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Re: linearity and signal level

Reply #1
"The Y axis on the right is the output, expressed in dBr. The Y axis on the left is voltage output, corresponding to the dBr values on the right"
32dBr = 4.4V
DAC1 : (-)28dB+32dB= 60dB of DR (90uV to 4.4V)
DAC2 : (-)21dB+32dB=53dB of DR (320uV to 4.4V)
Is my reading correct ?

Re: linearity and signal level

Reply #2
I've come across this web page
and have become confused.
Your suggested (controlled) listening test is not necessary to prove that the linearity roll-off is the cause of the emphasized low level detail.

I'll unconfuse you about this effect (link).
It's pervasive in audio...and beyond
Loudspeaker manufacturer

Re: linearity and signal level

Reply #3
Im not worried (care) about audibility if low level detail is emphasized or not (not the same thing as critisicing abx), just if the lower signals are being pushed up higher (if indeed this does happen) and how this happens.  I feel I don't understand something about signal basics that's why i'm asking. Thank you.

Re: linearity and signal level

Reply #4
... if the lower signals are being pushed up higher (if indeed this does happen) and how this happens.
This would amount to a compression effect if it were real. If the DAC is properly dithered, I don't see how such a thing can happen. The article doesn't show it happening, and seems to misinterpret the measurements.

It is unfortunate that the author calls himself JJ, since that will have people here on the forum think of a different JJ.

Re: linearity and signal level

Reply #5
Hi there.

I've come across this web page
and have become confused. Im not worried about audibility, just wanted to know if this theory is correct (that lower signals are pushed higher). Thank you.

Hmm, let's try to first judge this book by its cover, more particularly the author's name part. It is John E. Johnson, Jr. who is known to me as a long time shill for high end audio who has a reputation for not being the sharpest knife in the drawer when it comes to audio technology. This is not James Johnson AKA  JJ who is not a golden ear, is a true music-loving audiophile, and has an excellent reputation for being right about just everything in audio he deigns to talk about.  He was a researcher for Bell Labs, staryed on when it became known as AT&T labs, then he worked for Microsoft, and lately he is a top manager for DTS.

The title is: "DAC LINEARITY AND PERCEIVED AUDIO DETAIL"   Anybody who understands modern audio technology at a sufficiently detailed level already has those perceived warning bells and sirens going off!

The article is thus fundamentally and inherently flawed right at the title, and it is unfortunately consistently just as flawed to its regrettable title.

The flaw is as follows. Just about  ADC and DAC chip that is sold for audio purposes is a Sigma Delta DAC and they are inherently linear. 

There are a tiny number of exceptions. First exceptions are the  NOS DACs that are based on a chip family from the early-mid 80s that was dropped by the mainstream audio equipment producers because it was too expensive and had some other built-in performance problems.  This chip is typically abused by not being used with its companion chip. The companion chip corrects an inherent potentially audible roll off due to a little known effect known as "The Aperture Effect". This is a way to build a DAC with a built-in high end audio frequency roll off that most people have no idea where it comes from.

In addition to NOS DACs , there are some modern ADCs and DACs that were designed for other communications purposes such as the master modulators in Cell Phone Tower electronics but because they have incredible capabilities along the lines of sample rates, a few of which have been repurposed for audio. As audio devices the better of them are good enough for audio, but of course they are fiendishly expensive. This plays into golden ear supplier strategies because they justify higher prices for wildly overbuilt audio gear.

Getting back to Delta Sigma DACs and DACs they are inherently linear, just as surely as NOS DACs and the Cell Tower refugee chips are inherently nonlinear. Lest you think that I'm suggesting that they are perfect, let me add that instead of inherent nonlinearity, they have inherent noise.  I've done the experiment - if you set up a test jig that stabilizes the noise floor well below that of the chips, a large batch of them will all measure to have just about perfectly identical noise floors, because the noise floor was established when the chip was designed and it is literally cast in silicon.

So let's debug the Ersatz JJ's thesis paragraph from his article:

"DAC 1 is linear down to about -95 dB, where it begins to flatten out. The noise floor is -110 dB. What this means is that all the musical detail that is between -100 dB and -95 dB gets raised to -95 dB. We can’t say if detail lower than -110 dB is raised because that detail is buried in the noise floor."

The reality is that if its one of the 99.9% of modern (built since about 1993) DACs, the DAC is linear at all levels down to the limit for linearity that is set by how many bits it actually digitizes. Below that it is nonlinear, but if it is properly dithered (and for 16 bit DACs proper dithering is hard to avoid in the real world of recording and production) there is no nonlinear distortion and no change to musical dynamics at all.   Can't happen. The properly dithered sigma/delta DAC just does not have any nonlinearity bones. If there is any nonlinearity in it, it comes from the buffer/driver/amplifier  circuits that follow it. Making those clean enough to do a near-perfect job on 16 bit audio is no big challenge, at least until we get to power amp stages and speakers.

Poor technicians may look at the input-output measurements for a DAC and see that beyond a certain point the input level (digital signal) keeps going down, but the output voltage of the DAC becomes asymptotic (that is it closely approaches a fixed value somewhat gradually) to some constant number which is the noise floor.

Voltage meters aren't spectrum analyzers and they don't distinguish noise from distortion. Of course everybody with a brain tests DACs with a spectrum analyzer except for people who are dyed-in-the-wool traditionalists, poorly educated and trained, or have an agenda of making false claims to help people sell overbuilt and overpriced (or at least just overpriced) audio gear.

Now I could tear the whole article apart because it has other serious flaws, but if I can kill it off quickly and easily right at the title...  I believe in being merciful and Federal Regulations for slaughtering dumb animals say: "Be quick".

Re: linearity and signal level

Reply #6
Thanks for the explanation.
So delta sigma dac's are linear right down to there noise floor. Is noise floor the same thing as signal to noise ratio ?.

Re: linearity and signal level

Reply #7
Is noise floor the same thing as signal to noise ratio ?.
It is half of it. ;-)

To find the signal to noise ratio, you need to know the noise level and the signal level, and if you measure them in Volt, their ratio is what you want. If you measure them in dB, you subtract the values (because of the logarithmic nature of dB measurements).

The signal to noise ratio of a DAC is usually measured with the largest sine wave that can be reproduced undistorted. That's the signal level. Sometimes the signal level is taken as some other, lower value, for example in some cases in professional audio where there is a defined alignment level. But no consumer shop would ever do that because it results in lower SNR values.

The noise level can likewise be measured in different ways. The differences here are in the weighting of the frequencies contained in the noise and the detector used. Some people measure with a weighting curve that's flat in the range of audible frequencies (i.e. 20Hz-20kHz), others are using weighting that more closely mimicks the ear's characteristic. It is a surprisingly intricate matter to measure background noise (i.e. noise floor).

The result of all this is that you need to know the measurement method and conditions, otherwise you can't meaningfully compare the resulting values.

Re: linearity and signal level

Reply #8
Thanks for the explanation.
So delta sigma dac's are linear right down to there noise floor. Is noise floor the same thing as signal to noise ratio ?.

As has been said the noise is half of the calculation of the signal to noise ratio (obviously, the largest possible undistorted signal being the other half) but, the cause and nature of the noise floor of a converter is not always the same.

There are four possible sources of noise in a converter:

(1) Noise that is normally added to digital signals to linearize some processing step including the conversion itsself. (dither noise)
(2) Noise that comes from the analog components of the converter itself (thermal noise)
(3) Noise that is inherent in the particular conversion process used  (conversion noise)
(4) Noise that is inherent in conversion of an analog signal into a digital signal (quantization noise)

Article on Sigma Delta Converson

The article states and shows how that adding noise over and above the usual quantization noise is inherent in a sigma-delta converter.

A converter is inherently linear in that part of its operating range that is dithered.  Conversion noise can function as dither if of appropriate shape and amplitude.

The dither and its internal noise as well at Sigma-Delta conversoin noise produce an inhernently linear form of modulation that the article calls Pulse Proportion Modulation(PPM) which is similar to the more familiar Pulse Width Modulation (PWM).


Re: linearity and signal level

Reply #9
Oh great, another "jj".   The article does not understand the difference between step size and noise level.  Having a signal buried in the noise level is not equal to compression of low-level signals.

To say more it would be "complicated" but it's not like compression.
J. D. (jj) Johnston

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