An analog section for the PCM1794 DAC

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OK, Ken.
I'm bad at using software to draw things and I didn't want to attach a picture of some hand drawing so I tried to explain what I meant with plain text. ( Perhaps you can recommend some software ).
I'm copying it directly:
And please, do not get hooked by some minor error in my presentation. Try to figure out the general idea about this matter.

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About low level, high frequency shortcomings of a sigma delta DAC


Let us consider a hypothetical sigma delta converter that operates with 16bits. It updates it's output with a rate of fs*128. It has furthermore no hardware bits, so the signal is made up with just one bit.
Let us also assume that it operates with an fs of 44100hz.

When it idles, it outputs a constant bit-stream that is made up from the pattern 1,0,1,0 etc... In this way it settles at Vcc/2, which represents a zero.

Now consider this special case: We will feed the DAC with the following sample series:

1,-1,1,-1,1,-1 etc. This will output a 22050hz wave with the minimum possible amplitude: -96db.
Wrong. Why? Simply because it can't. Look at the following bit-train which shows a plausible pattern that represents the weakest possible signal.

Bit0: 0, 1, 0, 1, >1<, 0, 1, 0 ….... bit128.

Notice the “>1<” bit.
The DAC tries to output the lowest value it can by flipping one of the bits from 0 to 1. When this bit-train is integrated the sum will be ( over the actual sample that is comprised of 128 bits ) 1/128 of the maximum output which is 32767. When the "-1" bit is calculated it must flip at least one of the 1's to 0.
The resulting signal cannot be weaker than -21db and the DAC probably outputs zero's instead. That depends on the S/D algorithm.
The important thing is that when the signal is stronger or the frequency lower, the averaging algorithm start to do it's tricks in order to achieve a full 96db range.
So the DAC cannot deliver such a weak 22050 signal. Actually, it can't deliver a 10khz signal either.

The sample input will be:
1,0,-1,0,1,0 etc. Now it has 256 time slices to produce a -96db signal but can't represent a lower value than -27db.

Still, when you hook up the converter to a scope or THD analyzer the outcome will be very good, assuming we have not too high frequency or too low signal. These things are hard to see on a normal oscilloscope since the signal is very weak and the S/D algorithm probably tries to solve the problem by introducing occasional zero samples that will trig the scope.

This is one special case where the S/D devices are questionable. They also have problems with settling when a signal rapidly changes amplitude. But that's more complicated to describe, so I chose this low level issue example.

I think the nice figures of sigma delta devices are misleading. Graphs can be shown that the noise will be transferred very high up in the hf region. But the limitation is in low level hf performance. The hf noise is not very important since it is easy to filter away.
Still people reports perceived sound differences between DAC brands. This may be due to the way the SD algorithm works when it tries to achieve good low level performance.

Finally, I must again stress that this discussion is about sample to sample changes - the averaging S/D process will of course smooth things out if it gets a sufficient number of samples to operate on.

One may of course think that the SD devise is sufficiently good taken into account our limited ability to hear such high frequencies.
But - this is important - recent research in the psychoacoustics area has shown that human hearing is much more dependent on accurate phase when it comes to detecting air pressure attacks and decays. Some data indicates that our hearing can detect a phase relationship down to 1 us.

check out:

YouTube
 
...Still, when you hook up the converter to a scope or THD analyzer the outcome will be very good, assuming we have not too high frequency or too low signal. These things are hard to see on a normal oscilloscope since the signal is very weak and the S/D algorithm probably tries to solve the problem by introducing occasional zero samples that will trig the scope...I think the nice figures of sigma delta devices are misleading. Graphs can be shown that the noise will be transferred very high up in the hf region. But the limitation is in low level hf performance. The hf noise is not very important since it is easy to filter away.

Svitjod,

I can appreciate the intutively logical thinking which led you to develop your conclusion. Unfortunately, one of the truths of DSP science is that it is often non-intutive. Which is why the underlying math is so important.

Regarding your example, it appears to me that your have either ignored or largely discounted noise-shaping. Noise-shaping is what makes SDM practical for HiFi audio application. However, rather than us engaging in an conceptual theory debate, or even a mathematical one, I suggest that we simply look to the actual objectively measured results as the final judgement on what does or doesn't perform as advertised. You do acknowledge the good measured performance of SDM, yet then mysteriously dismiss the same without explanation.

As measured via spectrum analysis, HiFi application SDM shows good to excellent dynamic range at 20KHz. Far better than the 27dB you conclude as the limit for an 128Fs system. This good to excellent performance is mostly due to noise-shaping. Simply search Google for images of spectrum graphs within various SACD player reviews. Even though SACD is an 1-bit system at only 64Fs (aka; DSD64), you will still typically find the 20KHz D.R. measured as near 90dB. DSD128 and DSD256 offer progressively greater D.R., while PCM input SDM based DAC chips intended for HiFi utilize multibit quantizers typically offer even greater D.R.. Simply see the spectrum graphs provided in the datasheets of any of the better current production multibit DAC chips, such as the PCM1794A.
 
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Hi Ken

I'm tickled by Svitjod's arguments as I've seen very similar ones from Thorsten Loesch who's normally on the ball. Plus they do chime in well with my subjective impressions of various DACs of S-D flavour (ESS, Wolfson) - they do seem to have 'noisy treble'.

My question here is - how do we measure a DAC's dynamic range at a particular frequency? You mention measurements showing 90dB DR but do you know how those were done? A single frequency has zero bandwidth so presumably we'd need to consider a single bin in an FFT which does have finite bandwidth. What we need to know is what's the noise associated with the ~20kHz signal, assuming that the noise is close-in to that signal.
 
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Guy's, I was fairly eager to read your reactions. But I didn't hope very much. I was pretty sure that Ken would be skeptical, but I had a little more hope on Abraxalito. And I was right!

Ken, the thing is; to settle this issue we have two choices. The first is that you really ponder what I was trying to show. I think it's like the pictures that was popular some 25 years ago that consisted of strange dots scattered out. But if you focused hard enough a couple of minutes, suddenly a sailing ship in three dimensions was visible.


The second method is to feed a software simulator with a proper selected pattern of samples and observe the output. Some time ago some Marcel mentioned a pascal program that did just that.
The testing conditions must be exactly the following:

Feed the DAC with -1,1,-1,1 etc... for a sufficient long time and observe the output. Sufficient long time means it must be so long that the output stabilizes at a regular bit pattern.
Or to give it a more reasonable challenge: 10, -10, 10 etc.. that wont work either.
The proper output would be a signal of -76db. But that theoretical device cant output below -42db ( I wrote -21db above which was an error )



GUY's !!!!!!!
Make an effort! Think hard ! What if I'm right!?

Strange, when I first heard of sigma delta DACs some 25 years ago, I was immediately struck by this, but assumed I was wrong. Since then I have constructed several DACs and along the time I have been more and more convinced I'm right. I cannot measure it - I don't have accurate enough equipment.

We must settle this. Anyone with a simulator?

Finally, one last picture. How can we ever represent a value below -42db if we only have 128 time slices to integrate the signal.
And....
We only have 128 time slices since the next sample must represent another, equally weak signal with the opposite sign.

Actually, I really hope that someone can prove me wrong. If so I wouldn't resist the temptation to find out how such a miracle can happen. That would be truly humbling and that's what I need since my ego is fairly large.
 
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I can't resist coming up with a very subjective point of view.

I have an old PCM1704 equipped DAC that's beefed up in every aspect. It's as good as it can get, simply. Home brewed.
I have also a PCM1794 DAC. That one is also equipped with everything you can imagine. A good supply, jitter free source, shunt regulators, a discrete analog section. Home brewed of course.

Every time I reconnect my old PCM1704 DAC to my B&W804D etc... stereo after listening to the PCM1794 DAC, I'm really struck as by lightening.

It's simply no match. Everything becomes pure poetry.

But of course, this may be 100% placebo and doesn't prove anything. But it's perhaps a hint.
 
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Right.

I made some random search on S/D theory. It seems that the experts are so fixated on noise shaping that they perhaps has forgot this issue. Remember that it's not good for the public to know this, since it will make things much more expensive, suddenly.

I found this on a document:


4.4 multi bit converters
Multi bit converters have two main advantages over the signle bit one.
1. A higher performance: In fact, having the same OSR and the same order as a
monobit converter, the multibit converter could achieve a higher signal to noise
ration for two reasons:
• According the linear analysis of a Σ ∆ converter, the adding of a single bit
to the quantizer is equivalent to an SNR improvement of 6 dB.
• Besides, as we have seen before, the NTF constraint is less limiting for
multibit converters.
2. A better resolution: In fact, the output of the converter is closer to the desired
output. However, the main inconvenients of multibit converters is that the DAC
cannot be made perfectly linear since it is impossible to manufacture DAC’s
element sources with exactly the same step size


They actually confirms that the resolution will be improved in multibit converters!
In this case multibit SD devices.

http://www-soc.lip6.fr/~hassan/SD_simulator_kammoun04.pdf
 
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Actually, for me, the whole thing is confirmed now. I can withdraw from the diyaudio scene in peace.

But do the simulation! And spread the gospel of multibit DAC's.

In this world of smartphones and digital stress we will certainly need to go back to a meditative living. This includes a good stereo.
Actually, I don't even listen to my car stereo. I simply can't stand bad sound. It's better to listen to wheels and the wind and an occasional wasp hitting the screen.
 
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I had been looking into these claims just recently, again.
By the use of software upsampling to DSD, and using a DAC in DSD direct mode, so not even using the multibit output modulator. Again: the dac structure in the tests is a 1-bit classic SD configuration.
I had a look at the direct, time domain output signal so much cited as a final proof of the bad quality. Taken also by an analog oscilloscope. In the same time had taken the FFT spectra as well.
They both confirm the claims about the quality of DSD direct out signal -- to be false. Not valid any more for modern DSD applications. There is nothing wrong with it, even in 'objective' instrumental analysis.

http://www.diyaudio.com/forums/vend...4490-usb-dac-dsd-support-149.html#post5287551

Ciao, George
 
Hi Ken

My question here is - how do we measure a DAC's dynamic range at a particular frequency? You mention measurements showing 90dB DR but do you know how those were done? A single frequency has zero bandwidth so presumably we'd need to consider a single bin in an FFT which does have finite bandwidth. What we need to know is what's the noise associated with the ~20kHz signal, assuming that the noise is close-in to that signal.

Richard, that's a fair question. I don't believe that the details of exactly how those spectrum analyzer tests were conducted are typically published with the product reviews, or even the device datasheets. I have to believe, however, that any improper or misapplied test procedure giving the mistaken impression of a high level of SDM performance would have been identified decades ago by the many industry customers utilizing such converters.

The objective reason for the subjective perceptual differences between an SDM and an straight multi-bit DAC that both feature excellent in-band measured performance is another matter, however, and remains yet one more audio mystery.
 
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Guy's, I was fairly eager to read your reactions. But I didn't hope very much. I was pretty sure that Ken would be skeptical, but I had a little more hope on Abraxalito. And I was right!

Ken, the thing is; to settle this issue we have two choices. The first is that you really ponder what I was trying to show.

The second method is to feed a software simulator with a proper selected pattern of samples and observe the output. Some time ago some Marcel mentioned a pascal program that did just that.

Svitjod, I have pondered it. I believe that I understand your argument. It is an intuitively logical theoretical argument. Which is why I suggested that we avoid an conceptually theoretical debate, and simply refer to what should be the final arbitur of the objective (setting aside the subjective) performance. Theory which conflicts with observed results (measured performance) is rendered faulty. Again, I'm not addressing subjective listening performance. I should also clarify that I'm not advocating for SDM over straight multibit for audio listening.

Simulations are also proven faulty or incomplete if they conflict with actual properly measured results. Anyone designing circuits in SPICE and then building the same circuit has experienced that to be true. Assuming a validly conducted test prodecure, of course, theoretical arguments or simulation results counter to the measured results are necessarily proven lacking, yes? I also continue to assert that you appear to have completely ignored noise-shaping, which is the key to HiFi audio SDM, in your analysis.


GUY's !!!!!!!
Make an effort! Think hard ! What if I'm right!?

Actually, I really hope that someone can prove me wrong. If so I wouldn't resist the temptation to find out how such a miracle can happen. That would be truly humbling and that's what I need since my ego is fairly large.

You seem to assume that if we disagree with your analysis or conclusion it must be because we have not thought about that argument hard enough. Well, that might, or might not be so, but isn't particularly relevant if we have access to actual measured results. Which, we do.

Those familiar with me know that I'm not much of an objectivist. I believe that when it comes to music reproduction, human listening enjoyment should supersede the objective performance metrics when the two conflict. However, you presented an objective performance analysis, so, the objective results are the final arbitur.

You need not hope someone can prove you wrong, because the actual measured results prove you wrong, don't they? Hopefully, you're only joking about having a fairly large ego. My experience is that, the more one learns the smaller one's ego becomes, as the extent of knowledge yet to be acquired becomes more obviously apparent. Conversely, I've found that large ego's are usually the product of large ignorance. I sincerely hope that doesn't apply to you.
 
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Guy's, I was fairly eager to read your reactions. But I didn't hope very much. I was pretty sure that Ken would be skeptical, but I had a little more hope on Abraxalito. And I was right!

Ken, the thing is; to settle this issue we have two choices. The first is that you really ponder what I was trying to show. I think it's like the pictures that was popular some 25 years ago that consisted of strange dots scattered out. But if you focused hard enough a couple of minutes, suddenly a sailing ship in three dimensions was visible.


The second method is to feed a software simulator with a proper selected pattern of samples and observe the output. Some time ago some Marcel mentioned a pascal program that did just that.
The testing conditions must be exactly the following:

Feed the DAC with -1,1,-1,1 etc... for a sufficient long time and observe the output. Sufficient long time means it must be so long that the output stabilizes at a regular bit pattern.
Or to give it a more reasonable challenge: 10, -10, 10 etc.. that wont work either.
The proper output would be a signal of -76db. But that theoretical device cant output below -42db ( I wrote -21db above which was an error )



GUY's !!!!!!!
Make an effort! Think hard ! What if I'm right!?

Strange, when I first heard of sigma delta DACs some 25 years ago, I was immediately struck by this, but assumed I was wrong. Since then I have constructed several DACs and along the time I have been more and more convinced I'm right. I cannot measure it - I don't have accurate enough equipment.

We must settle this. Anyone with a simulator?

Finally, one last picture. How can we ever represent a value below -42db if we only have 128 time slices to integrate the signal.
And....
We only have 128 time slices since the next sample must represent another, equally weak signal with the opposite sign.

Actually, I really hope that someone can prove me wrong. If so I wouldn't resist the temptation to find out how such a miracle can happen. That would be truly humbling and that's what I need since my ego is fairly large.

Maybe you should consider 1 bit DSD to help you see that you are not making sense. Even at 2.8MHz it has very good resolution and low level detail. That's just 1 bit at 64 x FS (44.1KHz)... it makes modern multi level DS DACs look pretty good.

T
 
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OK, Guy's.

Even though I actually cited and gave a link to a document that supports this, you still don't follow me.

Recently I watched a Youtube video that also supported this, but I don't think it helps.
Sadly, I cannot find it again when I searched.

QUOTE******

2. A better resolution: In fact, the output of the converter is closer to the desired
output.


UNQUOTE*****

Please read the document I linked to in thread ¤27

But I don't think it will help. And honestly I don't care very much anymore.
No one here seems to have the motivation to perhaps find out if I'm right or wrong.
I promise you guy's If you really have the motivation to research this matter, then you will find out that I actually am right.

But I'm glad I took up this subject. It has forced me to ponder the issue very thoroughly, and I can't blame you guys not wanting to spend so much time to find it out.
 
...And honestly I don't care very much anymore.
No one here seems to have the motivation to perhaps find out if I'm right or wrong. I promise you guy's If you really have the motivation to research this matter, then you will find out that I actually am right.

You seem irrationally frustrated that we don't mathematically 'prove' your pet theory for you. That's really the only theoretical proof, a mathematical one. That's not our responsibility, it's yours. You admonish us for what you apparently are either unwilling or incapable of doing yourself.

You should, at the least, accept the possibility that your pet theory may be wrong. Not only aren't you ready to accept that possibility, your rigid attitude (or, perhaps, is it ego, as you had suggested) has forced you to reject, or ignore all of the actual measured proof that you are wrong. Haven't you been chastising us to keep an open mind, all while keeping your own closed? May be something for you to think about.
 
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