Fosi DS1 Portable DAC & Headphone Amp Review

[danadam]

When I do the same in REW, (1/3 octave from 20 to 20 k), I can set the level as high as about -8.7 dBV before it clips.

I don't think that says anything about the level of individual tones. Save that signal to a file, load the file to REW's RTA and you should get:

 

[danadam]

I don't think that says anything about the level of individual tones.

Or at least not so directly. What the generator shows is the RMS of the signal. I think this formula applies here for the RMS of sum of signals:
RMS_tot = sqrt( RMS_1^2 + ... + RMS_n^2 )

RMS of a sine is A/sqrt(2) and we have 31 sines, so:
RMS_tot = sqrt( 31 * (A/sqrt(2))^2 ) = sqrt( 31/2 * A^2 )
RMS_tot^2 = 31/2 * A^2
A = sqrt( RMS_tot^2 * 2/31 )

RMS_tot in our case is -8.79 dBFS, but because this is with "Full scale sine rms is 0 dBFS" setting, we'll use -11.79 dBFS = 0.257:
A = sqrt( 0.257^2 * 2/31 ) = 0.065
And 0.065 is -23.7 dBFS. If we zoom in the RTA:

 

[MRC01]

Or at least not so directly. What the generator shows is the RMS of the signal. I think this formula applies here for the RMS of sum of signals:
RMS_tot = sqrt( RMS_1^2 + ... + RMS_n^2 )

Thanks for the link. However, that formula applies only if the waves are orthogonal. Are they? Assuming they are, I got a different conclusion from the same formula -- then later figured it out and got the same thing.

Here's my thought process, because the way in which I resolved this confusion may be helpful to others.

RMS_tot in our case is -8.79 dBFS

That's not my understanding of how the wave generator works. But it is confusing. With a single tone, peak level and RMS are both 0 dBFS without clipping (which doesn't make sense to me). The RMS should be 20*log(.7071) = 3 dB less than peak even for a single wave.

Ah, I found the preferences setting for full scale sine and set it to -3.01 dB, which should be the default. That was very confusing. Now it makes sense. If you have a single tone wave, max value is -3.01. With a 2-tone wave, the highest level you can set is in the tool is -6.02 dB. Because of this, I thought the level you set in the tool is the RMS amplitude of each of the individual waves that comprise the multitone - not the amplitude of the multitone itself, which will be higher.

Assuming this and according to the equation you linked: With 31 waves of equal amplitude I get RMS total = 3.937 A, where A is the peak amplitude of each individual wave. That's because (31/2)^0.5 = 3.937. The RMS amplitude of the multi-tone is about 4x bigger which is about 12 dB - to be more precise, 20*log(3.937) = 11.9 dB bigger than the peak amplitudes of the individual waves. But that's the RMS of the multi-tone, so its peak is +3 dB more, so the peak A of the multi-tone is 14.9 dB bigger than the peaks of the individual tones.

That means when the multitone is just barely reaching full scale, each of the 31 tones that comprise it should be -14.9 dB. I still don't see how this becomes -24 dB for each of the individual waves.

Now let me think ... think ... think like a Pooh-bear... now a couple of hours later...

Alright, that last step was wrong. The RMS amplitude of a sine wave is peak Amp / (sqrt(2)), a difference of 20*log(.7071) = 3 dB. But only for pure sin waves, and a multi-tone is not a pure sine wave. The amplitude we enter in the REW tool must be the RMS amplitude of the entire multi-tone wave - not the amplitude of the individual waves that comprise it. If this is so, then we have to apply the formula in reverse, because each of the individual tones is a pure sine wave, but their sum is not. You did it this way and I didn't know why at first, but now I see why.

My confusion stemmed from 2 errors: (1) the amplitude we enter in the REW tool is the RMS amplitude of entire multitone wave, not the amplitudes of the individual waves in it, and (2) The simple peak to RMS amplitude conversion of +/- 3 dB only applies to pure sine waves.

Put differently: we know the RMS amplitude of the multitone is -11.8 dBFS, now solve for the value of A (peak amplitude of individual tones). And since each of those individual tones is a pure sine wave, you can -3 to get its RMS amplitude - an assumption you can't make with the multi-tone wave as a whole.

This leads directly to the equation you solved, and I get the same result myself: when the RMS amplitude of the 31-tone multitone is -11.8 dBFS, its peak amplitude is 0 dBFS and the peak amplitudes of each of the 31 tones is -23.7 dB.

 

[MRC01]

So compared to a single tone, the multitone test can go either way: the device can produce higher distortion or lower distortion (or the same).
...
So this Fossi looks like it's "the same" or close to that. Single tone shows about -100 dB and multitone around -110. But that -110 is the overall level of the peaks of the "grass". You need to add (roughly) 9 dB to that to get the overall level of their sum, which is about the same as the -100 dB of the single tone.

I'd like to apply the above lesson and correct my comparison of the Fossi's distortion single tone vs. multi-tone. Multi-tone, the tips of the "grass" are just reaching about -110 dBr. If you sum that up it's going to add about 30 dB making -80 dBr overall, and since the tones are at about -24 dBFS, that makes about -104 dBFS. Its single-tone distortion measures about -100 dBr, about 20 dB better than the multitone.

I have another device I measured recently, based on the WM8741 DAC that goes the opposite way. It measures about -80 dBr with a single tone and -96 dBr with multitone. Here, the multitone is about 16 dB better than single tone.

 

[Descartes]

So which one is better the DS1 or the DS2?

 

[Holy Spirit]

Works with Linux.