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.
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!