Hmm, still trying to make sense of this tbh but I read it differently.
I think we can both agree that optimum SINAD is achieved at 1V and 0dB attenuation but that likely to be very loud. However, if the objective is to reduce the signal voltage by say 10 times, we could divide the digital signal by 10 in a dsp and let it output 0.1V and use 0dB on the volume IC, that would get us 0.002% THD + N...however if we choose instead to keep the DAC output around 1V and attenuate in the volume IC by 10dB (as I believe is the normal way unless something fancy or hybrid is happening) we get around 0.001 % THD + N i.e. half the distortion.
Your math is not correct. Don't forget voltage ratio in dB is in log scale, so -10 dB is not the same as 1/10. Even if we do it your way, if you calculate it correctly:
From Amir's measurements, at 0 dBFS, volume 82, the pre out voltage was about 2 V, so for 1 V, volume will be 76, with 0 dBFS, (voltage halved for every 6 dB drop)
If you reduce the volume IC output by 10 dB from 1 V, then the pre out voltage will be 1*(1/√10) = 0.316 V, that's not at all!
So, of course the THD+N would be lowered if you drop the pre out voltage to 0.316 V, compared with that for 1 V.
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As I said before, it is better, simpler to just look at those two curves I posted, as they are the actual curve from the volume IC's data sheet; and you can see that if you lower the input signal level by 20 dB, from say,
1 V to about 0.1 V (your pick), THD+N drops from about 0.0002% to about 0.0023%, or SINAD of 97.7 dB
Now if want to keep the pre out voltage at 1 V, again, the volume will have to be at 76 (voltage halved for every 6 dB drop)
So, in order to drop the pre out voltage from 1 V to 0.1 V, the volume will have to be attenuated by 20 dB, from the curve, that is, from 76 to 56. In this case, you can see that for pre out voltage to drop from:
1 V to about 0.1 V, THD+N drops from 0.0002% to about 0.0013%, or SINAD of 93.98 dB.
To conclude:
A) If we keep the volume the same, that is 76, in order to get pre out voltage of 1 V, and vary the input signal from 0 dBFS to -20 dBFS, SINAD drops from 0.0002% to 0.0023%, or SINAD of 92.77 dB
B) If we keep the input signal at 0 dBFS, and vary the volume from 1 V to 0.1 V, that is -20 dB on the volume setting dial, SINAD would drop from 97.7 dB to 92.77 dB.
A) is the old method, and B) is the new method Amir used on measuring the 4800, that that means if Amir had used the same method, the 4800 would do a touch better under low level listening conditions, all else being equal. The new method, based on this example, using you choice of 1 V and 0.1 V, the old method would do better by 4.3 dB at the 0.1 V level. Again, that is opposite to what you seem to expect. We have opposing results!!
Regardless, since the AKM4700 has a better DAC, it is very likely that overall, it would still do better under all conditions including low level listening.
So our conclusions are different, quite the opposite.
Thats just the start though, now if we choose 0.01V DAC output vs 20dB attenuation we get 0.02% vs 0.003%. Almost an order of magnitude difference. Much better to attenuate than to reduce the incoming signal.
At 3 orders of magnitude the effect is even bigger at 0.001v@0dB = 0.2% vs 1V@-30dB = 0.01%. I read this as favouring use of the volume IC vs lowering the output in the DAC.
That of course is only considering the effect at the volume IC part of the chain. I would expect that a lower signal coming from the DAC would also have a much worse signal to noise ratio than a high signal which IMHO would further reduce SINAD
Again, to me, your calculations are not correct, so your numerical example do not represent an apples to apples comparisons.
The relevant formula used in my numerical example are included in the following linked calculators:
Decibels to Voltage Gain and Loss convert calculation conversion amplification amplifier electronics - sengpielaudio Sengpiel Berlin
Gain and loss - damping and amplification in dB voltage conversioncalculation amplification amplifier electronics - field parameter - Eberhard Sengpiel sengpielaudio
www.sengpielaudio.com
THD to dB - convert percent % to decibels dB percentage voltage % vs per cent converter THD+N total harmonic distortions calculation signal distortion factor attenuation in dB to distortion factor k in percent decibel damping - sengpielaudio Sengpiel
Calculate THD and distortions decibels dB to percentage % per cent percent voltage % vs converter and dB signal distortion THD+N total harmonic distortions factor attenuation damping - Eberhard Sengpiel sengpielaudio
www.sengpielaudio.com