Linearity Talk

Oh!!! Now I see what you are saying (BTW, I just came back from my son's bday party so I was a bit distracted).

Yes, that analog link there can be a bit misleading.

Check this publication also by Analog Devices:

http://www.analog.com/media/en/training-seminars/tutorials/MT-003.pdf

You can see that SNR and SINAD are not the same thing, and they are not related by that full scale and whatever scaling factor. SNR is S/N. SINAD is S/(N+D) where N+D = N+THD = THD+N.

The equations are actually approximations though (they actually depend on input signal in part because distortion does), and like @atomicbob said, hard to really say exactly how things are going to sound just by looking at the numbers. But if the basic numbers are really fouled up, don't expect things to sound great either.

EDIT: Regarding the article, I think I've used that 500 MSPS 12-bit DAC (or similar) in the past. ENOB is important for development (multibit DAC/ADC or not). And 12-bit with 10.5-bit ENOB is somewhat to be expected. If they said 12-bit with 3-bit ENOB I would be concerned because that is pretty shitty. All of the sudden, your system that was supposed to have a range of such an such meters, cannot get you more than a few centimeters (500 MSPS is not exactly audio range). There are no lies. The customer in that AD article was clueless and the dude gave a polite customer-is-always-right marketing like response. On a more serious interchange, that kind of customer remark would be a cause of concern. If it really happened it was definitively a face-palm moment.

 

The article is saying that ENOB = (SNR - 1.76) / 6.02 applies to an ideal ADC or DAC, which would have no distortion because it's ideal. We are not measuring ideal DACs, so we use SINAD, not SNR.

The correction factor in the SINAD equation is for measurements done at levels bellow full scale. You do have enough information to use the second formula because the THD+N @ Schiit's site is at full scale. So you do not need to apply the correction factor because it cancels out: 20*log10(Full scale/ Full scale) = 0.

I'm a firm believer that measurements mean quite a bit. But they will not tell you everything there is to know, nor do they replace subjective evaluation of performance.

As far as Amir, he is aimless. The fact that he is using linearity and a 0.1dB threshold to arrive at bits is enough for most to understand he is clueless.

 

I'm sure Amir would get far better Amir-bitness with 12 daisy-chained ap555s in parallel with 13 dScopes and AC coupled with 7 ap2722's.

 

Geek mode on. @ultrabike / @atomicbob: I was thinking a bit more about this and I do wonder if the method we've been using to derive the THD portion of THD+N (or SINAD) might be incorrect. We've been using THD at 0dbFS. This assumption would work if we assume that THD near the noise floor would be the same as at full output. Should we not take THD at the lowest level where either the signal or distortion components get buried? I was sort of thinking how those camera measurement sites measure dynamic range.

I mean, take at look at @atomicbob's Yggdrasil A2 1kHz sine measurements at -100db. They are pretty insane. And if we take a look at the FFT, there's barely a blip - distoriton components of the 1kHz are well under -150dbFS. Now we could say that AC mains components would lower the number of bits; howeve, the 60Hz and its harmonic components are not going to mask a 1kHz signal! This just points out how complex things really!

 

One could do THD at a few levels other than 0 dBFS. Likely we would have to look at distortion relative to the 1 kHz signal and not full scale.

The number of FFT bins may have to increase as well because some non-negligible distortion terms relative to the input signal my be somewhat buried in the noise. I know non-negligible and buried in the noise don't seem to go together, but again, I mean non-negligible relative to the level of the input signal.

Also, 0 dBFS is not the same across DAC products. Some may actually map 0 dBFS too low (way lower than clipping) or too high (well into clipping).

 

That is not false advertising. 21-bit is the number of quantization bits the DAC has. It's like TI's 24-bit DACs. They are not 24-bit ENOB.

That AD paper you linked where the AD representative was told by a customer that the number of bits was a lie had more to do with the poor understanding of how DACs and ADCs work by the customer, than with poor or misleading specs.

In layman's terms, that customer was an idiot (given it was his job to understand these things).

 

And regarding your 250 MPH analogy, do you expect the GT-350R to do 250 MPH on all types of terrain, slopes and while turning? Do you think tires mater? How about doing 250 MPH with strong winds against you? Really man, get that there are non-idealities that will affect performance.

As an engineer I can tell you I fully expect ENOB to not match quantization bits of an ADC or DAC.

 

Read chapter 1 on this fully please:

https://cdn.rohde-schwarz.com/pws/d...notes/1er03/ENOB_Technical_Paper_1ER03_1e.pdf

 

@winders, resolution can have a lot of meanings. But since you are using that stupid AD link let's get it clear for you.

In that paper they define N in the equation SNR = 6.02 × N + 1.76 dB as resolution. That SNR equation completely neglects thermal noise and non-linear distortion. It only includes quantization noise. On a 21-bit DAC, with no thermal noise or distortion taken into consideration, the SNR is 128 dB according to that equation (which is extremely ideal to the point that it can only yield a rough estimate, and in fact in some case a pretty useless one).

In other words, for them "resolution" is the number of quantization bits. Which in Schiit's case is indeed 21.

Schiit says their SNR is > 119 dB probably because they are including thermal noise. They may not be including non-linear distortion which would make that number SINAD.

Again, my understanding is that "resolution" according to that link for the Yggdrasil is 21-bits, which the Yggdrasil does. Like that link said, the DAC or ADC "resolution" (defined by the quantization levels of the device) will not match actual ENOB performance. Because in the real world there exists such things as thermal noise and non-linear distortion that further degrade "resolution".

 

Furthermore, stop going on the defensive with "now who is confusing ENOB with resolution?".

I'm not posting here to show you how awesome sauce my understanding of the subject is. I'm trying to help you understand what it is going on to the best of my abilities and given time constraints. I'm only human and my patience with those sorts of responses is limited.