Help with a math problem to determine SE output on a Sabaj A20h Amplifier

[Dunring]

I have a Sabaj A20h amplifier, but the only power output ratings are for the balanced outputs. The email to Sabaj bounced with an error, so I took what measurements I could. Here's the factory numbers for balanced: 4W(16Ω), 2W(32Ω), 1W(300Ω), 500mW(600Ω) I'm using the SMSL M300 DAC in DAC mode (not preamp, full power).

I set a 200mhz test tone and put the Hifiman Ananda in the same spot to measure with a decibel meter phone app. On XLR it measured 60db and on the single end 54db with everything else being the same. I know 6db either way could double or halve the volume, but most amplifiers I've seen only have 1/4 the power on the single ended side. Is there a formula to solve for SE output power using the known numbers? I have a spare to send in for measurements, but for now just using what I've got. Just got a new DT880 250 ohm in a few minutes ago (I get 4-5 headphones a week) and at -10 volume in medium gain it's about as loud as I'd go, amazing power but trying to pin down the SE number.

 

[NTK]

Power is the wrong metric. Output levels (SPL) of headphones and speakers respond to signal voltages*. Since the SE voltage is usually half of BAL, it is -6 dB (=20 * log10(1/2)) compared to BAL, which is reflected in your measurement.

* Power is the amp output voltage multiplying the current draw, which depends on the load as current = voltage / load impedance.

 

[DVDdoug]

-6dB is half the voltage (or half of the digital amplitude) and 1/4 of the power.

Power is calculated as Voltage X Current.

Current is proportional to voltage (and inversely proportional to resistance or impedance).

So when you cut the voltage in half you also cut the current in half for 1/4 of the power.

 

[djtetei]

The SMSL A300 dac unbalanced output level is 2 V RMS.
Sabaj A20H headphone amplifier, on unbalanced inputs to unbalanced outputs circuit, has the following gains: 0 dB (low), 6 dB (medium), 9 dB (high).
For a load of 250 ohms, Sabaj A20H should deliver the following power outputs:
- on low gain: 16 mW
- on medium gain: 63 mW
- on high gain: 127 mW
For a desired listening level of max 110 dB SPL, on Beyerdynamic DT 880, on medium gain, the Sabaj A20H headphone amplifier will have a headroom (power reserve) of 4 dB.