable.
Then I found this:
https://www.rockvilleaudio.com/headrock/
According to the website it requires a minimum load of 16ohms, but that might be ideal for ferrite-core antennas. Perhaps I'll give it a try!