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Really? Are you running the O2 with high gain or normal with the HE-500? At low gain, the O2 isn't loud enough. At high gain, it distorts.
If your HRT Music Streamer ii+ is anything like the non-plus version, it puts out 2.25Vrms. On AC power, the O2's maximum gain = 7 / Vinput. So a gain above ~3.1x is going to overload the input and clip. The default gains from JDS (and most anywhere else) are usually set to 2.5x and 6.5x. So high gain will definitely distort. An O2 definitely gives you enough rope to hang yourself with. Now as to why 2.5x gain isn't enough, next question...
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I have the JDS with stock AC. No one ever told me that I should upgrade the AC adaptor/plug. Why would they ship with a poor supply of power?
JDS ships the WAU12-200 wall wart. This is the default transformer listed for the O2, probably because it's cheaper (under $6) than the alternatives.
On the O2 details page, it states explicitly that if you plan to use power-hungry low impedance headphones (e.g. Hifiman planars), you should use a 14+VAC transformer at 400+mA. Specifically, that means a WAU16-400 (16VAC, 400mA) is probably the ideal O2 transformer for the princely sum of almost $11. You can use up to a 20VAC (with whatever current spec you can find) wall wart with the O2, but anything above a WAU16-400 is likely unnecessary.
I suspect running out of supply power is why the low gain is not loud enough for you. An O2 with 2.5x gain from 2.25Vrms theoretically hits 118dB with HE-500, but I think you run out of (chip) power at around 117dB.
But you could eek out a bit more gain with resistor swaps if you need it. Though it could also be a faulty build, I suppose.
Now back to MDs...
Got any CSD waterfalls for the Alpha pads yet, Dan?