Importance of Linearity vs Other measurements

[ShiZo]

I have a better understanding of the other measurements and what they mean compared to linearity. What is linearity measuring and what is the human audibility threshold?

I know audibility is no concern but from a technical perspective what of a dac that has a linearity till -110 and a multitone test below -120 compared to a dac that has linearity till -120 but a multitone test of below -110? But what is the ultimate importance of the linearity test?

Thanks for any input.

 

[Blumlein 88]

You might want to read this thread:https://www.audiosciencereview.com/forum/index.php?threads/on-dac-linearity-measurement.3754/

This article with illustrations might help too.
https://hometheaterhifi.com/blogs/jj-s-now-and-then-blog-dac-linearity-and-perceived-audio-detail/

Hopefully I'm not going too fundamentally on this. If so, please take no offense, I just don't know which level you are starting out with in your knowledge of linearity.

In a multi-bit PCM digital system, if you start with the largest bit (MSB-most significant bit) it should be exactly twice as high a voltage level as one bit lower. And exactly 4 times the voltage of 2 bits lower.

In the early days of multi-bit DACs there were 16 bits that could be turned on and off in various combinations. It was difficult to make the lower bits the right size. So down at some lower level you might drop down one bit, but the voltage level instead of being 50 % lower, it might be only 30% lower or 70% lower. So when the DAC is playing back a signal these lower bits were at slightly wrong levels which obviously distorts the waveform.

Now over-sampling Sigma-Delta DACs were made for among other reasons because it fixed the low level linearity issue. Most can get relatively close to perfect on linearity. I'll skip over the complex explanation of how they do this. So mostly with modern DACs linearity is a solved problem.

I don't know how to say at what level it is audible or even what it sounds like. Linearity is not important unless a DAC has very poor linearity. Which few do.

Crosstalk is almost never a real concern. LP's which can have good imaging never have better than 35 db crosstalk. It only takes about 18 db for good stereo separation. So a DAC with only 70 db crosstalk would be poor vs others, but still plenty in reality.

SINAD and multi-tone testing will be a better guide to you than linearity and crosstalk.

 

[ShiZo]

You might want to read this thread:https://www.audiosciencereview.com/forum/index.php?threads/on-dac-linearity-measurement.3754/

This article with illustrations might help too.
https://hometheaterhifi.com/blogs/jj-s-now-and-then-blog-dac-linearity-and-perceived-audio-detail/

Hopefully I'm not going too fundamentally on this. If so, please take no offense, I just don't know which level you are starting out with in your knowledge of linearity.

In a multi-bit PCM digital system, if you start with the largest bit (MSB-most significant bit) it should be exactly twice as high a voltage level as one bit lower. And exactly 4 times the voltage of 2 bits lower.

In the early days of multi-bit DACs there were 16 bits that could be turned on and off in various combinations. It was difficult to make the lower bits the right size. So down at some lower level you might drop down one bit, but the voltage level instead of being 50 % lower, it might be only 30% lower or 70% lower. So when the DAC is playing back a signal these lower bits were at slightly wrong levels which obviously distorts the waveform.

Now over-sampling Sigma-Delta DACs were made for among other reasons because it fixed the low level linearity issue. Most can get relatively close to perfect on linearity. I'll skip over the complex explanation of how they do this. So mostly with modern DACs linearity is a solved problem.

I don't know how to say at what level it is audible or even what it sounds like. Linearity is not important unless a DAC has very poor linearity. Which few do.

Crosstalk is almost never a real concern. LP's which can have good imaging never have better than 35 db crosstalk. It only takes about 18 db for good stereo separation. So a DAC with only 70 db crosstalk would be poor vs others, but still plenty in reality.

SINAD and multi-tone testing will be a better guide to you than linearity and crosstalk.

I'll admit I read that article before posting this and it went over my head .

Sounds like linearity is either nailed or not then.

 

[Mnyb]

Also I think the measurment amir uses for linearity filters out some of the noise hence why you can get different dB numbers. supose the DAC can be linear below the noise floor

 

[KSTR]

With Delta-Sigma converters linearity is perfectly fixed by design, even down to the lowest (24th) bit, I have actually measured this. Of course this is buried in the random analog noise + any modulator noise (mind the noise-shaping here) which will kick in way above the lowest bit. That's why the linearity measurement is very tricky to actually show the true linearity in the lowest bits. The simplest technique is using the RMS level measured divided by the calculated ideal noise-free level. The wider the bandwidth the larger the error at the lower bits.

That's why the measured output signal is usually bandpassed at least to be within the audio range, as explained in the link given by @Blumlein 88 . The narrower the bandwith around the test frequency the lower you can get the disturbing noise levels. But narrowing the bandwith to a single frequency also means that you must make sure the test signal is just that frequency which involves heavy dithering once only a few bits are left to build up a sine, so this doesn't truly measure the low bits's individual linearity.

Only way to get the true linearity is heavy time-domain averaging to get the noise below the lowest bit and then you can actually see the individual bits when outputting a stair-case waveform, see here for an example.

Bottom line: With the majority of DAC being Delta-Sigma type, the linearity plot contains no actual information other than the noise floor limit which depends on the exact details of the measurement. Only when something is completely broken you will have any deviation from straight line above the (unknown) noise floor. With non Delta-Sigma design there typically is something happening above the noise floor. Think of it as a simple static distortion which is percetually benign so not much relevance actually (as for static distortion in general).

 

[Blumlein 88]

https://www.audiosciencereview.com/...on-dac-linearity-measurement.3754/post-158703

Here is a post of measurements I performed on a March Audio DAC 1. The linearity is nigh on perfect down to the lowest bit.

 

[bennetng]

Also I think the measurment amir uses for linearity filters out some of the noise hence why you can get different dB numbers. supose the DAC can be linear below the noise floor

Yes. With a stronger filter it is possible to dig deeper into the noise floor. You can do this in Audacity as well.
https://www.audiosciencereview.com/...measurements-of-aune-s8-dac.10486/post-289595